Herbie run
| Date: | Thursday, March 27th, 2025 |
|---|---|
| Commit: | 6a59e611 on merge-improve-alternatives |
| Seed: | 2025086 |
| 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: | 167 817.5 MB |
Time bar (total: 2.6min)
| 24.5s | 44 628× | 2 | valid |
| 16.4s | 97 205× | 1 | valid |
| 15.3s | 147 531× | 0 | invalid |
| 8.7s | 6 245× | 5 | exit |
| 6.0s | 85 738× | 0 | valid |
| 2.6s | 3 595× | 3 | valid |
| 342.0ms | 4 269× | 0 | exit |
| 182.0ms | 1 135× | 1 | exit |
| 51.0ms | 1× | 3 | exit |
| 21.0ms | 7× | 4 | exit |
| 3.0ms | 1× | 2 | exit |
| 2.0ms | 2× | 4 | valid |
ival-tan: 11.6s (19.5% of total)ival-pow: 9.2s (15.5% of total)adjust: 5.6s (9.4% of total)ival-mult!: 4.7s (7.9% of total)ival-cos: 3.8s (6.4% of total)ival-log: 3.6s (6.1% of total)ival-div!: 3.2s (5.3% of total)ival-sin: 3.2s (5.3% of total)ival-exp: 2.2s (3.7% of total)ival-expm1: 2.1s (3.6% of total)ival-add!: 1.8s (3.1% of total)ival-sub!: 1.8s (3% of total)ival-sqrt: 1.7s (2.8% of total)ival-fabs: 1.6s (2.7% of total)ival-log1p: 1.0s (1.7% of total)ival-<: 593.0ms (1% of total)ival-neg: 437.0ms (0.7% of total)ival-atan: 370.0ms (0.6% of total)ival-<=: 362.0ms (0.6% of total)ival-and: 355.0ms (0.6% of total)ival-cbrt: 258.0ms (0.4% of total)ival-assert: 71.0ms (0.1% of total)ival-fmin: 66.0ms (0.1% of total)ival->: 1.0ms (0% of total)| 258× | iter limit |
| 108× | node limit |
| 56× | iter limit |
| 51× | node limit |
| 5× | saturated |
Compiled 23 562 to 6 261 computations (73.4% saved)
| 23× | fuel |
| 5× | done |
Compiled 9 869 to 2 000 computations (79.7% saved)
Compiled 1 625 355 to 173 240 computations (89.3% saved)
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | #f | cancellation | 4156 | 21 |
log.f64 | #f | sensitivity | 763 | 3 |
/.f64 | #f | u/u | 446 | 0 |
sqrt.f64 | #f | oflow-rescue | 398 | 0 |
+.f64 | #f | cancellation | 330 | 0 |
/.f64 | #f | u/n | 104 | 0 |
pow.f64 | (pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n)) | sensitivity | 68 | 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 | 24 | 0 |
| ↳ | (*.f64 b eps) | underflow | 151 | |
| ↳ | (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) | underflow | 150 | |
| ↳ | (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)) | underflow | 151 | |
| ↳ | (*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))) | underflow | 238 | |
| ↳ | (*.f64 a eps) | underflow | 150 | |
sqrt.f64 | #f | uflow-rescue | 16 | 0 |
-.f64 | #f | nan-rescue | 10 | 0 |
/.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 | 7 | 0 |
| ↳ | (exp.f64 (*.f64 #s(literal 2 binary64) x)) | overflow | 8 | |
| ↳ | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) | overflow | 8 | |
| ↳ | (exp.f64 x) | overflow | 7 | |
| ↳ | (-.f64 (exp.f64 x) #s(literal 1 binary64)) | overflow | 7 | |
/.f64 | (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)) | n/o | 4 | 0 |
| ↳ | (*.f64 x x) | overflow | 55 | |
sin.f64 | (sin.f64 (+.f64 x eps)) | sensitivity | 3 | 0 |
tan.f64 | (tan.f64 (+.f64 x eps)) | sensitivity | 3 | 0 |
cos.f64 | (cos.f64 (+.f64 x eps)) | sensitivity | 3 | 0 |
exp.f64 | #f | sensitivity | 2 | 0 |
/.f64 | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) | o/n | 1 | 0 |
| ↳ | (exp.f64 (*.f64 #s(literal 2 binary64) x)) | overflow | 8 | |
| ↳ | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) | overflow | 8 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 5196 | 18 |
| - | 157 | 1797 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 5196 | 15 | 3 |
| - | 157 | 8 | 1789 |
| number | freq |
|---|---|
| 0 | 1815 |
| 1 | 4565 |
| 2 | 642 |
| 3 | 95 |
| 4 | 51 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 28 | 0 | 0 |
| - | 0 | 0 | 0 |
| 1.4s | 2 726× | 2 | valid |
| 1.0s | 6 098× | 1 | valid |
| 742.0ms | 226× | 3 | valid |
| 469.0ms | 5 286× | 0 | valid |
Compiled 2 154 to 763 computations (64.6% saved)
ival-tan: 1.2s (40.9% of total)adjust: 273.0ms (9.3% of total)ival-log: 207.0ms (7% of total)ival-cos: 198.0ms (6.7% of total)ival-sin: 183.0ms (6.2% of total)ival-div!: 171.0ms (5.8% of total)ival-pow: 130.0ms (4.4% of total)ival-exp: 127.0ms (4.3% of total)ival-mult!: 98.0ms (3.3% of total)ival-sqrt: 85.0ms (2.9% of total)ival-sub!: 73.0ms (2.5% of total)ival-add!: 61.0ms (2.1% of total)ival-log1p: 59.0ms (2% of total)ival-expm1: 24.0ms (0.8% of total)ival-atan: 21.0ms (0.7% of total)ival-cbrt: 16.0ms (0.5% of total)ival-neg: 13.0ms (0.4% of total)504 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 69.0ms | x | @ | inf | ((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (neg (/ (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) n)) (/ (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) n) (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)) (log (+ 1 x)) x (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n) (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)) (pow (log (+ 1 x)) 3) 3 (pow (log x) 3) (log x) 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) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) 1 (pow x (/ 1 n)) (/ 1 n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (+ (/ x n) 1) (/ x n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (exp (neg (/ (neg (log x)) n))) (* n x)) (exp (neg (/ (neg (log x)) n))) (neg (/ (neg (log x)) n)) (/ (neg (log x)) n) (neg (log x)) (* n x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (+ (* (exp (neg (/ (neg (log x)) n))) (/ (- (* (pow n -2) 1/2) (/ 1/2 n)) x)) (/ (exp (neg (/ (neg (log x)) n))) n)) x) (+ (* (exp (neg (/ (neg (log x)) n))) (/ (- (* (pow n -2) 1/2) (/ 1/2 n)) x)) (/ (exp (neg (/ (neg (log x)) n))) n)) (/ (- (* (pow n -2) 1/2) (/ 1/2 n)) x) (- (* (pow n -2) 1/2) (/ 1/2 n)) (* (pow n -2) 1/2) (pow n -2) -2 (/ 1/2 n) (/ (exp (neg (/ (neg (log x)) n))) n)) |
| 66.0ms | x | @ | 0 | ((- (cbrt (+ x 1)) (cbrt x)) (* (* (cbrt (pow x -1)) (cbrt (pow x -1))) 1/3) (* (cbrt (pow x -1)) (cbrt (pow x -1))) (cbrt (pow x -1)) (pow x -1) x -1 1/3 (- (cbrt (+ x 1)) (cbrt x)) (+ (* 1/3 x) (- 1 (cbrt x))) (- 1 (cbrt x)) 1 (cbrt x) (- (cbrt (+ x 1)) (cbrt x)) (* (pow (pow x -2) 1/3) 1/3) (pow (pow x -2) 1/3) (pow x -2) -2 (- (cbrt (+ x 1)) (cbrt x)) (* (cbrt (exp (* (log x) -2))) 1/3) (cbrt (exp (* (log x) -2))) (exp (* (log x) -2)) (* (log x) -2) (log x) (- (cbrt (pow (cbrt (- x -1)) 3)) (cbrt x)) (cbrt (pow (cbrt (- x -1)) 3)) (pow (cbrt (- x -1)) 3) (cbrt (- x -1)) (- x -1) 3) |
| 57.0ms | x | @ | -inf | ((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (neg (/ (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) n)) (/ (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) n) (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)) (log (+ 1 x)) x (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n) (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)) (pow (log (+ 1 x)) 3) 3 (pow (log x) 3) (log x) 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) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) 1 (pow x (/ 1 n)) (/ 1 n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (+ (/ x n) 1) (/ x n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (exp (neg (/ (neg (log x)) n))) (* n x)) (exp (neg (/ (neg (log x)) n))) (neg (/ (neg (log x)) n)) (/ (neg (log x)) n) (neg (log x)) (* n x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (+ (* (exp (neg (/ (neg (log x)) n))) (/ (- (* (pow n -2) 1/2) (/ 1/2 n)) x)) (/ (exp (neg (/ (neg (log x)) n))) n)) x) (+ (* (exp (neg (/ (neg (log x)) n))) (/ (- (* (pow n -2) 1/2) (/ 1/2 n)) x)) (/ (exp (neg (/ (neg (log x)) n))) n)) (/ (- (* (pow n -2) 1/2) (/ 1/2 n)) x) (- (* (pow n -2) 1/2) (/ 1/2 n)) (* (pow n -2) 1/2) (pow n -2) -2 (/ 1/2 n) (/ (exp (neg (/ (neg (log x)) n))) n)) |
| 51.0ms | b | @ | 0 | ((/ (+ (neg b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)) (+ (neg b) (sqrt (- (* b b) (* 4 (* a c))))) (neg b) b (sqrt (- (* b b) (* 4 (* a c)))) (- (* b b) (* 4 (* a c))) (* b b) (* 4 (* a c)) 4 (* a c) a c (* 2 a) 2) |
| 51.0ms | 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))) |
Compiled 103 921 to 50 992 computations (50.9% saved)
43 calls:
| 959.0ms | x |
| 467.0ms | b_2 |
| 323.0ms | eps |
| 154.0ms | (/.f64 #s(literal 1 binary64) n) |
| 118.0ms | a |
Compiled 2 044 to 1 901 computations (7% saved)
| 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 |
| 116× | binary-search |
| 19× | left-value |
| 110× | narrow-enough |
| 6× | predicate-same |
| 361.0ms | 4 807× | 0 | valid |
| 257.0ms | 1 484× | 1 | valid |
| 187.0ms | 344× | 2 | valid |
| 108.0ms | 1 584× | 0 | invalid |
| 2.0ms | 20× | 0 | exit |
| 1.0ms | 5× | 3 | valid |
Compiled 49 481 to 34 261 computations (30.8% saved)
ival-pow: 163.0ms (25.7% of total)ival-mult!: 116.0ms (18.3% of total)ival-neg: 90.0ms (14.2% of total)adjust: 63.0ms (9.9% of total)ival-sqrt: 54.0ms (8.5% of total)ival-div!: 51.0ms (8.1% of total)ival-add!: 43.0ms (6.8% of total)ival-sub!: 30.0ms (4.7% of total)ival-cos: 11.0ms (1.7% of total)ival-cbrt: 10.0ms (1.6% of total)ival-expm1: 2.0ms (0.3% of total)Loading profile data...