Herbie run
| Date: | Tuesday, August 6th, 2024 |
|---|---|
| Commit: | 2.2 on release |
| Hostname: | nightly with Racket 8.11.1 |
| Seed: | 2024219 |
| Parameters: | 256 points for 4 iterations |
| Flags: | localize:costslocalize:errorsreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionssetup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:proofs default |
Time bar (total: 27.0min)
| 2 059 160× | lower-fma.f32 |
| 2 058 732× | lower-fma.f64 |
| 1 020 560× | lower-*.f32 |
| 1 019 338× | lower-*.f64 |
| 593 520× | lower-+.f32 |
| 330× | iter limit |
| 214× | node limit |
| 34× | fuel |
| 20× | done |
| 2× | unsound |
| 1× | saturated |
Compiled 33 355 to 14 662 computations (56% saved)
| 192× | batch-egg-rewrite |
| 1 000 918× | lower-fma.f32 |
| 1 000 132× | lower-fma.f64 |
| 781 618× | lower-*.f32 |
| 779 466× | lower-*.f64 |
| 586 074× | lower-/.f32 |
| 404× | iter limit |
| 182× | node limit |
| 8× | saturated |
| 4× | unsound |
Compiled 157 408 to 70 394 computations (55.3% saved)
| 440× | egg-herbie |
| 3 606 604× | lower-fma.f32 |
| 3 605 802× | lower-fma.f64 |
| 1 282 634× | lower-*.f32 |
| 1 280 326× | lower-*.f64 |
| 865 594× | lower-+.f32 |
| 575× | iter limit |
| 261× | node limit |
| 182× | saturated |
| 46.6s | 438 824× | 0 | valid |
| 24.7s | 3 778× | 5 | exit |
| 7.1s | 22 284× | 1 | valid |
| 3.8s | 8 611× | 2 | valid |
| 634.0ms | 7 853× | 0 | exit |
| 350.0ms | 539× | 0 | invalid |
| 292.0ms | 874× | 3 | valid |
ival-sin: 19.6s (29.4% of total)ival-mult: 12.7s (19% of total)adjust: 4.9s (7.3% of total)ival-add: 4.8s (7.1% of total)const: 4.0s (6% of total)ival-div: 3.5s (5.2% of total)ival-exp: 2.9s (4.3% of total)ival-hypot: 2.7s (4% of total)ival-log: 2.6s (3.9% of total)ival-sub: 1.9s (2.8% of total)ival-asin: 1.3s (2% of total)ival-sqrt: 853.0ms (1.3% of total)ival-atan2: 807.0ms (1.2% of total)ival-cos: 796.0ms (1.2% of total)ival-<=: 413.0ms (0.6% of total)ival-pi: 370.0ms (0.6% of total)exact: 337.0ms (0.5% of total)ival->: 319.0ms (0.5% of total)ival-pow: 312.0ms (0.5% of total)ival-asinh: 292.0ms (0.4% of total)ival-true: 256.0ms (0.4% of total)ival-neg: 238.0ms (0.4% of total)ival-atanh: 226.0ms (0.3% of total)ival-acosh: 214.0ms (0.3% of total)ival-fabs: 213.0ms (0.3% of total)ival->=: 191.0ms (0.3% of total)ival-assert: 179.0ms (0.3% of total)ival-and: 74.0ms (0.1% of total)128 calls:
| 41.2s | x |
| 4.6s | (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) |
| 1.2s | im |
| 1.2s | re |
| 513.0ms | (sin.f64 re) |
Compiled 15 567 to 9 382 computations (39.7% saved)
| 21.5s | 3 545× | 1 | valid |
| 9.4s | 39 775× | 0 | valid |
| 1.7s | 4 126× | 0 | invalid |
| 1.4s | 1 191× | 2 | valid |
| 206.0ms | 330× | 1 | exit |
| 110.0ms | 135× | 0 | exit |
| 79.0ms | 55× | 3 | valid |
| 17.0ms | 11× | 2 | exit |
| 9.0ms | 11× | 4 | valid |
Compiled 49 959 to 5 181 computations (89.6% saved)
ival-mult: 23.0s (75.4% of total)ival-div: 1.6s (5.1% of total)ival-add: 1.3s (4.3% of total)const: 724.0ms (2.4% of total)ival-log: 714.0ms (2.3% of total)adjust: 413.0ms (1.4% of total)ival-sub: 375.0ms (1.2% of total)ival-exp: 359.0ms (1.2% of total)ival-sqrt: 343.0ms (1.1% of total)ival-hypot: 278.0ms (0.9% of total)ival-asin: 236.0ms (0.8% of total)ival-sin: 180.0ms (0.6% of total)ival-pow: 171.0ms (0.6% of total)ival-cos: 129.0ms (0.4% of total)ival-copysign: 126.0ms (0.4% of total)ival-acos: 113.0ms (0.4% of total)ival-neg: 103.0ms (0.3% of total)ival-atan2: 94.0ms (0.3% of total)exact: 56.0ms (0.2% of total)ival-pow2: 52.0ms (0.2% of total)ival-fabs: 42.0ms (0.1% of total)ival-true: 38.0ms (0.1% of total)ival-log1p: 32.0ms (0.1% of total)ival-pi: 27.0ms (0.1% of total)ival-assert: 19.0ms (0.1% of total)ival-cosh: 16.0ms (0.1% of total)ival-expm1: 2.0ms (0% of total)Compiled 13 330 190 to 539 692 computations (96% saved)
| 57× | egg-herbie |
| 296 104× | lower-fma.f64 |
| 296 104× | lower-fma.f32 |
| 79 264× | lower-*.f32 |
| 78 898× | lower-*.f64 |
| 56 582× | lower-+.f32 |
| 114× | iter limit |
| 76× | saturated |
| 38× | node limit |
Compiled 36 872 to 9 736 computations (73.6% saved)
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
sqrt.f64 | #f | oflow-rescue | 1177 | 0 |
-.f64 | #f | cancellation | 794 | 4 |
/.f64 | #f | o/o | 614 | 0 |
sin.f64 | #f | sensitivity | 196 | 0 |
cos.f64 | (cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))) | sensitivity | 193 | 0 |
/.f64 | #f | o/n | 188 | 0 |
sqrt.f32 | #f | oflow-rescue | 184 | 0 |
+.f64 | #f | cancellation | 145 | 0 |
sqrt.f64 | #f | uflow-rescue | 143 | 0 |
log.f64 | (log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))) | sensitivity | 132 | 0 |
log.f32 | (log.f32 (+.f32 (fabs.f32 x) (sqrt.f32 (+.f32 (*.f32 x x) #s(literal 1 binary32))))) | sensitivity | 127 | 5 |
-.f64 | #f | nan-rescue | 102 | 0 |
/.f64 | #f | n/o | 93 | 0 |
*.f64 | #f | n*u | 60 | 0 |
/.f64 | (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i))) | u/u | 59 | 0 |
| ↳ | (*.f64 (*.f64 i i) (*.f64 i i)) | underflow | 92 | |
| ↳ | (*.f64 i i) | underflow | 118 | |
| ↳ | (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)) | underflow | 59 | |
+.f64 | #f | nan-rescue | 52 | 0 |
*.f64 | #f | n*o | 40 | 0 |
/.f64 | #f | u/n | 38 | 0 |
/.f64 | #f | n/u | 9 | 0 |
*.f64 | (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1/2 binary64)))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64))))) | o*u | 3 | 0 |
| ↳ | (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1/2 binary64)))) | overflow | 3 | |
| ↳ | (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1/2 binary64))) | overflow | 3 | |
| ↳ | (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)))) | underflow | 3 | |
log.f32 | #f | oflow-rescue | 2 | 0 |
cos.f64 | (cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))) | oflow-rescue | 1 | 0 |
| ↳ | (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)) | overflow | 1 | |
| ↳ | (*.f64 x.re x.re) | overflow | 59 | |
| ↳ | (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) | overflow | 103 | |
| ↳ | (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) | overflow | 1 | |
| ↳ | (*.f64 x.im x.im) | overflow | 66 | |
exp.f64 | (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))) | sensitivity | 1 | 0 |
sin.f64 | (sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))) | oflow-rescue | 1 | 0 |
| ↳ | (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)) | overflow | 1 | |
| ↳ | (*.f64 x.re x.re) | overflow | 59 | |
| ↳ | (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) | overflow | 103 | |
| ↳ | (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) | overflow | 1 | |
| ↳ | (*.f64 x.im x.im) | overflow | 66 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 3599 | 46 |
| - | 197 | 10750 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 3599 | 6 | 40 |
| - | 197 | 5 | 10745 |
| number | freq |
|---|---|
| 0 | 10796 |
| 1 | 3240 |
| 2 | 554 |
| 3 | 2 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 37 | 0 | 0 |
| - | 0 | 0 | 20 |
| 3.2s | 25 726× | 0 | valid |
| 981.0ms | 2 500× | 1 | valid |
| 553.0ms | 906× | 2 | valid |
| 21.0ms | 52× | 3 | valid |
Compiled 15 068 to 2 968 computations (80.3% saved)
ival-mult: 980.0ms (29.2% of total)ival-div: 446.0ms (13.3% of total)ival-add: 340.0ms (10.1% of total)const: 202.0ms (6% of total)ival-exp: 200.0ms (6% of total)ival-log: 194.0ms (5.8% of total)adjust: 186.0ms (5.5% of total)ival-hypot: 180.0ms (5.4% of total)ival-sub: 168.0ms (5% of total)ival-asin: 69.0ms (2.1% of total)ival-sin: 68.0ms (2% of total)ival-sqrt: 64.0ms (1.9% of total)ival-cos: 59.0ms (1.8% of total)ival-atan2: 55.0ms (1.6% of total)ival-true: 24.0ms (0.7% of total)ival-pow: 23.0ms (0.7% of total)exact: 19.0ms (0.6% of total)ival-pi: 17.0ms (0.5% of total)ival-fabs: 16.0ms (0.5% of total)ival-copysign: 12.0ms (0.4% of total)ival-assert: 12.0ms (0.4% of total)ival-neg: 11.0ms (0.3% of total)ival-log1p: 8.0ms (0.2% of total)8559 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 380.0ms | x | @ | 0 | (/ (- (* 1 (+ (* (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))) (+ 1 (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))))) 1)) (* (+ (* (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))) (+ 1 (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))))) 1) (pow (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))) 3))) (* (+ (* (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))) (+ 1 (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))))) 1) (+ (* (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))) (+ 1 (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))))) 1))) |
| 279.0ms | im | @ | -inf | (* (+ 0 (log (/ (log base) (atan2 im re)))) -1) |
| 132.0ms | y.im | @ | 0 | (cos (* y.im (* 1/2 (log (+ (* x.im x.im) (* x.re x.re)))))) |
| 128.0ms | x | @ | -inf | (sqrt (+ x -1)) |
| 127.0ms | x.re | @ | 0 | (* (cos (* y.re (atan2 x.im x.re))) (pow (neg x.im) y.re)) |
| 283× | left-value |
| 202× | binary-search |
| 192× | narrow-enough |
| 10× | predicate-same |
| 1.6s | 14 463× | 0 | valid |
| 838.0ms | 1 693× | 1 | valid |
| 89.0ms | 204× | 2 | valid |
| 19.0ms | 72× | 3 | valid |
Compiled 51 996 to 33 713 computations (35.2% saved)
ival-mult: 631.0ms (32.8% of total)ival-log: 242.0ms (12.6% of total)ival-hypot: 198.0ms (10.3% of total)ival-add: 179.0ms (9.3% of total)ival-sin: 113.0ms (5.9% of total)ival-exp: 101.0ms (5.3% of total)adjust: 89.0ms (4.6% of total)ival-atan2: 81.0ms (4.2% of total)const: 75.0ms (3.9% of total)ival-sub: 73.0ms (3.8% of total)ival-cos: 54.0ms (2.8% of total)ival-div: 48.0ms (2.5% of total)ival-sqrt: 15.0ms (0.8% of total)ival-true: 12.0ms (0.6% of total)ival-assert: 6.0ms (0.3% of total)exact: 5.0ms (0.3% of total)| 58× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 86.3% | 13.7% | 0% | 0% | 0% | 0 |
| 55.4% | 47.8% | 38.5% | 13.7% | 0% | 0% | 0% | 1 |
| 65.9% | 55.7% | 28.9% | 13.7% | 0% | 1.7% | 0% | 2 |
| 71.2% | 58.4% | 23.6% | 13.7% | 0% | 4.3% | 0% | 3 |
| 77.4% | 62% | 18.1% | 13.7% | 0% | 6.2% | 0% | 4 |
| 83.5% | 66.8% | 13.2% | 13.7% | 0% | 6.3% | 0% | 5 |
| 85.8% | 68.3% | 11.3% | 13.7% | 0% | 6.6% | 0% | 6 |
| 88.3% | 70.3% | 9.4% | 13.7% | 0% | 6.6% | 0% | 7 |
| 89.9% | 71.5% | 8% | 13.7% | 0% | 6.8% | 0% | 8 |
| 91.1% | 72.5% | 7.1% | 13.7% | 0% | 6.8% | 0% | 9 |
| 92.6% | 73.6% | 5.9% | 13.7% | 0% | 6.8% | 0% | 10 |
| 94% | 74.7% | 4.8% | 13.7% | 0% | 6.8% | 0% | 11 |
| 94.5% | 75.1% | 4.4% | 13.7% | 0% | 6.9% | 0% | 12 |
Compiled 1 498 to 821 computations (45.2% saved)
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