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: 1.9hr)

simplify24.5min (21%)

Memory
-1 791.1MiB live, 1 589 647.2MiB allocated
Algorithm
4 433×egg-herbie
Rules
30 993 330×lower-fma.f32
30 987 038×lower-fma.f64
12 642 052×lower-*.f32
12 625 010×lower-*.f64
7 110 900×lower-+.f32
Stop Event
5 776×iter limit
2 660×node limit
1 839×saturated
4×unsound
Counts
571 416 → 561 233

soundness18.2min (15.6%)

Memory
-27.5MiB live, 423 386.8MiB allocated
Rules
19 673 344×lower-fma.f32
19 669 996×lower-fma.f64
11 099 898×lower-*.f32
11 089 962×lower-*.f64
5 721 874×lower-/.f32
Stop Event
3 573×iter limit
2 314×node limit
358×fuel
182×done
37×saturated
15×unsound
Compiler

Compiled 380 986 to 176 467 computations (53.7% saved)

sample17.9min (15.4%)

Memory
5 238.7MiB live, 1 267 763.7MiB allocated
Samples
7.2min3 904 611×0valid
2.6min427 625×1valid
1.3min30 325×5exit
1.1min128 133×2valid
49.1s317 047×0invalid
13.3s14 361×3valid
7.8s49 653×0exit
6.8s25 100×1invalid
5.7s25 116×1exit
783.0ms554×4exit
424.0ms1 250×2invalid
269.0ms128×3exit
84.0ms23×4valid
69.0ms14×2exit
Precisions
Click to see histograms. Total time spent on operations: 10.4min
ival-mult: 2.1min (19.7% of total)
ival-div: 1.1min (10.1% of total)
ival-sin: 49.9s (8% of total)
ival-pow: 45.3s (7.3% of total)
ival-sub: 42.8s (6.9% of total)
ival-add: 42.2s (6.8% of total)
const: 40.0s (6.4% of total)
ival-cos: 32.0s (5.1% of total)
adjust: 31.9s (5.1% of total)
ival-log: 23.0s (3.7% of total)
ival-tan: 20.0s (3.2% of total)
ival-exp: 19.7s (3.2% of total)
ival-sqrt: 16.6s (2.7% of total)
ival-<=: 13.2s (2.1% of total)
ival-pow2: 11.5s (1.8% of total)
ival-neg: 5.3s (0.8% of total)
ival-hypot: 4.7s (0.8% of total)
ival-fabs: 4.6s (0.7% of total)
exact: 3.4s (0.5% of total)
ival-<: 3.0s (0.5% of total)
ival-true: 2.8s (0.5% of total)
ival-and: 2.6s (0.4% of total)
ival-pi: 2.5s (0.4% of total)
ival-expm1: 2.0s (0.3% of total)
ival-assert: 1.9s (0.3% of total)
ival-asin: 1.9s (0.3% of total)
ival-acos: 1.7s (0.3% of total)
ival-atan2: 1.5s (0.2% of total)
ival-log1p: 1.4s (0.2% of total)
ival-atan: 1.2s (0.2% of total)
ival-sinh: 979.0ms (0.2% of total)
ival-cbrt: 929.0ms (0.1% of total)
ival-floor: 866.0ms (0.1% of total)
ival-==: 864.0ms (0.1% of total)
ival->: 764.0ms (0.1% of total)
ival-fmod: 743.0ms (0.1% of total)
ival-asinh: 634.0ms (0.1% of total)
ival->=: 484.0ms (0.1% of total)
ival-fmin: 438.0ms (0.1% of total)
ival-if: 400.0ms (0.1% of total)
ival-acosh: 364.0ms (0.1% of total)
ival-fmax: 280.0ms (0% of total)
ival-log2: 269.0ms (0% of total)
ival-cosh: 246.0ms (0% of total)
ival-atanh: 153.0ms (0% of total)
ival-tanh: 98.0ms (0% of total)
ival-or: 38.0ms (0% of total)
Bogosity

rewrite15.4min (13.2%)

Memory
4 862.0MiB live, 1 006 049.0MiB allocated
Algorithm
1 946×batch-egg-rewrite
Rules
10 187 770×lower-fma.f32
10 181 532×lower-fma.f64
8 067 262×lower-*.f32
8 050 626×lower-*.f64
6 438 762×lower-/.f32
Stop Event
4 009×iter limit
1 859×node limit
94×saturated
36×unsound
Counts
23 984 → 1 262 431

prune9.4min (8.1%)

Memory
-10 979.9MiB live, 626 165.6MiB allocated
Counts
2 233 158 → 42 179
Compiler

Compiled 2 238 680 to 1 040 100 computations (53.5% saved)

eval7.6min (6.6%)

Memory
10 827.6MiB live, 625 343.8MiB allocated
Compiler

Compiled 107 769 819 to 5 041 469 computations (95.3% saved)

localize7.0min (6%)

Memory
1 423.0MiB live, 380 798.9MiB allocated
Samples
1.6min410 426×0valid
1.3min44 090×1valid
1.1min17 229×2valid
7.1s18 236×0invalid
4.7s1 070×5exit
3.7s2 239×3valid
1.7s3 011×1exit
1.4s380×4exit
992.0ms117×3exit
394.0ms1 104×0exit
265.0ms195×1invalid
220.0ms272×2exit
80.0ms43×4valid
15.0ms14×2invalid
7.0ms6×3invalid
Compiler

Compiled 474 744 to 51 655 computations (89.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.8min
ival-mult: 55.3s (32.7% of total)
const: 30.4s (18% of total)
ival-div: 17.0s (10.1% of total)
ival-add: 13.4s (7.9% of total)
ival-cos: 8.4s (5% of total)
adjust: 7.6s (4.5% of total)
ival-sin: 6.8s (4% of total)
ival-sub: 5.1s (3% of total)
ival-sqrt: 4.1s (2.4% of total)
ival-neg: 3.0s (1.8% of total)
ival-tan: 2.8s (1.6% of total)
ival-pow: 2.7s (1.6% of total)
ival-log: 2.5s (1.5% of total)
ival-pow2: 1.9s (1.1% of total)
ival-exp: 1.4s (0.8% of total)
ival-atan2: 818.0ms (0.5% of total)
ival-cbrt: 812.0ms (0.5% of total)
ival-asin: 676.0ms (0.4% of total)
exact: 613.0ms (0.4% of total)
ival-hypot: 567.0ms (0.3% of total)
ival-acos: 459.0ms (0.3% of total)
ival-log1p: 446.0ms (0.3% of total)
ival-true: 441.0ms (0.3% of total)
ival-pi: 298.0ms (0.2% of total)
ival-fabs: 255.0ms (0.2% of total)
ival-atan: 213.0ms (0.1% of total)
ival-assert: 212.0ms (0.1% of total)
ival-if: 169.0ms (0.1% of total)
ival-fmax: 141.0ms (0.1% of total)
ival-floor: 133.0ms (0.1% of total)
ival-fmod: 124.0ms (0.1% of total)
ival-sinh: 103.0ms (0.1% of total)
ival-tanh: 93.0ms (0.1% of total)
ival-copysign: 91.0ms (0.1% of total)
ival-log2: 91.0ms (0.1% of total)
ival-cosh: 76.0ms (0% of total)
ival-expm1: 67.0ms (0% of total)
ival->=: 29.0ms (0% of total)
ival->: 14.0ms (0% of total)
ival-e: 9.0ms (0% of total)
ival-<: 4.0ms (0% of total)

regimes4.5min (3.8%)

Memory
-2 304.9MiB live, 373 437.0MiB allocated
Counts
136 731 → 10 073
Calls

1 219 calls:

19.1s
x
14.4s
y
11.7s
z
8.6s
t
8.6s
a
Compiler

Compiled 205 729 to 133 868 computations (34.9% saved)

preprocess3.1min (2.6%)

Memory
-236.5MiB live, 199 021.2MiB allocated
Algorithm
542×egg-herbie
Rules
2 120 258×lower-fma.f32
2 120 256×lower-fma.f64
556 378×lower-*.f32
554 402×lower-*.f64
388 484×unsub-neg
Stop Event
1 080×iter limit
743×saturated
345×node limit
Compiler

Compiled 447 704 to 125 336 computations (72% saved)

end3.0min (2.5%)

Memory
45.4MiB live, 29 998.9MiB allocated

explain2.0min (1.7%)

Memory
-1 887.3MiB live, 167 080.8MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation902061
sqrt.f64#foflow-rescue52270
log.f64#fsensitivity35062
cos.f64#fsensitivity32669
+.f64#fcancellation3041133
sin.f64#fsensitivity19722
/.f64#fo/n19100
/.f64#fo/o16760
-.f64#fnan-rescue13060
log.f32#fsensitivity116690
*.f64#fn*o11520
/.f64#fu/u10120
/.f64#fn/o9840
sqrt.f64#fuflow-rescue9490
+.f64#fnan-rescue8010
/.f64#fu/n7390
sqrt.f32#foflow-rescue5360
acos.f64#fsensitivity5297
*.f64#fn*u4650
tan.f64#fsensitivity4041
pow.f64#fsensitivity40355
-.f32#fcancellation38451
/.f64#fn/u2720
-.f64(-.f64 (*.f64 #s(literal 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) t) #s(literal 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64))oflow-left2310
exp.f64#fsensitivity20828
cos.f32#fsensitivity19315
cos.f64#foflow-rescue1890
*.f64#fu*o1880
tan.f32(tan.f32 (+.f32 (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))cancellation18313
/.f32#fo/n1480
pow.f64#foflow-rescue1480
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)))))))sensitivity1230
*.f64#fo*u1200
cbrt.f64#foflow-rescue930
log.f64#foflow-rescue930
log.f64#fuflow-rescue770
pow.f64#fuflow-rescue650
exp.f32#fsensitivity3616
sin.f64#foflow-rescue360
tan.f64(tan.f64 (/.f64 x (*.f64 y #s(literal 2 binary64))))oflow-rescue350
↳(/.f64 x (*.f64 y #s(literal 2 binary64)))overflow35
cbrt.f64#fuflow-rescue340
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)underflow284
↳(-.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))))underflow142
↳(*.f32 eta eta)underflow18
/.f32#fu/n170
/.f32#fo/o140
/.f32#fn/o100
*.f32(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))n*u40
log.f32#foflow-rescue30
tan.f64(tan.f64 (+.f64 x eps))cancellation10
sin.f64(sin.f64 (+.f64 x eps))cancellation10
Confusion
Predicted +Predicted -
+303071178
-6072101195
Precision
0.8330905192556145
Recall
0.962585358107035
Confusion?
Predicted +Predicted MaybePredicted -
+30307280898
-6072440100755
Precision?
0.8244696622550473
Recall?
0.9714784818167381
Freqs
test
numberfreq
0102373
130538
24782
3602
4303
587
635
717
811
94
Total Confusion?
Predicted +Predicted MaybePredicted -
+34432
-100183
Precision?
0.9719887955182073
Recall?
0.994269340974212
Samples
27.1s234 710×0valid
10.3s30 914×1valid
6.5s10 608×2valid
1.0s1 166×3valid
12.0ms90×1exit
7.0ms14×5exit
1.0ms2×4valid
Compiler

Compiled 106 318 to 25 502 computations (76% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.7s
ival-mult: 6.7s (22.7% of total)
ival-div: 3.0s (10.2% of total)
ival-sin: 2.6s (8.9% of total)
ival-add: 2.5s (8.5% of total)
ival-sub: 2.5s (8.3% of total)
ival-cos: 2.1s (7.2% of total)
adjust: 1.5s (5.2% of total)
ival-log: 1.5s (5.1% of total)
ival-tan: 1.3s (4.4% of total)
ival-exp: 916.0ms (3.1% of total)
const: 815.0ms (2.7% of total)
ival-sqrt: 813.0ms (2.7% of total)
ival-pow2: 660.0ms (2.2% of total)
ival-pow: 480.0ms (1.6% of total)
ival-hypot: 288.0ms (1% of total)
ival-true: 249.0ms (0.8% of total)
ival-atan: 221.0ms (0.7% of total)
ival-neg: 220.0ms (0.7% of total)
exact: 163.0ms (0.5% of total)
ival-assert: 115.0ms (0.4% of total)
ival-pi: 108.0ms (0.4% of total)
ival-asin: 97.0ms (0.3% of total)
ival-atan2: 95.0ms (0.3% of total)
ival-log1p: 81.0ms (0.3% of total)
ival-acos: 80.0ms (0.3% of total)
ival-fabs: 57.0ms (0.2% of total)
ival-sinh: 54.0ms (0.2% of total)
ival-log2: 41.0ms (0.1% of total)
ival-cbrt: 40.0ms (0.1% of total)
ival-copysign: 39.0ms (0.1% of total)
ival-floor: 38.0ms (0.1% of total)
ival-expm1: 36.0ms (0.1% of total)
ival-fmod: 29.0ms (0.1% of total)
ival-cosh: 28.0ms (0.1% of total)
ival-if: 23.0ms (0.1% of total)
ival-fmax: 17.0ms (0.1% of total)
ival->=: 10.0ms (0% of total)
ival-tanh: 6.0ms (0% of total)
ival->: 3.0ms (0% of total)
ival-<: 1.0ms (0% of total)

series1.6min (1.4%)

Memory
-384.0MiB live, 125 375.8MiB allocated
Counts
23 984 → 571 416
Calls

106485 calls:

TimeVariablePointExpression
702.0ms
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)))
374.0ms
x
@0
(log (* x 2))
323.0ms
z
@inf
(* (log (* (/ y (* (* x (pow a (+ t -1))) (pow z y))) (exp b))) -1)
319.0ms
y
@inf
(pow (fabs (- x y)) 1/4)
317.0ms
x
@-inf
(* 1/10 x)

analyze1.3min (1.1%)

Memory
381.7MiB live, 106 825.4MiB 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 12 518 to 7 841 computations (37.4% saved)

bsearch58.8s (0.8%)

Memory
-77.7MiB live, 75 084.4MiB allocated
Algorithm
2 728×binary-search
2 524×left-value
Stop Event
2 631×narrow-enough
88×predicate-same
9×predicate-failed
Samples
26.6s186 309×0valid
9.3s16 702×1valid
1.8s2 889×2valid
1.2s9 728×0invalid
525.0ms292×3valid
58.0ms132×1exit
52.0ms86×0exit
12.0ms61×1invalid
1.0ms2×5exit
1.0ms4×2invalid
Compiler

Compiled 742 949 to 520 764 computations (29.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.9s
ival-mult: 8.7s (29.2% of total)
ival-sin: 3.3s (11.1% of total)
ival-sub: 3.0s (10% of total)
ival-cos: 2.8s (9.4% of total)
ival-div: 2.7s (9.1% of total)
ival-add: 2.6s (8.8% of total)
adjust: 985.0ms (3.3% of total)
ival-log: 760.0ms (2.5% of total)
ival-pow2: 750.0ms (2.5% of total)
const: 750.0ms (2.5% of total)
ival-pow: 509.0ms (1.7% of total)
ival-sqrt: 504.0ms (1.7% of total)
ival-exp: 470.0ms (1.6% of total)
ival-hypot: 354.0ms (1.2% of total)
ival-atan2: 293.0ms (1% of total)
ival-tan: 293.0ms (1% of total)
ival-pi: 250.0ms (0.8% of total)
ival-true: 156.0ms (0.5% of total)
ival-neg: 122.0ms (0.4% of total)
ival-acos: 105.0ms (0.4% of total)
ival-assert: 98.0ms (0.3% of total)
exact: 90.0ms (0.3% of total)
ival-atan: 75.0ms (0.3% of total)
ival-fabs: 38.0ms (0.1% of total)
ival-fmod: 28.0ms (0.1% of total)
ival-expm1: 25.0ms (0.1% of total)
ival-tanh: 12.0ms (0% of total)
ival-asin: 12.0ms (0% of total)
ival-cosh: 10.0ms (0% of total)
ival-if: 8.0ms (0% of total)
ival-sinh: 6.0ms (0% of total)
ival->=: 5.0ms (0% of total)
ival-log1p: 2.0ms (0% of total)

Profiling

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