From 075521e8a036f6738f12156f317112e129f6d616 Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Sun, 12 Feb 2023 23:02:53 -0500
Subject: [PATCH 01/13] a new failing test case

---
 test/modules/acos.js | 1 +
 1 file changed, 1 insertion(+)

diff --git a/test/modules/acos.js b/test/modules/acos.js
index 66a9dbb..49bdc6d 100644
--- a/test/modules/acos.js
+++ b/test/modules/acos.js
@@ -68,6 +68,7 @@ T('acos', function () {
   t('0.41923186648524998285699814886092351368793359300547574', 42, 3, '1.13819724675000902666504291062053681280681');
   t('-0.19508761025300975791021816036', 27, 1, '1.76714310275532020878366926');
   t('0.0623252416', 19, 0, '1.508430664767542249');
+  t('0.9999999297625', 14, 4, '0.00037479994883195');
 
   /*
   t('0.95', 6, 5, '0.31756');

From 05c3fd3fae7b6045674f328b36f4d64d3d5f5394 Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Sun, 12 Feb 2023 23:08:43 -0500
Subject: [PATCH 02/13] test case finder

---
 test/hypothesis/.gitignore       |   3 +
 test/hypothesis/error_hunt.py    | 125 +++++++++++++++++++++++++++++++
 test/hypothesis/evaluate.mjs     |  26 +++++++
 test/hypothesis/requirements.txt |   3 +
 4 files changed, 157 insertions(+)
 create mode 100644 test/hypothesis/.gitignore
 create mode 100644 test/hypothesis/error_hunt.py
 create mode 100644 test/hypothesis/evaluate.mjs
 create mode 100644 test/hypothesis/requirements.txt

diff --git a/test/hypothesis/.gitignore b/test/hypothesis/.gitignore
new file mode 100644
index 0000000..6694234
--- /dev/null
+++ b/test/hypothesis/.gitignore
@@ -0,0 +1,3 @@
+__pycache__
+.hypothesis
+.ipynb_checkpoints
diff --git a/test/hypothesis/error_hunt.py b/test/hypothesis/error_hunt.py
new file mode 100644
index 0000000..7d5e952
--- /dev/null
+++ b/test/hypothesis/error_hunt.py
@@ -0,0 +1,125 @@
+from decimal import Decimal, getcontext
+import json
+import subprocess
+import hypothesis
+from hypothesis import given, settings
+from hypothesis.strategies import decimals, integers, tuples
+from mpmath import mp
+
+mp.prec = 500
+
+node = subprocess.Popen(
+    ["node", "evaluate.mjs"], stdout=subprocess.PIPE, stdin=subprocess.PIPE
+)
+
+
+def get_decimal(func: str, args: list, config: dict):
+    arg = json.dumps({"func": func, "args": args, "config": config}).encode() + b"\r"
+    node.stdin.write(arg)
+    node.stdin.flush()
+    return Decimal(node.stdout.readline().strip().decode())
+
+
+def to_precision(x, precision=14):
+    getcontext().prec = precision
+    return Decimal(str(x)) * Decimal("1.0")
+
+
+decimal_fixed_precision = tuples(
+    decimals(
+        allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
+    ),
+    integers(min_value=-99, max_value=99),
+).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
+
+decimal_positive = tuples(
+    decimals(
+        allow_nan=False, allow_infinity=False, min_value=1e-13, max_value=1, places=14
+    ),
+    integers(min_value=-99, max_value=99),
+).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
+
+
+@given(decimal_fixed_precision)
+@settings(max_examples=100)
+def test_tangent(x):
+    y = to_precision(mp.tan(x))
+    z = get_decimal("tan", [str(x)], {"precision": 14})
+    assert y == z
+
+
+@given(decimal_fixed_precision)
+@settings(max_examples=100)
+def test_cosine(x):
+    y = to_precision(mp.cos(x))
+    z = get_decimal("cos", [str(x)], {"precision": 14})
+    assert y == z
+
+
+@given(decimal_fixed_precision)
+@settings(max_examples=100)
+def test_sine(x):
+    y = to_precision(mp.sin(x))
+    z = get_decimal("sin", [str(x)], {"precision": 14})
+    assert y == z
+
+
+@given(decimal_positive)
+@settings(max_examples=100)
+def test_log(x):
+    y = to_precision(mp.log10(x))
+    z = get_decimal("log", [str(x)], {"precision": 14})
+    assert y == z
+
+
+inverse_trig_strat = decimals(
+    allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
+)
+
+
+@given(inverse_trig_strat)
+@settings(max_examples=100)
+def test_acos(x):
+    y = to_precision(mp.acos(x))
+    z = get_decimal("acos", [str(x)], {"precision": 14})
+    assert y == z
+
+
+@given(inverse_trig_strat)
+@settings(max_examples=100)
+def test_asin(x):
+    y = to_precision(mp.asin(x))
+    z = get_decimal("asin", [str(x)], {"precision": 14})
+    assert y == z
+
+
+@given(decimal_fixed_precision)
+@settings(max_examples=100)
+def test_atan(x):
+    y = to_precision(mp.atan(x))
+    z = get_decimal("atan", [str(x)], {"precision": 14})
+    assert y == z
+
+
+@given(decimal_fixed_precision)
+@settings(max_examples=10)
+def test_cosh(x):
+    y = to_precision(mp.cosh(x))
+    z = get_decimal("cosh", [str(x)], {"precision": 14})
+    assert y == z
+
+
+@given(decimal_fixed_precision)
+@settings(max_examples=4)
+def test_sinh(x):
+    y = to_precision(mp.sinh(x))
+    z = get_decimal("sinh", [str(x)], {"precision": 14})
+    assert y == z
+
+
+@given(decimal_fixed_precision)
+@settings(max_examples=4)
+def test_tanh(x):
+    y = to_precision(mp.tanh(x))
+    z = get_decimal("tanh", [str(x)], {"precision": 14})
+    assert y == z
diff --git a/test/hypothesis/evaluate.mjs b/test/hypothesis/evaluate.mjs
new file mode 100644
index 0000000..bf31f47
--- /dev/null
+++ b/test/hypothesis/evaluate.mjs
@@ -0,0 +1,26 @@
+// listen for test cases, and provide the results.
+// give JSON of the test case, receive the result
+// Example: 
+// > {"func":"tan", "args":["12.5"], "config":{"precision":8}}
+// -0.066468242
+
+
+import {Decimal} from '../../decimal.mjs';
+import {createInterface} from 'readline';
+
+const readline = createInterface({
+	input: process.stdin,
+	output: process.stdout
+});
+
+readline.on("close", () => {console.log('\n'); process.exit(0);});
+
+readline.on("line", (line) => {
+    if (line) {
+        const {func, args, config} = JSON.parse(line);
+        config.defaults = true;
+        Decimal.set(config);
+        const result = Decimal[func](...args);
+        console.log(result);
+    }
+});
\ No newline at end of file
diff --git a/test/hypothesis/requirements.txt b/test/hypothesis/requirements.txt
new file mode 100644
index 0000000..ab25b9f
--- /dev/null
+++ b/test/hypothesis/requirements.txt
@@ -0,0 +1,3 @@
+hypothesis
+mpmath
+node
\ No newline at end of file

From 4c52aec1cd4e4cbdb400fc1edb8804f7ce82b3ed Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Mon, 13 Feb 2023 01:43:52 -0500
Subject: [PATCH 03/13] additional falsifyer

---
 test/modules/acos.js | 1 +
 1 file changed, 1 insertion(+)

diff --git a/test/modules/acos.js b/test/modules/acos.js
index 49bdc6d..5fffc01 100644
--- a/test/modules/acos.js
+++ b/test/modules/acos.js
@@ -69,6 +69,7 @@ T('acos', function () {
   t('-0.19508761025300975791021816036', 27, 1, '1.76714310275532020878366926');
   t('0.0623252416', 19, 0, '1.508430664767542249');
   t('0.9999999297625', 14, 4, '0.00037479994883195');
+  t('0.99999999467518', 14, 4, '0.00010319709302810');
 
   /*
   t('0.95', 6, 5, '0.31756');

From 0f36747c05c15f734e86f920a099ffbc0fa8b5a9 Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Mon, 13 Feb 2023 01:44:14 -0500
Subject: [PATCH 04/13] parametrize tests

---
 test/hypothesis/error_hunt.py | 152 ++++++++++++----------------------
 1 file changed, 55 insertions(+), 97 deletions(-)

diff --git a/test/hypothesis/error_hunt.py b/test/hypothesis/error_hunt.py
index 7d5e952..7523551 100644
--- a/test/hypothesis/error_hunt.py
+++ b/test/hypothesis/error_hunt.py
@@ -5,8 +5,10 @@ import hypothesis
 from hypothesis import given, settings
 from hypothesis.strategies import decimals, integers, tuples
 from mpmath import mp
+import pytest
 
 mp.prec = 500
+getcontext().prec = 14
 
 node = subprocess.Popen(
     ["node", "evaluate.mjs"], stdout=subprocess.PIPE, stdin=subprocess.PIPE
@@ -20,106 +22,62 @@ def get_decimal(func: str, args: list, config: dict):
     return Decimal(node.stdout.readline().strip().decode())
 
 
-def to_precision(x, precision=14):
-    getcontext().prec = precision
-    return Decimal(str(x)) * Decimal("1.0")
-
-
-decimal_fixed_precision = tuples(
-    decimals(
-        allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
-    ),
-    integers(min_value=-99, max_value=99),
-).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
-
-decimal_positive = tuples(
-    decimals(
-        allow_nan=False, allow_infinity=False, min_value=1e-13, max_value=1, places=14
-    ),
-    integers(min_value=-99, max_value=99),
-).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
-
-
-@given(decimal_fixed_precision)
-@settings(max_examples=100)
-def test_tangent(x):
-    y = to_precision(mp.tan(x))
-    z = get_decimal("tan", [str(x)], {"precision": 14})
-    assert y == z
-
-
-@given(decimal_fixed_precision)
-@settings(max_examples=100)
-def test_cosine(x):
-    y = to_precision(mp.cos(x))
-    z = get_decimal("cos", [str(x)], {"precision": 14})
+def assert_matches(x, mpfunc, jsfunc=None):
+    if jsfunc is None:
+        jsfunc = mpfunc
+    y = Decimal(str(getattr(mp, mpfunc)(x))) * Decimal("1.0")
+    z = get_decimal(jsfunc, [str(x)], {"precision": 14})
     assert y == z
 
 
-@given(decimal_fixed_precision)
-@settings(max_examples=100)
-def test_sine(x):
-    y = to_precision(mp.sin(x))
-    z = get_decimal("sin", [str(x)], {"precision": 14})
-    assert y == z
-
-
-@given(decimal_positive)
-@settings(max_examples=100)
-def test_log(x):
-    y = to_precision(mp.log10(x))
-    z = get_decimal("log", [str(x)], {"precision": 14})
-    assert y == z
-
-
-inverse_trig_strat = decimals(
-    allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
+@pytest.mark.parametrize("fn", "sin cos tan atan".split())
+@given(
+    x=tuples(
+        decimals(
+            allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
+        ),
+        integers(min_value=-99, max_value=99),
+    ).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
 )
+def test_matches(x, fn):
+    assert_matches(x, fn)
+
+
+@pytest.mark.parametrize("fn", "ln log10".split())
+@given(
+    x=tuples(
+        decimals(
+            allow_nan=False,
+            allow_infinity=False,
+            min_value=1e-13,
+            max_value=1,
+            places=14,
+        ),
+        integers(min_value=-99, max_value=99),
+    ).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
+)
+def test_positive_domain(x, fn):
+    assert_matches(x, fn)
 
 
-@given(inverse_trig_strat)
-@settings(max_examples=100)
-def test_acos(x):
-    y = to_precision(mp.acos(x))
-    z = get_decimal("acos", [str(x)], {"precision": 14})
-    assert y == z
-
-
-@given(inverse_trig_strat)
-@settings(max_examples=100)
-def test_asin(x):
-    y = to_precision(mp.asin(x))
-    z = get_decimal("asin", [str(x)], {"precision": 14})
-    assert y == z
-
-
-@given(decimal_fixed_precision)
-@settings(max_examples=100)
-def test_atan(x):
-    y = to_precision(mp.atan(x))
-    z = get_decimal("atan", [str(x)], {"precision": 14})
-    assert y == z
-
-
-@given(decimal_fixed_precision)
-@settings(max_examples=10)
-def test_cosh(x):
-    y = to_precision(mp.cosh(x))
-    z = get_decimal("cosh", [str(x)], {"precision": 14})
-    assert y == z
-
-
-@given(decimal_fixed_precision)
-@settings(max_examples=4)
-def test_sinh(x):
-    y = to_precision(mp.sinh(x))
-    z = get_decimal("sinh", [str(x)], {"precision": 14})
-    assert y == z
-
-
-@given(decimal_fixed_precision)
-@settings(max_examples=4)
-def test_tanh(x):
-    y = to_precision(mp.tanh(x))
-    z = get_decimal("tanh", [str(x)], {"precision": 14})
-    assert y == z
+@pytest.mark.parametrize("fn", "asin acos".split())
+@given(
+    x=decimals(
+        allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
+    )
+)
+def test_inverse_trig(x, fn):
+    assert_matches(x, fn)
+
+
+@pytest.mark.parametrize("fn", "sinh cosh tanh".split())
+@given(
+    x=tuples(
+        decimals(
+            allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
+        ),
+        integers(min_value=-99, max_value=3),
+    ).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
+)
+def test_small_domain(x, fn):
+    assert_matches(x, fn)

From 727eae8053b0e76d629281836fa98ee9f3bdd0f9 Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Mon, 13 Feb 2023 01:56:56 -0500
Subject: [PATCH 05/13] check more cases

---
 test/hypothesis/error_hunt.py | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/test/hypothesis/error_hunt.py b/test/hypothesis/error_hunt.py
index 7523551..d8be7ee 100644
--- a/test/hypothesis/error_hunt.py
+++ b/test/hypothesis/error_hunt.py
@@ -39,11 +39,12 @@ def assert_matches(x, mpfunc, jsfunc=None):
         integers(min_value=-99, max_value=99),
     ).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
 )
+@settings(max_examples=1000)
 def test_matches(x, fn):
     assert_matches(x, fn)
 
 
-@pytest.mark.parametrize("fn", "ln log10".split())
+@pytest.mark.parametrize("fn", "ln log10 sqrt".split())
 @given(
     x=tuples(
         decimals(
@@ -56,6 +57,7 @@ def test_matches(x, fn):
         integers(min_value=-99, max_value=99),
     ).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
 )
+@settings(max_examples=1000)
 def test_positive_domain(x, fn):
     assert_matches(x, fn)
 
@@ -66,11 +68,12 @@ def test_positive_domain(x, fn):
         allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
     )
 )
+@settings(max_examples=1000)
 def test_inverse_trig(x, fn):
     assert_matches(x, fn)
 
 
-@pytest.mark.parametrize("fn", "sinh cosh tanh".split())
+@pytest.mark.parametrize("fn", "sinh cosh tanh exp".split())
 @given(
     x=tuples(
         decimals(
@@ -79,5 +82,6 @@ def test_inverse_trig(x, fn):
         integers(min_value=-99, max_value=3),
     ).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
 )
+@settings(max_examples=1000)
 def test_small_domain(x, fn):
     assert_matches(x, fn)

From 24981236086cefc713e0ad4edf6f130ded5abdb4 Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Mon, 13 Feb 2023 02:18:42 -0500
Subject: [PATCH 06/13] test acosh

---
 test/hypothesis/error_hunt.py | 16 ++++++++++++++--
 1 file changed, 14 insertions(+), 2 deletions(-)

diff --git a/test/hypothesis/error_hunt.py b/test/hypothesis/error_hunt.py
index d8be7ee..08d9806 100644
--- a/test/hypothesis/error_hunt.py
+++ b/test/hypothesis/error_hunt.py
@@ -30,7 +30,7 @@ def assert_matches(x, mpfunc, jsfunc=None):
     assert y == z
 
 
-@pytest.mark.parametrize("fn", "sin cos tan atan".split())
+@pytest.mark.parametrize("fn", "sin cos tan atan asinh".split())
 @given(
     x=tuples(
         decimals(
@@ -62,7 +62,7 @@ def test_positive_domain(x, fn):
     assert_matches(x, fn)
 
 
-@pytest.mark.parametrize("fn", "asin acos".split())
+@pytest.mark.parametrize("fn", "asin acos atanh".split())
 @given(
     x=decimals(
         allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
@@ -85,3 +85,15 @@ def test_inverse_trig(x, fn):
 @settings(max_examples=1000)
 def test_small_domain(x, fn):
     assert_matches(x, fn)
+
+@given(
+    x=tuples(
+        decimals(
+            allow_nan=False, allow_infinity=False, min_value=1, max_value=10, places=14
+        ),
+        integers(min_value=0, max_value=99),
+    ).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
+)
+@settings(max_examples=1000)
+def test_acosh(x, fn):
+    assert_matches(x, 'acosh')
\ No newline at end of file

From 0316809a806d54f18990c001645397e55595b24e Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Mon, 13 Feb 2023 02:19:00 -0500
Subject: [PATCH 07/13] remove extranous zero

---
 test/modules/acos.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/modules/acos.js b/test/modules/acos.js
index 5fffc01..0b5036c 100644
--- a/test/modules/acos.js
+++ b/test/modules/acos.js
@@ -69,7 +69,7 @@ T('acos', function () {
   t('-0.19508761025300975791021816036', 27, 1, '1.76714310275532020878366926');
   t('0.0623252416', 19, 0, '1.508430664767542249');
   t('0.9999999297625', 14, 4, '0.00037479994883195');
-  t('0.99999999467518', 14, 4, '0.00010319709302810');
+  t('0.99999999467518', 14, 4, '0.0001031970930281');
 
   /*
   t('0.95', 6, 5, '0.31756');

From e634266aadd86fde3161068f71467c6de87baaf7 Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Mon, 13 Feb 2023 03:19:39 -0500
Subject: [PATCH 08/13] remove extraneous parameter

---
 test/hypothesis/error_hunt.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/hypothesis/error_hunt.py b/test/hypothesis/error_hunt.py
index 08d9806..e5fc6fc 100644
--- a/test/hypothesis/error_hunt.py
+++ b/test/hypothesis/error_hunt.py
@@ -95,5 +95,5 @@ def test_small_domain(x, fn):
     ).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
 )
 @settings(max_examples=1000)
-def test_acosh(x, fn):
+def test_acosh(x):
     assert_matches(x, 'acosh')
\ No newline at end of file

From 2b1298cd69fe014dc61b73db47daefacf0328cce Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Mon, 13 Feb 2023 03:50:30 -0500
Subject: [PATCH 09/13] use a method less prone to cancellation near x=1

---
 decimal.js  | 7 +++----
 decimal.mjs | 5 ++---
 2 files changed, 5 insertions(+), 7 deletions(-)

diff --git a/decimal.js b/decimal.js
index aa6526a..8eabf43 100644
--- a/decimal.js
+++ b/decimal.js
@@ -744,14 +744,13 @@
 
     Ctor.precision = pr + 6;
     Ctor.rounding = 1;
-
-    x = x.asin();
-    halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
+    
+    x = (new Ctor(1)).minus(x).div(x.plus(1)).sqrt().atan();
 
     Ctor.precision = pr;
     Ctor.rounding = rm;
 
-    return halfPi.minus(x);
+    return x.times(2);
   };
 
 
diff --git a/decimal.mjs b/decimal.mjs
index 909300c..293ee8e 100644
--- a/decimal.mjs
+++ b/decimal.mjs
@@ -741,13 +741,12 @@ P.inverseCosine = P.acos = function () {
   Ctor.precision = pr + 6;
   Ctor.rounding = 1;
 
-  x = x.asin();
-  halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
+  x = (new Ctor(1)).minus(x).div(x.plus(1)).sqrt().atan();
 
   Ctor.precision = pr;
   Ctor.rounding = rm;
 
-  return halfPi.minus(x);
+  return x.times(2);
 };
 
 

From b3142b4c60ccd760c0c62f87d1fda51533560a6e Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Mon, 13 Feb 2023 14:34:55 -0500
Subject: [PATCH 10/13] new falisifying test for sine

---
 test/modules/sin.js | 1 +
 1 file changed, 1 insertion(+)

diff --git a/test/modules/sin.js b/test/modules/sin.js
index d90ea99..05036fe 100644
--- a/test/modules/sin.js
+++ b/test/modules/sin.js
@@ -119,4 +119,5 @@ T('sin', function () {
   t('22011131111011111.111111611113111111111151111111', 143, 2, '0.82582504036277799386306063085803210583251158969990606609364360685569588545519071481543672724620118406694191888115120286393881609546697317692404');
   t('996270725099515169352424536636186062915113219400094989.8763797268889422850038402633796294758036260533902551191769915343780424028900449342752548782035', 46, 2, '0.6613706114081017074779805460666900787572253475');
   t('0.780360750628373', 37, 5, '0.7035358359376557390803090830882458906');
+  t('5900', 14, 4, '0.088879123681079');
 });

From 64906296b6ee4c04fdda2d57665feb451a09a508 Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Mon, 13 Feb 2023 14:35:27 -0500
Subject: [PATCH 11/13] search for more exampoles

---
 test/hypothesis/error_hunt.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/test/hypothesis/error_hunt.py b/test/hypothesis/error_hunt.py
index e5fc6fc..af9df0b 100644
--- a/test/hypothesis/error_hunt.py
+++ b/test/hypothesis/error_hunt.py
@@ -39,7 +39,7 @@ def assert_matches(x, mpfunc, jsfunc=None):
         integers(min_value=-99, max_value=99),
     ).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
 )
-@settings(max_examples=1000)
+@settings(max_examples=100_000)
 def test_matches(x, fn):
     assert_matches(x, fn)
 
@@ -57,7 +57,7 @@ def test_matches(x, fn):
         integers(min_value=-99, max_value=99),
     ).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
 )
-@settings(max_examples=1000)
+@settings(max_examples=100_000)
 def test_positive_domain(x, fn):
     assert_matches(x, fn)
 
@@ -68,7 +68,7 @@ def test_positive_domain(x, fn):
         allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
     )
 )
-@settings(max_examples=1000)
+@settings(max_examples=100_000)
 def test_inverse_trig(x, fn):
     assert_matches(x, fn)
 
@@ -82,7 +82,7 @@ def test_inverse_trig(x, fn):
         integers(min_value=-99, max_value=3),
     ).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
 )
-@settings(max_examples=1000)
+@settings(max_examples=100_000)
 def test_small_domain(x, fn):
     assert_matches(x, fn)
 
@@ -94,6 +94,6 @@ def test_small_domain(x, fn):
         integers(min_value=0, max_value=99),
     ).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
 )
-@settings(max_examples=1000)
+@settings(max_examples=100_000)
 def test_acosh(x):
     assert_matches(x, 'acosh')
\ No newline at end of file

From 780480cc2ac7f4a95f4de5501c0c360b53da90f0 Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Mon, 13 Feb 2023 16:32:13 -0500
Subject: [PATCH 12/13] additional cosine test showing cancellation

---
 test/modules/acos.js | 1 +
 1 file changed, 1 insertion(+)

diff --git a/test/modules/acos.js b/test/modules/acos.js
index 0b5036c..4537c33 100644
--- a/test/modules/acos.js
+++ b/test/modules/acos.js
@@ -70,6 +70,7 @@ T('acos', function () {
   t('0.0623252416', 19, 0, '1.508430664767542249');
   t('0.9999999297625', 14, 4, '0.00037479994883195');
   t('0.99999999467518', 14, 4, '0.0001031970930281');
+  t('0.9999999999999999995', 25, 4, '0.000000001000000000000000000041667');
 
   /*
   t('0.95', 6, 5, '0.31756');

From d130921f982b5b59e9875f00ec2982724ed1f2f2 Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Mon, 13 Feb 2023 17:11:19 -0500
Subject: [PATCH 13/13] additional case showing loss of significance near x=1

---
 test/modules/acos.js | 1 +
 1 file changed, 1 insertion(+)

diff --git a/test/modules/acos.js b/test/modules/acos.js
index 4537c33..b2ef48c 100644
--- a/test/modules/acos.js
+++ b/test/modules/acos.js
@@ -71,6 +71,7 @@ T('acos', function () {
   t('0.9999999297625', 14, 4, '0.00037479994883195');
   t('0.99999999467518', 14, 4, '0.0001031970930281');
   t('0.9999999999999999995', 25, 4, '0.000000001000000000000000000041667');
+  t('0.99999999999999999999995', 30, 4, '0.0000000000100000000000000000000000416667');
 
   /*
   t('0.95', 6, 5, '0.31756');