Herbie run
| Date: | Friday, March 14th, 2025 |
|---|---|
| Commit: | a50d62fb on warn-mpfr-threads |
| Seed: | 2025073 |
| Parameters: | 256 points for 4 iterations |
| Flags: | reduce:regimesreduce:binary-searchreduce:branch-expressionsreduce:simplifysetup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:proofs default |
| Memory: | 156 507.8 MB |
Time bar (total: 3.0min)
| 27.3s | 44 027× | 2 | valid |
| 21.2s | 96 882× | 1 | valid |
| 18.7s | 144 445× | 0 | invalid |
| 16.5s | 6 963× | 5 | exit |
| 8.6s | 86 971× | 0 | valid |
| 2.3s | 3 280× | 3 | valid |
| 419.0ms | 4 167× | 0 | exit |
| 10.0ms | 8× | 4 | valid |
ival-pow: 15.5s (19.6% of total)ival-tan: 11.7s (14.8% of total)adjust: 8.3s (10.5% of total)ival-mult: 5.7s (7.3% of total)ival-cos: 4.4s (5.6% of total)ival-div: 4.2s (5.3% of total)ival-sub: 4.0s (5.1% of total)ival-add: 3.8s (4.9% of total)ival-log: 3.5s (4.5% of total)ival-sin: 3.1s (3.9% of total)const: 2.7s (3.4% of total)ival-expm1: 2.1s (2.7% of total)ival-log1p: 1.9s (2.4% of total)ival-exp: 1.8s (2.3% of total)ival-fabs: 1.8s (2.2% of total)ival-sqrt: 1.1s (1.4% of total)ival-<: 711.0ms (0.9% of total)ival-atan: 560.0ms (0.7% of total)ival-cbrt: 491.0ms (0.6% of total)ival-<=: 424.0ms (0.5% of total)ival-and: 383.0ms (0.5% of total)ival-neg: 335.0ms (0.4% of total)exact: 153.0ms (0.2% of total)ival-assert: 135.0ms (0.2% of total)ival-fmin: 79.0ms (0.1% of total)ival->: 1.0ms (0% of total)| 259× | iter limit |
| 106× | node limit |
| 56× | iter limit |
| 51× | node limit |
| 5× | saturated |
Compiled 19 256 to 5 131 computations (73.4% saved)
Compiled 1 583 633 to 177 848 computations (88.8% saved)
| 21× | fuel |
| 7× | done |
Compiled 8 445 to 1 859 computations (78% saved)
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | #f | cancellation | 4166 | 32 |
log.f64 | #f | sensitivity | 763 | 1 |
/.f64 | #f | u/u | 441 | 0 |
sqrt.f64 | #f | oflow-rescue | 384 | 0 |
+.f64 | #f | cancellation | 356 | 0 |
/.f64 | #f | u/n | 102 | 0 |
pow.f64 | (pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n)) | sensitivity | 70 | 0 |
sqrt.f64 | #f | uflow-rescue | 32 | 0 |
-.f64 | #f | nan-rescue | 25 | 0 |
/.f64 | (/.f64 (*.f64 eps (-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))) | n/u | 19 | 0 |
| ↳ | (*.f64 b eps) | underflow | 143 | |
| ↳ | (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) | underflow | 166 | |
| ↳ | (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)) | underflow | 143 | |
| ↳ | (*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))) | underflow | 236 | |
| ↳ | (*.f64 a eps) | underflow | 166 | |
/.f64 | (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)) | n/o | 4 | 0 |
| ↳ | (*.f64 x x) | overflow | 67 | |
/.f64 | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) | o/o | 4 | 0 |
| ↳ | (exp.f64 (*.f64 #s(literal 2 binary64) x)) | overflow | 4 | |
| ↳ | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) | overflow | 4 | |
| ↳ | (exp.f64 x) | overflow | 4 | |
| ↳ | (-.f64 (exp.f64 x) #s(literal 1 binary64)) | overflow | 4 | |
exp.f64 | (exp.f64 (neg.f64 x)) | sensitivity | 2 | 1 |
sin.f64 | (sin.f64 (+.f64 x eps)) | sensitivity | 1 | 1 |
tan.f64 | (tan.f64 (+.f64 x eps)) | sensitivity | 1 | 1 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 5236 | 19 |
| - | 151 | 1762 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 5236 | 16 | 3 |
| - | 151 | 20 | 1742 |
| number | freq |
|---|---|
| 0 | 1781 |
| 1 | 4595 |
| 2 | 646 |
| 3 | 101 |
| 4 | 45 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 28 | 0 | 0 |
| - | 0 | 0 | 0 |
| 1.6s | 2 768× | 2 | valid |
| 1.5s | 6 118× | 1 | valid |
| 445.0ms | 5 256× | 0 | valid |
| 147.0ms | 194× | 3 | valid |
Compiled 2 154 to 763 computations (64.6% saved)
ival-tan: 608.0ms (20.7% of total)adjust: 431.0ms (14.7% of total)ival-log: 297.0ms (10.1% of total)ival-cos: 219.0ms (7.5% of total)ival-sin: 188.0ms (6.4% of total)ival-sub: 185.0ms (6.3% of total)ival-sqrt: 179.0ms (6.1% of total)ival-div: 161.0ms (5.5% of total)ival-exp: 135.0ms (4.6% of total)ival-pow: 134.0ms (4.6% of total)ival-add: 127.0ms (4.3% of total)ival-mult: 92.0ms (3.1% of total)ival-log1p: 77.0ms (2.6% of total)ival-expm1: 30.0ms (1% of total)ival-atan: 21.0ms (0.7% of total)ival-cbrt: 16.0ms (0.5% of total)ival-true: 12.0ms (0.4% of total)ival-neg: 12.0ms (0.4% of total)exact: 9.0ms (0.3% of total)ival-assert: 6.0ms (0.2% of total)498 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 565.0ms | N | @ | inf | ((atan2 (- (- N -1) N) (- (+ (* N N) N) -1)) (- (- N -1) N) 1 (- (+ (* N N) N) -1) (+ (* N N) N) N -1 (atan2 (- (- N -1) N) (+ N (+ (* N N) 1))) (+ N (+ (* N N) 1)) (- N -1) (atan2 (- (- N -1) N) (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (atan2 (- (- N -1) N) (+ (* (/ (- (pow N 3) -1) (+ (* N N) (- 1 N))) N) 1)) (+ (* (/ (- (pow N 3) -1) (+ (* N N) (- 1 N))) N) 1) (/ (- (pow N 3) -1) (+ (* N N) (- 1 N))) (- (pow N 3) -1) (pow N 3) 3 (+ (* N N) (- 1 N)) (- 1 N) (atan2 (- (- N -1) N) (+ N (/ (- (pow N 6) -1) (+ (* (* N N) (+ (* N N) -1)) 1)))) (- (- N -1) N) (+ N (/ (- (pow N 6) -1) (+ (* (* N N) (+ (* N N) -1)) 1))) (/ (- (pow N 6) -1) (+ (* (* N N) (+ (* N N) -1)) 1)) (- (pow N 6) -1) (pow N 6) 6 (+ (* (* N N) (+ (* N N) -1)) 1) (* N N) (+ (* N N) -1)) |
| 418.0ms | x | @ | inf | ((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (neg (/ (/ (- (* (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n))) (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n)))) (pow (log x) 2)) (- (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n))) (log x))) n)) (/ (/ (- (* (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n))) (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n)))) (pow (log x) 2)) (- (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n))) (log x))) n) (/ (- (* (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n))) (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n)))) (pow (log x) 2)) (- (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n))) (log x))) (- (* (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n))) (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n)))) (pow (log x) 2)) (* (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n))) (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n)))) (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n))) (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n)) (log (+ 1 x)) x (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) (pow (log (+ 1 x)) 2) 2 (pow (log x) 2) (log x) n (- (neg (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n))) (log x)) (/ (- (* -1 (* n (+ (log x) (log (+ 1 x))))) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n) (- (* -1 (* n (+ (log x) (log (+ 1 x))))) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) (* -1 (* n (+ (log x) (log (+ 1 x))))) -1 (* n (+ (log x) (log (+ 1 x)))) (+ (log x) (log (+ 1 x))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (neg (/ (+ (* -1 (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n))) (log x)) n)) (- (/ x n) (+ (* 1/2 (/ (pow (log x) 2) (* n n))) (/ (log x) n))) (/ x n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (neg (/ (+ (* -1 (+ (log (+ 1 x)) (/ (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) n))) (log x)) n)) (- (/ x n) (+ (* 1/2 (/ (pow (log x) 2) (* n n))) (/ (log x) n))) (+ (* 1/2 (/ (pow (log x) 2) (* n n))) (/ (log x) n)) (/ (log x) n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (exp (/ (log (+ 1 x)) n)) (/ (log (+ 1 x)) n) (pow x (/ 1 n)) 1 (- (/ (pow (pow (+ 1 x) (pow n -1)) 2) (+ (pow (+ 1 x) (pow n -1)) (pow x (pow n -1)))) (/ (pow (pow x (pow n -1)) 2) (+ (pow (+ 1 x) (pow n -1)) (pow x (pow n -1))))) (/ (pow (pow (+ 1 x) (pow n -1)) 2) (+ (pow (+ 1 x) (pow n -1)) (pow x (pow n -1)))) (pow (pow (+ 1 x) (pow n -1)) 2) (pow (+ 1 x) (pow n -1)) (+ 1 x) (pow n -1) (+ (pow (+ 1 x) (pow n -1)) (pow x (pow n -1))) (pow x (pow n -1)) (/ (pow (pow x (pow n -1)) 2) (+ (pow (+ 1 x) (pow n -1)) (pow x (pow n -1)))) (pow (pow x (pow n -1)) 2)) |
| 97.0ms | eps | @ | inf | ((/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ (/ (+ b a) a) b) (/ (+ b a) a) (+ b a) b a (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (pow a -1) -1 (/ (* (- (exp (* (+ b a) eps)) 1) eps) (* (- (exp (* b eps)) 1) (- (exp (* a eps)) 1))) (* (- (exp (* (+ b a) eps)) 1) eps) (- (exp (* (+ b a) eps)) 1) (* (+ b a) eps) eps (* (- (exp (* b eps)) 1) (- (exp (* a eps)) 1)) (- (exp (* b eps)) 1) (* b eps) (- (exp (* a eps)) 1) (* a eps) (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ (+ (* (+ (* eps (/ (pow (exp eps) b) (- (exp (* b eps)) 1))) (* -1/2 eps)) a) 1) a) (+ (* (+ (* eps (/ (pow (exp eps) b) (- (exp (* b eps)) 1))) (* -1/2 eps)) a) 1) (+ (* eps (/ (pow (exp eps) b) (- (exp (* b eps)) 1))) (* -1/2 eps)) (/ (pow (exp eps) b) (- (exp (* b eps)) 1)) (pow (exp eps) b) (exp eps) (* -1/2 eps) -1/2 1 (* (/ eps (- (exp (* a eps)) 1)) (/ (- (exp (* (+ b a) eps)) 1) (- (exp (* b eps)) 1))) (/ eps (- (exp (* a eps)) 1)) (/ (- (exp (* (+ b a) eps)) 1) (- (exp (* b eps)) 1))) |
| 80.0ms | n | @ | 0 | ((- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (- (* (+ n 1) (log (+ n 1))) (* n (log n))) (* (+ n 1) (log (+ n 1))) (+ n 1) n 1 (log (+ n 1)) (* n (log n)) (log n)) |
| 63.0ms | x | @ | -inf | ((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (+ x 1) x 1 (/ 1 n) n (pow x (/ 1 n))) |
43 calls:
| 822.0ms | x |
| 322.0ms | eps |
| 137.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 101.0ms | (exp.f64 x) |
| 101.0ms | b |
Compiled 1 987 to 1 903 computations (4.2% saved)
Compiled 86 927 to 45 194 computations (48% saved)
| 99× | binary-search |
| 16× | left-value |
| 92× | narrow-enough |
| 7× | predicate-same |
| 441.0ms | 4 934× | 0 | valid |
| 298.0ms | 1 252× | 1 | valid |
| 288.0ms | 704× | 2 | valid |
| 81.0ms | 1 008× | 0 | invalid |
| 6.0ms | 22× | 3 | valid |
| 5.0ms | 59× | 0 | exit |
Compiled 39 438 to 28 397 computations (28% saved)
ival-pow: 289.0ms (33.2% of total)ival-mult: 198.0ms (22.7% of total)adjust: 90.0ms (10.3% of total)ival-div: 77.0ms (8.8% of total)ival-sub: 66.0ms (7.6% of total)ival-sqrt: 46.0ms (5.3% of total)ival-add: 41.0ms (4.7% of total)ival-neg: 31.0ms (3.6% of total)ival-cbrt: 9.0ms (1% of total)ival-cos: 7.0ms (0.8% of total)ival-true: 6.0ms (0.7% of total)exact: 5.0ms (0.6% of total)ival-assert: 3.0ms (0.3% of total)ival-expm1: 2.0ms (0.2% of total)| 28× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 61.1% | 38.9% | 0% | 0% | 0% | 0 |
| 7.4% | 4.5% | 56.6% | 38.9% | 0% | 0% | 0% | 1 |
| 22.3% | 13.6% | 47.5% | 38.9% | 0% | 0% | 0% | 2 |
| 40.2% | 23.5% | 34.9% | 38.9% | 0% | 2.7% | 0% | 3 |
| 53.4% | 31.1% | 27.2% | 38.9% | 0% | 2.8% | 0% | 4 |
| 63% | 36.3% | 21.3% | 38.9% | 0% | 3.6% | 0% | 5 |
| 65.9% | 37.5% | 19.4% | 38.9% | 0% | 4.2% | 0% | 6 |
| 70.4% | 38.8% | 16.3% | 38.9% | 0% | 6% | 0% | 7 |
| 73.6% | 40.2% | 14.4% | 38.9% | 0% | 6.5% | 0% | 8 |
| 76.3% | 40.9% | 12.7% | 38.9% | 0% | 7.5% | 0% | 9 |
| 78.4% | 41.4% | 11.4% | 38.9% | 0% | 8.3% | 0% | 10 |
| 81.1% | 42.4% | 9.9% | 38.9% | 0% | 8.8% | 0% | 11 |
| 82.3% | 42.7% | 9.2% | 38.9% | 0% | 9.3% | 0% | 12 |
Compiled 483 to 337 computations (30.2% saved)
| 28× | node limit |
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