Herbie run

Date:Saturday, August 31st, 2024
Commit:ac261103 on main
Hostname:nightly with Racket 8.11.1
Seed:2024244
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: 16.0min)

sample3.9min (24.4%)

Memory
976.3MiB live, 123 672.5MiB allocated
Samples
1.9min3 708×5exit
1.3min438 757×0valid
7.4s22 304×1valid
4.3s8 649×2valid
985.0ms8 901×0exit
283.0ms925×3valid
77.0ms542×0invalid
Precisions
Click to see histograms. Total time spent on operations: 3.2min
ival-sin: 1.6min (49.6% of total)
ival-add: 19.6s (10.3% of total)
ival-div: 19.2s (10.1% of total)
adjust: 18.9s (9.9% of total)
ival-mult: 15.0s (7.9% of total)
const: 4.0s (2.1% of total)
ival-exp: 3.7s (1.9% of total)
ival-hypot: 2.6s (1.4% of total)
ival-log: 2.3s (1.2% of total)
ival-sub: 2.2s (1.2% of total)
ival-cos: 1.4s (0.7% of total)
ival-asin: 1.3s (0.7% of total)
ival-sqrt: 909.0ms (0.5% of total)
ival->: 689.0ms (0.4% of total)
ival-atan2: 659.0ms (0.3% of total)
ival-pi: 425.0ms (0.2% of total)
ival-pow: 403.0ms (0.2% of total)
exact: 356.0ms (0.2% of total)
ival-acosh: 342.0ms (0.2% of total)
ival-asinh: 277.0ms (0.1% of total)
ival-true: 266.0ms (0.1% of total)
ival-fabs: 232.0ms (0.1% of total)
ival-neg: 222.0ms (0.1% of total)
ival-assert: 186.0ms (0.1% of total)
ival-<=: 171.0ms (0.1% of total)
ival-atanh: 156.0ms (0.1% of total)
ival->=: 137.0ms (0.1% of total)
ival-and: 76.0ms (0% of total)
Bogosity

soundness3.1min (19.1%)

Memory
330.3MiB live, 34 830.7MiB allocated
Rules
2 000 016×lower-fma.f32
1 999 676×lower-fma.f64
982 106×lower-*.f32
980 830×lower-*.f64
564 608×lower-+.f32
Stop Event
328×iter limit
211×node limit
37×fuel
19×done
3×saturated
3×unsound
Compiler

Compiled 37 031 to 17 054 computations (53.9% saved)

eval2.8min (17.8%)

Memory
585.9MiB live, 68 136.9MiB allocated
Compiler

Compiled 11 327 132 to 547 240 computations (95.2% saved)

localize2.4min (15.2%)

Memory
-126.2MiB live, 35 125.8MiB allocated
Samples
1.5min3 641×1valid
33.4s1 252×2valid
12.4s40 625×0valid
1.6s3 242×0invalid
381.0ms244×5exit
378.0ms431×1exit
100.0ms101×3valid
75.0ms123×0exit
41.0ms5×2exit
Compiler

Compiled 65 248 to 5 846 computations (91% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.7min
ival-div: 44.5s (43.6% of total)
ival-mult: 34.7s (34.1% of total)
adjust: 15.4s (15.1% of total)
ival-add: 1.7s (1.7% of total)
ival-log: 705.0ms (0.7% of total)
ival-pow: 677.0ms (0.7% of total)
const: 613.0ms (0.6% of total)
ival-hypot: 522.0ms (0.5% of total)
ival-sub: 521.0ms (0.5% of total)
ival-exp: 455.0ms (0.4% of total)
ival-sqrt: 381.0ms (0.4% of total)
ival-pow2: 349.0ms (0.3% of total)
ival-asin: 271.0ms (0.3% of total)
ival-sin: 185.0ms (0.2% of total)
ival-neg: 180.0ms (0.2% of total)
ival-cos: 170.0ms (0.2% of total)
ival-acos: 127.0ms (0.1% of total)
exact: 105.0ms (0.1% of total)
ival-fabs: 84.0ms (0.1% of total)
ival-atan2: 75.0ms (0.1% of total)
ival-log1p: 60.0ms (0.1% of total)
ival-copysign: 53.0ms (0.1% of total)
ival-true: 39.0ms (0% of total)
ival-pi: 29.0ms (0% of total)
ival-assert: 20.0ms (0% of total)
ival-cosh: 8.0ms (0% of total)
ival-cbrt: 3.0ms (0% of total)

simplify1.2min (7.5%)

Memory
668.2MiB live, 70 316.5MiB allocated
Algorithm
444×egg-herbie
Rules
3 422 092×lower-fma.f32
3 421 338×lower-fma.f64
1 231 628×lower-*.f32
1 229 578×lower-*.f64
802 490×lower-+.f32
Stop Event
582×iter limit
261×node limit
183×saturated
Counts
56 700 → 55 918

rewrite53.8s (5.6%)

Memory
-241.6MiB live, 54 190.6MiB allocated
Rules
1 003 992×lower-fma.f32
1 003 240×lower-fma.f64
783 096×lower-*.f32
781 182×lower-*.f64
596 362×lower-/.f32
Stop Event
407×iter limit
185×node limit
5×saturated
4×unsound
Counts
2 763 → 107 385

regimes21.2s (2.2%)

Memory
-108.2MiB live, 18 937.1MiB allocated
Counts
8 136 → 888
Calls

130 calls:

7.5s
(cos.f64 im)
827.0ms
im
755.0ms
re
710.0ms
x
495.0ms
y.re
Compiler

Compiled 13 130 to 9 605 computations (26.8% saved)

explain16.8s (1.7%)

Memory
132.7MiB live, 15 742.4MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64#foflow-rescue11790
-.f64#fcancellation7163
/.f64#fo/o6260
/.f64#fo/n2000
sqrt.f32#foflow-rescue1860
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)))sensitivity1770
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)))sensitivity1761
+.f64#fcancellation1450
sqrt.f64#fuflow-rescue1390
log.f32(log.f32 (+.f32 (fabs.f32 x) (sqrt.f32 (+.f32 (*.f32 x x) #s(literal 1 binary32)))))sensitivity1321
log.f64(log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))sensitivity1170
/.f64#fn/o850
*.f64#fn*u800
-.f64#fnan-rescue750
/.f64#fu/u600
+.f64#fnan-rescue450
/.f64#fu/n440
*.f64#fn*o320
/.f64#fn/u180
log.f32#foflow-rescue60
Confusion
Predicted +Predicted -
+3545296
-14610349
Precision
0.9604443240314278
Recall
0.9229367352252018
Confusion?
Predicted +Predicted MaybePredicted -
+35453293
-146510344
Precision?
0.9591781562584483
Recall?
0.9237177818276491
Freqs
test
numberfreq
010645
13144
2547
Total Confusion?
Predicted +Predicted MaybePredicted -
+3511
-0019
Precision?
1.0
Recall?
0.972972972972973
Samples
3.1s25 858×0valid
812.0ms2 084×1valid
278.0ms670×2valid
21.0ms58×3valid
1.0ms2×5exit
Compiler

Compiled 11 645 to 2 099 computations (82% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.7s
ival-mult: 830.0ms (30.2% of total)
ival-log: 311.0ms (11.3% of total)
ival-add: 241.0ms (8.8% of total)
ival-hypot: 202.0ms (7.4% of total)
ival-exp: 166.0ms (6% of total)
ival-sin: 165.0ms (6% of total)
ival-sub: 152.0ms (5.5% of total)
ival-div: 133.0ms (4.8% of total)
const: 105.0ms (3.8% of total)
adjust: 89.0ms (3.2% of total)
ival-asin: 77.0ms (2.8% of total)
ival-sqrt: 59.0ms (2.1% of total)
ival-cos: 56.0ms (2% of total)
ival-atan2: 41.0ms (1.5% of total)
ival-pi: 24.0ms (0.9% of total)
ival-true: 24.0ms (0.9% of total)
ival-fabs: 18.0ms (0.7% of total)
exact: 17.0ms (0.6% of total)
ival-assert: 12.0ms (0.4% of total)
ival-copysign: 11.0ms (0.4% of total)
ival-log1p: 7.0ms (0.3% of total)
ival-neg: 6.0ms (0.2% of total)

series16.7s (1.7%)

Memory
-298.9MiB live, 21 885.4MiB allocated
Counts
2 763 → 56 700
Calls

1197 calls:

TimeVariablePointExpression
1.0s
x
@0
((+ (pow (+ (* (/ (/ (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) (+ (* (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (/ (pow (exp x) (neg x)) (+ (* (fabs x) 3275911/10000000) 1))) 1)) 1) -1) (* (pow (+ (* (/ (/ (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) (+ (* (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (/ (pow (exp x) (neg x)) (+ (* (fabs x) 3275911/10000000) 1))) 1)) 1) -1) (pow (/ (/ (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) 3))) (- (pow (+ (* (/ (/ (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) (+ (* (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (/ (pow (exp x) (neg x)) (+ (* (fabs x) 3275911/10000000) 1))) 1)) 1) -2) (pow (* (neg (pow (/ (/ (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) 3)) (pow (+ (* (/ (/ (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) (+ (* (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (/ (pow (exp x) (neg x)) (+ (* (fabs x) 3275911/10000000) 1))) 1)) 1) -1)) 2)) (* (neg (pow (/ (/ (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) 3)) (pow (+ (* (/ (/ (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) (+ (* (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (/ (pow (exp x) (neg x)) (+ (* (fabs x) 3275911/10000000) 1))) 1)) 1) -1)) (* (pow (+ (* (/ (/ (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) (+ (* (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (/ (pow (exp x) (neg x)) (+ (* (fabs x) 3275911/10000000) 1))) 1)) 1) -1) (pow (/ (/ (+ (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) 3)) (- 1 (* (/ (+ (* (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* (* x x) 10731592879921/100000000000000) -1)) (+ (* 3275911/10000000 (fabs x)) -1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (exp (neg (* (fabs x) (fabs x)))))) (* (fabs x) (fabs x)) (/ (+ (* (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* (* x x) 10731592879921/100000000000000) -1)) (+ (* 3275911/10000000 (fabs x)) -1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (+ (* (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* (* x x) 10731592879921/100000000000000) -1)) (+ (* 3275911/10000000 (fabs x)) -1)) 31853699/125000000) (+ (* (/ 1061405429/1000000000 (+ (* (* x x) 10731592879921/100000000000000) -1)) (+ (* (fabs x) 3275911/10000000) -1)) -1453152027/1000000000) (* (/ (+ (* (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ (* (/ 1061405429/1000000000 (+ (* (* x x) 10731592879921/100000000000000) -1)) (+ (* (fabs x) 3275911/10000000) -1)) -1453152027/1000000000) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* (* x x) 10731592879921/100000000000000) -1)) (+ (* 3275911/10000000 (fabs x)) -1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (exp (neg (* (fabs x) (fabs x))))) (+ (* (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ (* (/ 1061405429/1000000000 (+ (* (* x x) 10731592879921/100000000000000) -1)) (+ (* (fabs x) 3275911/10000000) -1)) -1453152027/1000000000) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* (* x x) 10731592879921/100000000000000) -1)) (+ (* 3275911/10000000 (fabs x)) -1)) 31853699/125000000) (/ (/ (+ (/ (+ (/ (+ (* (pow (+ (* (fabs x) 3275911/10000000) 1) -2) 1061405429/1000000000) (+ (/ -1453152027/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000)) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) (/ (/ (+ (/ (+ (/ (+ (* (pow (+ (* (fabs x) 3275911/10000000) 1) -2) 1061405429/1000000000) (+ (/ -1453152027/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000)) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* -3275911/10000000 (fabs x)) -1)) (pow (exp x) x)) (* (- (pow (/ (/ (+ (/ (+ (/ (+ (* (pow (+ (* (fabs x) 3275911/10000000) 1) -2) 1061405429/1000000000) (+ (/ -1453152027/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000)) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) 2) 1) (/ 1 (- (/ (/ (+ (/ (+ (/ (+ (* (pow (+ (* (fabs x) 3275911/10000000) 1) -2) 1061405429/1000000000) (+ (/ -1453152027/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000)) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* -3275911/10000000 (fabs x)) -1)) (pow (exp x) x)) 1))) (- (pow (/ (/ (+ (/ (+ (/ (+ (* (pow (+ (* (fabs x) 3275911/10000000) 1) -2) 1061405429/1000000000) (+ (/ -1453152027/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000)) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) 2) 1) (+ (- 1 (/ (/ (+ (/ (+ (/ (+ (* (pow (+ (* (fabs x) 3275911/10000000) 1) -2) 1061405429/1000000000) (+ (/ -1453152027/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000)) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x))) (pow (/ (/ (+ (/ (+ (/ (+ (* (pow (+ (* (fabs x) 3275911/10000000) 1) -2) 1061405429/1000000000) (+ (/ -1453152027/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000)) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) 2)) (+ (* (/ 1 (+ (pow (/ (/ (+ (/ (+ (/ (+ (* (pow (+ (* (fabs x) 3275911/10000000) 1) -2) 1061405429/1000000000) (+ (/ -1453152027/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000)) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1)) 31853699/125000000) (+ (* (fabs x) 3275911/10000000) 1)) (pow (exp x) x)) 3) 1)) (+ (- 1 (/ (/ (+ (/ (+ (/ (+ (* (pow (+ (* (fabs x) 3275911/10000000) 1) -2) 1061405429/1000000000) (+ (/ -1453152027/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000)) (+ (* (fabs x) 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177.0ms
x
@0
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31853699/125000000) (+ (* 3275911/10000000 (fabs x)) 1)) (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs 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))) (* (pow (exp x) x) (+ (* 3275911/10000000 (fabs x)) 1))) 3) (pow (+ (* (+ (* (/ (pow (exp x) (neg x)) (+ (* 3275911/10000000 (fabs 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)))) 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))) (* (pow (exp x) x) (+ (* 3275911/10000000 (fabs x)) 1)))) 1) -2) (* (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* (* x x) 10731592879921/100000000000000) -1)) (+ (* 3275911/10000000 (fabs x)) -1)) (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* (* x x) 10731592879921/100000000000000) -1)) (+ 1421413741/1000000000 (/ 1453152027/1000000000 (+ (* -3275911/10000000 (fabs x)) -1))) (/ 1061405429/1000000000 (pow (+ (* 3275911/10000000 (fabs x)) 1) 2)) (/ (+ (/ (+ (+ 1421413741/1000000000 (/ 1453152027/1000000000 (+ (* -3275911/10000000 (fabs x)) -1))) (/ 1061405429/1000000000 (pow (+ (* 3275911/10000000 (fabs x)) 1) 2))) (+ (* 3275911/10000000 (fabs x)) 1)) -8890523/31250000) (+ (* 3275911/10000000 (fabs x)) 1)) (pow (/ (/ (+ (/ (+ (/ (+ (+ 1421413741/1000000000 (/ 1453152027/1000000000 (+ (* -3275911/10000000 (fabs x)) -1))) (/ 1061405429/1000000000 (pow (+ (* 3275911/10000000 (fabs x)) 1) 2))) (+ (* 3275911/10000000 (fabs x)) 1)) -8890523/31250000) (+ (* 3275911/10000000 (fabs x)) 1)) 31853699/125000000) (+ (* 3275911/10000000 (fabs x)) 1)) (pow (exp x) x)) 2))
162.0ms
x.im
@0
((/ 1 (/ (pow (exp y.im) (atan2 x.im x.re)) (* (pow (sqrt (+ (* x.im x.im) (* x.re x.re))) y.re) (sin (+ (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))) (* y.re (atan2 x.im x.re))))))) (pow (exp y.im) (atan2 x.im x.re)) (exp y.im) (atan2 x.im x.re) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (sin (* (atan2 x.im x.re) y.re))) (* y.re (atan2 x.im x.re)) (+ 1 (* y.re (log (sqrt (+ (* x.im x.im) (* x.re x.re)))))) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (sin (* (atan2 x.im x.re) y.re))) (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (log (* (atan2 x.im x.re) y.re))) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (sin (exp (log (* (atan2 x.im x.re) y.re))))) (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)) (* (neg y.im) (atan2 x.im x.re)) (+ (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))) (* y.re (atan2 x.im x.re))) (/ (pow (exp y.im) (atan2 x.im x.re)) (* (pow (sqrt (+ (* x.im x.im) (* x.re x.re))) y.re) (sin (+ (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))) (* y.re (atan2 x.im x.re)))))) (* y.re (log (sqrt (+ (* x.im x.im) (* x.re x.re))))) (* (atan2 x.im x.re) y.re) (log (* (atan2 x.im x.re) y.re)) (+ (* (* (cos (* (atan2 x.im x.re) y.re)) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) y.im) (sin (* (atan2 x.im x.re) y.re))))
161.0ms
x.re
@0
((* (pow (sqrt (+ (* x.im x.im) (* x.re x.re))) y.re) (* (pow (exp (atan2 x.im x.re)) (neg y.im)) (sin (+ (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))) (* y.re (atan2 x.im x.re)))))) (pow (sqrt (+ (* x.im x.im) (* x.re x.re))) y.re) (sqrt (+ (* x.im x.im) (* x.re x.re))) (pow (exp (atan2 x.im x.re)) (neg y.im)) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (sin (* (atan2 x.im x.re) y.re))) (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* (neg y.im) (log (/ -1 x.re))) (* (atan2 x.im x.re) y.re)) (neg (+ (* (log (/ -1 x.re)) y.re) (* y.im (atan2 x.im x.re)))) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (* (sin (+ (* (neg y.im) (log (/ -1 x.re))) (* (atan2 x.im x.re) y.re))) (exp (neg (+ (* (log (/ -1 x.re)) y.re) (* y.im (atan2 x.im x.re)))))) (+ (* x.re x.re) (* x.im x.im)) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)) (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (neg (/ (pow (* y.re (atan2 x.im x.re)) 2) (+ (* (neg (atan2 x.im x.re)) y.re) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re)))))))) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (* (pow (log (sqrt (+ (* x.im x.im) (* x.re x.re)))) 2) y.im) (/ y.im (+ (* (neg (atan2 x.im x.re)) y.re) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re)))))))) (neg (/ (pow (* y.re (atan2 x.im x.re)) 2) (+ (* (neg (atan2 x.im x.re)) y.re) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))))))))) (sin (+ (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))) (* y.re (atan2 x.im x.re)))) (exp (atan2 x.im x.re)) (* y.re (atan2 x.im x.re)) (sin (* (atan2 x.im x.re) y.re)) (* (atan2 x.im x.re) y.re) (sin (+ (* (neg y.im) (log (/ -1 x.re))) (* (atan2 x.im x.re) y.re))) (* y.im (atan2 x.im x.re)) (sqrt (+ (* x.re x.re) (* x.im x.im))) (cos (* (atan2 x.im x.re) y.re)) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) (sin (+ (* (* (pow (log (sqrt (+ (* x.im x.im) (* x.re x.re)))) 2) y.im) (/ y.im (+ (* (neg (atan2 x.im x.re)) y.re) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re)))))))) (neg (/ (pow (* y.re (atan2 x.im x.re)) 2) (+ (* (neg (atan2 x.im x.re)) y.re) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re)))))))))) (/ (pow (* y.re (atan2 x.im x.re)) 2) (+ (* (neg (atan2 x.im x.re)) y.re) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))))) (pow (log (sqrt (+ (* x.im x.im) (* x.re x.re)))) 2))
154.0ms
x.im
@-inf
((* (pow (sqrt (+ (* x.im x.im) (* x.re x.re))) y.re) (* (pow (exp (atan2 x.im x.re)) (neg y.im)) (sin (+ (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))) (* y.re (atan2 x.im x.re)))))) (pow (sqrt (+ (* x.im x.im) (* x.re x.re))) y.re) (sqrt (+ (* x.im x.im) (* x.re x.re))) (pow (exp (atan2 x.im x.re)) (neg y.im)) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (sin (* (atan2 x.im x.re) y.re))) (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* (neg y.im) (log (/ -1 x.re))) (* (atan2 x.im x.re) y.re)) (neg (+ (* (log (/ -1 x.re)) y.re) (* y.im (atan2 x.im x.re)))) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (* (sin (+ (* (neg y.im) (log (/ -1 x.re))) (* (atan2 x.im x.re) y.re))) (exp (neg (+ (* (log (/ -1 x.re)) y.re) (* y.im (atan2 x.im x.re)))))) (+ (* x.re x.re) (* x.im x.im)) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))) (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)) (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (neg (/ (pow (* y.re (atan2 x.im x.re)) 2) (+ (* (neg (atan2 x.im x.re)) y.re) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re)))))))) (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (* (pow (log (sqrt (+ (* x.im x.im) (* x.re x.re)))) 2) y.im) (/ y.im (+ (* (neg (atan2 x.im x.re)) y.re) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re)))))))) (neg (/ (pow (* y.re (atan2 x.im x.re)) 2) (+ (* (neg (atan2 x.im x.re)) y.re) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))))))))) (sin (+ (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))) (* y.re (atan2 x.im x.re)))) (exp (atan2 x.im x.re)) (* y.re (atan2 x.im x.re)) (sin (* (atan2 x.im x.re) y.re)) (* (atan2 x.im x.re) y.re) (sin (+ (* (neg y.im) (log (/ -1 x.re))) (* (atan2 x.im x.re) y.re))) (* y.im (atan2 x.im x.re)) (sqrt (+ (* x.re x.re) (* x.im x.im))) (cos (* (atan2 x.im x.re) y.re)) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) (sin (+ (* (* (pow (log (sqrt (+ (* x.im x.im) (* x.re x.re)))) 2) y.im) (/ y.im (+ (* (neg (atan2 x.im x.re)) y.re) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re)))))))) (neg (/ (pow (* y.re (atan2 x.im x.re)) 2) (+ (* (neg (atan2 x.im x.re)) y.re) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re)))))))))) (/ (pow (* y.re (atan2 x.im x.re)) 2) (+ (* (neg (atan2 x.im x.re)) y.re) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))))) (pow (log (sqrt (+ (* x.im x.im) (* x.re x.re)))) 2))

prune16.6s (1.7%)

Memory
-543.2MiB live, 25 042.1MiB allocated
Counts
212 588 → 2 968
Compiler

Compiled 168 506 to 72 672 computations (56.9% saved)

preprocess16.0s (1.7%)

Memory
32.2MiB live, 15 572.2MiB allocated
Algorithm
56×egg-herbie
Rules
290 162×lower-fma.f64
290 162×lower-fma.f32
74 512×lower-*.f32
74 158×lower-*.f64
52 750×lower-+.f32
Stop Event
112×iter limit
76×saturated
36×node limit
Compiler

Compiled 45 537 to 14 461 computations (68.2% saved)

end7.2s (0.8%)

Memory
-9.8MiB live, 4 927.0MiB allocated

bsearch3.4s (0.4%)

Memory
130.5MiB live, 4 414.7MiB allocated
Algorithm
222×binary-search
216×left-value
Stop Event
205×narrow-enough
17×predicate-same
Samples
1.5s13 044×0valid
526.0ms1 470×1valid
18.0ms98×2valid
7.0ms28×3valid
Compiler

Compiled 43 811 to 39 561 computations (9.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.6s
ival-mult: 626.0ms (38.9% of total)
ival-log: 155.0ms (9.6% of total)
ival-hypot: 144.0ms (9% of total)
ival-add: 108.0ms (6.7% of total)
ival-sub: 79.0ms (4.9% of total)
ival-cos: 78.0ms (4.8% of total)
ival-div: 75.0ms (4.7% of total)
ival-atan2: 71.0ms (4.4% of total)
ival-sin: 65.0ms (4% of total)
ival-exp: 53.0ms (3.3% of total)
adjust: 50.0ms (3.1% of total)
const: 43.0ms (2.7% of total)
ival-copysign: 28.0ms (1.7% of total)
ival-sqrt: 15.0ms (0.9% of total)
ival-true: 10.0ms (0.6% of total)
ival-assert: 6.0ms (0.4% of total)
exact: 4.0ms (0.2% of total)
ival-fabs: 1.0ms (0.1% of total)

analyze2.4s (0.3%)

Memory
42.4MiB live, 3 270.7MiB allocated
Algorithm
58×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
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
Compiler

Compiled 1 498 to 821 computations (45.2% saved)

start2.0ms (0%)

Memory
4.7MiB live, 4.6MiB allocated

Profiling

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