Herbie run

Date:Wednesday, July 17th, 2024
Commit:c34c16ee on main
Hostname:nightly with Racket 8.11.1
Seed:2024199
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: 1.8hr)

simplify23.5min (21.3%)

Memory
-1 285.2MiB live, 1 712 754.5MiB allocated
Algorithm
4 446×egg-herbie
Rules
32 014 074×accelerator-lowering-fma.f32
32 014 074×accelerator-lowering-fma.f64
12 907 684×*-lowering-*.f32
12 907 684×*-lowering-*.f64
7 302 886×+-lowering-+.f32
Stop Event
3 866×iter limit
2 706×node limit
1 781×saturated
3×unsound
Counts
569 604 → 569 604

sample17.6min (15.9%)

Memory
4 710.0MiB live, 1 275 051.4MiB allocated
Samples
7.5min3 903 635×0valid
2.5min417 951×1valid
1.2min136 663×2valid
1.2min30 891×5exit
50.0s317 629×0invalid
13.5s15 722×3valid
7.2s50 934×0exit
6.9s25 469×1invalid
5.8s24 587×1exit
761.0ms1 423×2invalid
741.0ms793×4valid
734.0ms518×4exit
380.0ms1 205×2exit
293.0ms111×3exit
Precisions
Click to see histograms. Total time spent on operations: 10.3min
ival-mult: 2.1min (20.9% of total)
ival-div: 55.6s (9% of total)
ival-sin: 50.8s (8.3% of total)
ival-add: 44.0s (7.1% of total)
ival-sub: 43.7s (7.1% of total)
ival-pow: 41.7s (6.8% of total)
const: 36.3s (5.9% of total)
ival-cos: 32.3s (5.2% of total)
adjust: 26.2s (4.3% of total)
ival-log: 21.3s (3.5% of total)
ival-tan: 20.6s (3.3% of total)
ival-exp: 20.0s (3.2% of total)
ival-sqrt: 19.0s (3.1% of total)
ival-<=: 12.8s (2.1% of total)
ival-pow2: 12.6s (2% of total)
ival-fabs: 5.6s (0.9% of total)
ival-neg: 5.4s (0.9% of total)
ival-hypot: 4.4s (0.7% of total)
exact: 3.8s (0.6% of total)
ival-<: 3.2s (0.5% of total)
ival-true: 2.7s (0.4% of total)
ival-and: 2.6s (0.4% of total)
ival-pi: 2.2s (0.4% of total)
ival-acos: 2.1s (0.3% of total)
ival-expm1: 2.0s (0.3% of total)
ival-assert: 1.9s (0.3% of total)
ival-asin: 1.7s (0.3% of total)
ival-atan2: 1.6s (0.3% of total)
ival-log1p: 1.3s (0.2% of total)
ival-floor: 1.1s (0.2% of total)
ival-sinh: 930.0ms (0.2% of total)
ival-atan: 929.0ms (0.2% of total)
ival->: 876.0ms (0.1% of total)
ival-fmod: 811.0ms (0.1% of total)
ival-fmin: 688.0ms (0.1% of total)
ival-log2: 549.0ms (0.1% of total)
ival-==: 543.0ms (0.1% of total)
ival-cbrt: 531.0ms (0.1% of total)
ival-if: 513.0ms (0.1% of total)
ival-fmax: 422.0ms (0.1% of total)
ival-atanh: 302.0ms (0% of total)
ival-acosh: 275.0ms (0% of total)
ival-cosh: 250.0ms (0% of total)
ival->=: 242.0ms (0% of total)
ival-asinh: 218.0ms (0% of total)
ival-tanh: 135.0ms (0% of total)
ival-or: 37.0ms (0% of total)
Bogosity

rewrite14.2min (12.9%)

Memory
3 183.6MiB live, 1 121 220.2MiB allocated
Algorithm
1 953×batch-egg-rewrite
Rules
10 218 032×accelerator-lowering-fma.f32
10 218 032×accelerator-lowering-fma.f64
8 131 916×*-lowering-*.f32
8 131 916×*-lowering-*.f64
6 555 092×/-lowering-/.f32
Stop Event
2 086×iter limit
1 873×node limit
67×saturated
34×unsound
Counts
24 031 → 1 278 125

soundness13.9min (12.6%)

Memory
233.5MiB live, 410 811.4MiB allocated
Rules
19 365 312×accelerator-lowering-fma.f32
19 365 312×accelerator-lowering-fma.f64
10 742 300×*-lowering-*.f32
10 742 300×*-lowering-*.f64
5 508 270×/-lowering-/.f32
Stop Event
2 368×iter limit
2 245×node limit
367×fuel
173×done
33×saturated
16×unsound
Compiler

Compiled 373 158 to 179 473 computations (51.9% saved)

eval8.0min (7.3%)

Memory
10 230.4MiB live, 641 353.6MiB allocated
Compiler

Compiled 107 942 945 to 5 082 463 computations (95.3% saved)

prune7.8min (7%)

Memory
-9 635.8MiB live, 629 048.1MiB allocated
Counts
2 258 366 → 42 525
Compiler

Compiled 2 268 042 to 1 049 630 computations (53.7% saved)

localize7.2min (6.6%)

Memory
-738.8MiB live, 423 864.0MiB allocated
Samples
1.6min409 431×0valid
1.5min43 647×1valid
59.9s22 268×2valid
8.0s1 646×5exit
5.9s16 024×0invalid
4.9s3 023×3valid
2.9s708×4exit
974.0ms118×3exit
932.0ms1 664×0exit
912.0ms448×4valid
816.0ms329×1invalid
375.0ms559×2exit
288.0ms359×1exit
Compiler

Compiled 476 533 to 52 273 computations (89% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.4min
ival-mult: 50.7s (25.1% of total)
ival-add: 27.8s (13.7% of total)
adjust: 23.2s (11.5% of total)
const: 21.1s (10.4% of total)
ival-div: 18.3s (9.1% of total)
ival-exp: 15.3s (7.5% of total)
ival-cos: 8.8s (4.4% of total)
ival-sin: 7.8s (3.8% of total)
ival-sub: 5.8s (2.9% of total)
ival-sqrt: 3.8s (1.9% of total)
ival-log: 3.3s (1.6% of total)
ival-tan: 2.9s (1.4% of total)
ival-pow: 2.6s (1.3% of total)
ival-neg: 1.9s (0.9% of total)
ival-pow2: 1.7s (0.8% of total)
ival-asin: 881.0ms (0.4% of total)
ival-acos: 826.0ms (0.4% of total)
exact: 651.0ms (0.3% of total)
ival-atan2: 616.0ms (0.3% of total)
ival-cbrt: 454.0ms (0.2% of total)
ival-log1p: 450.0ms (0.2% of total)
ival-hypot: 444.0ms (0.2% of total)
ival-true: 408.0ms (0.2% of total)
ival-fmod: 407.0ms (0.2% of total)
ival-if: 319.0ms (0.2% of total)
ival-fabs: 287.0ms (0.1% of total)
ival-atan: 271.0ms (0.1% of total)
ival-pi: 249.0ms (0.1% of total)
ival-assert: 200.0ms (0.1% of total)
ival-copysign: 154.0ms (0.1% of total)
ival-fmax: 112.0ms (0.1% of total)
ival-log2: 103.0ms (0.1% of total)
ival-expm1: 98.0ms (0% of total)
ival-floor: 82.0ms (0% of total)
ival-e: 68.0ms (0% of total)
ival-sinh: 65.0ms (0% of total)
ival-cosh: 64.0ms (0% of total)
ival-tanh: 25.0ms (0% of total)
ival->=: 21.0ms (0% of total)
ival->: 15.0ms (0% of total)
ival-<: 4.0ms (0% of total)

regimes4.5min (4.1%)

Memory
-1 100.2MiB live, 372 995.5MiB allocated
Counts
137 881 → 10 444
Calls

1 223 calls:

20.3s
x
14.3s
y
12.0s
z
8.3s
a
8.0s
t
Compiler

Compiled 203 154 to 134 885 computations (33.6% saved)

series3.6min (3.3%)

Memory
143.8MiB live, 138 760.2MiB allocated
Counts
24 059 → 569 940
Calls

106386 calls:

TimeVariablePointExpression
1.9min
x
@0
(/ (- (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)))) (+ 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) -2) (* (/ (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)) (/ (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)))) (+ (/ 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 (/ (- (/ 2020417023103615081/1000000000000000000 (- 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1)))) (/ (/ (* (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1)))) (* (+ (* 3275911/10000000 (fabs x)) 1) (+ (* 3275911/10000000 (fabs x)) 1))) (- 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))))
3.6s
x
@0
(/ (- (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)))) (+ 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) -2) (* (/ (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)) (/ (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)))) (+ (/ 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))))
1.3s
x
@0
(+ (* (/ 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)))) (+ 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)))))) 2) -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)) (neg (/ (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))))
979.0ms
y
@0
(* (/ y (sqrt t)) 18)
912.0ms
x
@0
(- (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)))) (+ 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) -2) (* (/ (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)) (/ (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))))

preprocess3.1min (2.8%)

Memory
1 085.6MiB live, 208 908.8MiB allocated
Algorithm
1 084×egg-herbie
Rules
2 132 886×accelerator-lowering-fma.f32
2 132 886×accelerator-lowering-fma.f64
560 322×*-lowering-*.f32
560 322×*-lowering-*.f64
393 922×unsub-neg
Stop Event
740×saturated
539×iter limit
347×node limit
Compiler

Compiled 462 188 to 132 158 computations (71.4% saved)

bsearch2.6min (2.4%)

Memory
175.8MiB live, 164 578.9MiB allocated
Algorithm
3 018×binary-search
2 431×left-value
Stop Event
2 932×narrow-enough
83×predicate-same
3×predicate-failed
Samples
59.6s334 500×0valid
34.4s6 067×5exit
13.4s28 138×1valid
3.0s5 879×2valid
2.6s21 239×0invalid
1.0s241×4valid
861.0ms564×3valid
313.0ms284×1invalid
153.0ms258×1exit
35.0ms103×0exit
5.0ms20×2invalid
Compiler

Compiled 769 555 to 545 339 computations (29.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.4min
ival-pow: 32.8s (38.9% of total)
ival-mult: 15.3s (18.2% of total)
ival-sub: 6.2s (7.4% of total)
ival-div: 6.0s (7.1% of total)
ival-add: 4.6s (5.5% of total)
ival-sin: 3.7s (4.4% of total)
ival-cos: 3.3s (3.9% of total)
adjust: 2.8s (3.4% of total)
ival-log: 1.9s (2.2% of total)
const: 1.5s (1.7% of total)
ival-pow2: 1.3s (1.5% of total)
ival-exp: 1.2s (1.4% of total)
ival-sqrt: 790.0ms (0.9% of total)
ival-neg: 530.0ms (0.6% of total)
ival-hypot: 462.0ms (0.5% of total)
ival-tan: 407.0ms (0.5% of total)
ival-true: 280.0ms (0.3% of total)
ival-atan2: 269.0ms (0.3% of total)
exact: 231.0ms (0.3% of total)
ival-assert: 147.0ms (0.2% of total)
ival-acos: 132.0ms (0.2% of total)
ival-fmod: 132.0ms (0.2% of total)
ival-pi: 123.0ms (0.1% of total)
ival-atan: 80.0ms (0.1% of total)
ival-if: 51.0ms (0.1% of total)
ival-fabs: 27.0ms (0% of total)
ival-cosh: 18.0ms (0% of total)
ival-cbrt: 15.0ms (0% of total)
ival->=: 11.0ms (0% of total)
ival-tanh: 7.0ms (0% of total)
ival-log1p: 6.0ms (0% of total)
ival-expm1: 5.0ms (0% of total)
ival-copysign: 1.0ms (0% of total)

explain2.0min (1.8%)

Memory
-757.2MiB live, 170 363.5MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation893258
sqrt.f64#foflow-rescue52130
log.f64#fsensitivity34503
cos.f64#fsensitivity32405
+.f64#fcancellation3083131
sin.f64#fsensitivity19794
/.f64#fo/n19130
/.f64#fo/o16850
-.f64#fnan-rescue13660
*.f64#fn*o11540
log.f32#fsensitivity109885
/.f64#fu/u10320
sqrt.f64#fuflow-rescue10200
/.f64#fn/o10050
+.f64#fnan-rescue8500
/.f64#fu/n6500
acos.f64#fsensitivity5295
sqrt.f32#foflow-rescue5010
*.f64#fn*u4550
-.f32#fcancellation42022
pow.f64#fsensitivity39448
tan.f64#fsensitivity3912
/.f64#fn/u3180
-.f64(-.f64 (*.f64 #s(literal 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) t) #s(literal 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64))oflow-left2200
*.f64#fu*o2030
cos.f64#foflow-rescue1890
cos.f32#fsensitivity18520
exp.f64#fsensitivity18337
tan.f32(tan.f32 (+.f32 (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))cancellation17519
pow.f64#foflow-rescue1660
asin.f64(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))sensitivity1250
*.f64#fo*u1200
/.f32#fo/n1060
log.f64#foflow-rescue1050
cbrt.f64#foflow-rescue830
log.f64#fuflow-rescue730
pow.f64#fuflow-rescue710
cbrt.f64#fuflow-rescue440
sin.f64#foflow-rescue340
tan.f64(tan.f64 (/.f64 x (*.f64 y #s(literal 2 binary64))))oflow-rescue330
↳(/.f64 x (*.f64 y #s(literal 2 binary64)))overflow33
exp.f32#fsensitivity3318
/.f32#fu/n220
sqrt.f32(sqrt.f32 (-.f32 (*.f32 eta eta) (/.f32 (*.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O))))))uflow-rescue180
↳(*.f32 sinTheta_O sinTheta_O)underflow302
↳(-.f32 (*.f32 eta eta) (/.f32 (*.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O)))))underflow18
↳(/.f32 (*.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O))))underflow151
↳(*.f32 eta eta)underflow18
/.f32(/.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))n/o60
↳(/.f32 sin2phi (*.f32 alphay alphay))overflow13
↳(+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay)))overflow13
/.f32#fo/o60
*.f32(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))n*u30
log.f32#foflow-rescue20
*.f32(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))n*o10
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)))cancellation10
Confusion
Predicted +Predicted -
+303191151
-5926101356
Precision
0.8365015864257139
Recall
0.963425484588497
Confusion?
Predicted +Predicted MaybePredicted -
+30319273878
-5926414100942
Precision?
0.8283331528214015
Recall?
0.9721004130918335
Freqs
test
numberfreq
0102507
130402
24780
3590
4299
5111
639
712
85
96
101
Total Confusion?
Predicted +Predicted MaybePredicted -
+34133
-143178
Precision?
0.9529085872576177
Recall?
0.9913544668587896
Samples
26.4s235 006×0valid
11.0s29 930×1valid
7.4s10 942×2valid
1.1s1 326×3valid
118.0ms100×4valid
96.0ms88×5exit
17.0ms112×1exit
Compiler

Compiled 106 238 to 25 502 computations (76% saved)

Precisions
Click to see histograms. Total time spent on operations: 30.8s
ival-mult: 6.6s (21.3% of total)
ival-div: 3.3s (10.6% of total)
ival-add: 3.0s (9.9% of total)
ival-sub: 2.9s (9.3% of total)
ival-sin: 2.3s (7.5% of total)
ival-cos: 2.2s (7.1% of total)
adjust: 1.8s (5.7% of total)
ival-log: 1.6s (5.2% of total)
ival-exp: 1.2s (4% of total)
ival-tan: 1.2s (3.8% of total)
ival-sqrt: 821.0ms (2.7% of total)
const: 738.0ms (2.4% of total)
ival-pow2: 628.0ms (2% of total)
ival-pow: 509.0ms (1.7% of total)
ival-neg: 315.0ms (1% of total)
ival-true: 236.0ms (0.8% of total)
ival-hypot: 228.0ms (0.7% of total)
exact: 187.0ms (0.6% of total)
ival-pi: 160.0ms (0.5% of total)
ival-atan2: 130.0ms (0.4% of total)
ival-assert: 125.0ms (0.4% of total)
ival-asin: 103.0ms (0.3% of total)
ival-fabs: 83.0ms (0.3% of total)
ival-log1p: 80.0ms (0.3% of total)
ival-acos: 75.0ms (0.2% of total)
ival-atan: 63.0ms (0.2% of total)
ival-sinh: 55.0ms (0.2% of total)
ival-copysign: 50.0ms (0.2% of total)
ival-floor: 38.0ms (0.1% of total)
ival-cbrt: 35.0ms (0.1% of total)
ival-if: 35.0ms (0.1% of total)
ival-fmod: 32.0ms (0.1% of total)
ival-expm1: 30.0ms (0.1% of total)
ival-fmax: 16.0ms (0.1% of total)
ival-cosh: 15.0ms (0% of total)
ival-log2: 13.0ms (0% of total)
ival-tanh: 7.0ms (0% of total)
ival->=: 6.0ms (0% of total)
ival->: 3.0ms (0% of total)
ival-<: 1.0ms (0% of total)

analyze1.2min (1.1%)

Memory
260.1MiB live, 106 506.6MiB allocated
Algorithm
545×search
2×random
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%84.4%15.6%0%0%0%0
39.8%33.6%50.8%15.6%0%0%0%1
45.9%38.4%45.3%15.6%0%0.8%0%2
54.5%44.5%37.2%15.6%0%2.8%0%3
61.4%49.5%31.1%15.6%0%3.8%0%4
67.7%54.3%25.9%15.6%0%4.3%0%5
71.6%57.1%22.7%15.6%0%4.7%0%6
75.5%59.8%19.4%15.6%0%5.2%0%7
77.5%61.1%17.7%15.6%0%5.6%0%8
80.1%62.9%15.6%15.6%0%5.9%0%9
81.7%63.9%14.3%15.6%0%6.2%0%10
83.9%65.5%12.6%15.6%0%6.4%0%11
85%66.2%11.6%15.6%0%6.6%0%12
Compiler

Compiled 12 512 to 7 841 computations (37.3% saved)

end1.0min (0.9%)

Memory
9.2MiB live, 29 647.9MiB allocated

Profiling

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