Herbie run

Date:Thursday, June 20th, 2024
Commit:aefdd770 on main
Hostname:nightly with Racket 8.11.1
Seed:2024172
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: 7.4min)

simplify1.5min (20.8%)

Memory
667.7MiB live, 105 418.8MiB allocated
Algorithm
286×egg-herbie
Rules
109 576×fma-define
66 862×*-commutative
62 214×fmm-def
60 729×associate-*r*
60 159×times-frac
Stop Event
220×node limit
66×saturated
Counts
98 462 → 82 333

sample1.5min (20%)

Memory
-219.5MiB live, 102 766.5MiB allocated
Samples
36.5s221 272×0valid
14.3s34 846×1valid
9.1s57 094×0invalid
3.3s11 550×1invalid
2.4s4 580×2valid
1.6s2 611×3valid
772.0ms879×4valid
565.0ms912×2invalid
26.0ms207×0exit
3.0ms6×5exit
3.0ms4×5valid
Precisions
Click to see histograms. Total time spent on operations: 53.5s
ival-mult: 14.6s (27.4% of total)
ival-div: 7.6s (14.2% of total)
ival-tan: 4.5s (8.4% of total)
ival-sub: 3.9s (7.3% of total)
ival-add: 3.6s (6.8% of total)
ival-pow2: 3.6s (6.7% of total)
ival-sqrt: 2.9s (5.5% of total)
ival-exp: 2.6s (4.8% of total)
ival-sin: 2.4s (4.4% of total)
ival-pow: 1.7s (3.2% of total)
adjust: 1.4s (2.7% of total)
ival-cos: 1.2s (2.2% of total)
ival-neg: 543.0ms (1% of total)
ival-acos: 473.0ms (0.9% of total)
...in/eval/compile.rkt:77:19: 420.0ms (0.8% of total)
ival-pi: 383.0ms (0.7% of total)
ival-log: 371.0ms (0.7% of total)
ival-hypot: 267.0ms (0.5% of total)
ival-true: 237.0ms (0.4% of total)
...in/eval/compile.rkt:76:19: 226.0ms (0.4% of total)
ival-asin: 216.0ms (0.4% of total)
ival-assert: 137.0ms (0.3% of total)
ival-fabs: 103.0ms (0.2% of total)
ival-atan: 81.0ms (0.2% of total)
ival-<: 39.0ms (0.1% of total)
ival-and: 11.0ms (0% of total)
Bogosity

soundness1.0min (13.9%)

Memory
-157.2MiB live, 60 412.7MiB allocated
Rules
57 167×fma-define
48 220×log1p-expm1-u
36 496×times-frac
36 222×associate-*r*
36 186×*-commutative
Stop Event
182×node limit
31×fuel
9×saturated
1×unsound
1×done
Compiler

Compiled 46 594 to 13 983 computations (70% saved)

localize35.3s (7.9%)

Memory
164.6MiB live, 47 465.6MiB allocated
Samples
8.6s644×5exit
7.4s22 013×0valid
3.7s4 112×1valid
2.4s4 284×0invalid
1.4s859×2valid
977.0ms261×3valid
321.0ms79×4valid
144.0ms187×0exit
60.0ms66×1invalid
43.0ms7×5valid
Compiler

Compiled 37 416 to 4 555 computations (87.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 20.3s
ival-tan: 7.2s (35.5% of total)
ival-mult: 2.8s (13.7% of total)
ival-div: 1.9s (9.6% of total)
ival-expm1: 1.0s (5.1% of total)
ival-log1p: 868.0ms (4.3% of total)
ival-pow: 775.0ms (3.8% of total)
ival-add: 767.0ms (3.8% of total)
ival-sqrt: 725.0ms (3.6% of total)
ival-pow2: 528.0ms (2.6% of total)
ival-sub: 505.0ms (2.5% of total)
adjust: 437.0ms (2.2% of total)
ival-sin: 424.0ms (2.1% of total)
ival-cbrt: 372.0ms (1.8% of total)
ival-pi: 301.0ms (1.5% of total)
ival-log: 298.0ms (1.5% of total)
ival-hypot: 287.0ms (1.4% of total)
ival-cos: 258.0ms (1.3% of total)
ival-exp: 242.0ms (1.2% of total)
...in/eval/compile.rkt:77:19: 127.0ms (0.6% of total)
ival-acos: 111.0ms (0.5% of total)
ival-fabs: 60.0ms (0.3% of total)
ival-asin: 60.0ms (0.3% of total)
...in/eval/compile.rkt:76:19: 52.0ms (0.3% of total)
ival-neg: 48.0ms (0.2% of total)
ival-atan: 30.0ms (0.1% of total)
ival-true: 28.0ms (0.1% of total)
ival-assert: 14.0ms (0.1% of total)

rewrite35.0s (7.9%)

Memory
112.2MiB live, 34 461.6MiB allocated
Algorithm
127×batch-egg-rewrite
Rules
73 252×log1p-expm1-u
49 487×expm1-log1p-u
33 826×add-exp-log
33 701×add-log-exp
33 374×pow1
Stop Event
126×node limit
1×unsound
Counts
1 968 → 51 709

prune29.8s (6.7%)

Memory
-523.6MiB live, 46 098.5MiB allocated
Counts
116 100 → 3 355
Compiler

Compiled 156 256 to 86 681 computations (44.5% saved)

eval23.2s (5.2%)

Memory
656.5MiB live, 34 278.7MiB allocated
Compiler

Compiled 3 789 210 to 492 836 computations (87% saved)

regimes19.2s (4.3%)

Memory
-139.8MiB live, 25 656.5MiB allocated
Counts
10 702 → 692
Calls

156 calls:

1.5s
l
1.2s
t
677.0ms
k
618.0ms
kx
529.0ms
v
Compiler

Compiled 8 493 to 6 251 computations (26.4% saved)

series18.7s (4.2%)

Memory
-188.5MiB live, 25 209.7MiB allocated
Counts
1 968 → 46 753
Calls

12753 calls:

TimeVariablePointExpression
394.0ms
t
@-inf
(exp (* (+ (log (* U 2)) (log (* n t))) 1/2))
298.0ms
f
@inf
(/ -1 (- (exp (* (* -1/2 (PI)) f)) 1))
267.0ms
k
@0
(/ (/ (cbrt (* (pow l 2) (/ 2 (tan k)))) (* t (cbrt (sin k)))) (sqrt (+ (* 1 1) (* (sqrt (+ (* 1 1) (* (/ k t) (/ k t)))) (sqrt (+ (* 1 1) (* (/ k t) (/ k t))))))))
256.0ms
kx
@0
(sqrt (+ 1/2 (* 1/2 (log (exp (/ 1 (sqrt (+ (* 1 1) (* (* (/ 2 (/ Om l)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (/ 2 (/ Om l)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))))))))))
227.0ms
l
@0
(* (/ (pow t 3) (* l l)) (sin k))

explain11.3s (2.5%)

Memory
-65.1MiB live, 15 225.7MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64#foflow-rescue5010
-.f64#fcancellation4380
cos.f64#fsensitivity4302
acos.f64(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))sensitivity2540
+.f64#fnan-rescue2450
*.f64#fn*o2380
pow.f64#foflow-rescue1560
sqrt.f64#fuflow-rescue1530
*.f64#fu*o1350
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)))))))sensitivity1261
-.f64#fnan-rescue1240
tan.f64(tan.f64 (*.f64 (PI.f64) l))sensitivity1200
/.f64#fo/o830
+.f64#fcancellation811
pow.f64(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))sensitivity8017
pow.f64#fuflow-rescue660
/.f64#fo/n590
*.f64#fo*u590
/.f64#fu/u500
*.f64#fn*u500
cos.f64(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))oflow-rescue490
↳(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))overflow49
↳(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)overflow49
↳(*.f64 K (+.f64 m n))overflow49
/.f64#fn/o440
/.f64#fn/u310
/.f64#fu/n90
log.f64(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))sensitivity70
exp.f64#fsensitivity50
tan.f64(tan.f64 (*.f64 (PI.f64) l))oflow-rescue10
↳(*.f64 (PI.f64) l)overflow1
Confusion
Predicted +Predicted -
+197636
-11285052
Precision
0.6365979381443299
Recall
0.9821073558648111
Confusion?
Predicted +Predicted MaybePredicted -
+1976234
-1128195033
Precision?
0.63296
Recall?
0.9831013916500994
Freqs
test
numberfreq
05088
12692
2347
354
49
52
Total Confusion?
Predicted +Predicted MaybePredicted -
+2500
-106
Precision?
0.9615384615384616
Recall?
1.0
Samples
2.5s13 160×0valid
1.2s2 606×1valid
405.0ms364×2valid
210.0ms198×3valid
27.0ms44×4valid
8.0ms10×5exit
1.0ms2×5valid
Compiler

Compiled 8 430 to 2 164 computations (74.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.8s
ival-mult: 714.0ms (25.5% of total)
ival-exp: 324.0ms (11.6% of total)
ival-tan: 301.0ms (10.7% of total)
ival-div: 286.0ms (10.2% of total)
ival-pow2: 266.0ms (9.5% of total)
ival-sub: 204.0ms (7.3% of total)
ival-add: 122.0ms (4.3% of total)
ival-sqrt: 103.0ms (3.7% of total)
ival-sin: 101.0ms (3.6% of total)
ival-pow: 73.0ms (2.6% of total)
adjust: 68.0ms (2.4% of total)
ival-cos: 66.0ms (2.4% of total)
ival-neg: 51.0ms (1.8% of total)
ival-hypot: 18.0ms (0.6% of total)
ival-pi: 17.0ms (0.6% of total)
ival-true: 15.0ms (0.5% of total)
ival-acos: 14.0ms (0.5% of total)
ival-log: 14.0ms (0.5% of total)
...in/eval/compile.rkt:76:19: 13.0ms (0.5% of total)
...in/eval/compile.rkt:77:19: 9.0ms (0.3% of total)
ival-asin: 9.0ms (0.3% of total)
ival-assert: 7.0ms (0.2% of total)
ival-atan: 6.0ms (0.2% of total)
ival-fabs: 4.0ms (0.1% of total)

analyze10.5s (2.4%)

Memory
-10.2MiB live, 12 472.3MiB allocated
Algorithm
32×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%98.2%1.8%0%0%0%0
22.2%21.8%76.4%1.8%0%0%0%1
22.6%21.8%74.8%1.8%0%1.6%0%2
28.8%26.5%65.5%1.8%0%6.2%0%3
33.1%29.6%60%1.8%0%8.6%0%4
36.2%32.3%56.8%1.8%0%9.2%0%5
40.6%36.1%52.9%1.8%0%9.3%0%6
45.8%40.6%48.1%1.8%0%9.5%0%7
48.3%42.1%45%1.8%0%11.1%0%8
51.5%44.7%42%1.8%0%11.6%0%9
52.7%45.5%40.8%1.8%0%11.9%0%10
54.5%46.8%39%1.8%0%12.5%0%11
56.2%47.9%37.4%1.8%0%12.9%0%12
Compiler

Compiled 793 to 574 computations (27.6% saved)

bsearch10.0s (2.2%)

Memory
28.9MiB live, 12 538.0MiB allocated
Algorithm
252×binary-search
98×left-value
Stop Event
244×narrow-enough
8×predicate-same
Samples
5.5s30 243×0valid
1.2s5 649×0invalid
377.0ms1 091×1valid
138.0ms500×2valid
35.0ms192×1invalid
31.0ms86×3valid
18.0ms58×2invalid
1.0ms1×5exit
Compiler

Compiled 76 405 to 55 338 computations (27.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.7s
ival-mult: 1.2s (21% of total)
ival-div: 949.0ms (16.7% of total)
ival-pow: 694.0ms (12.2% of total)
ival-add: 600.0ms (10.5% of total)
ival-sin: 519.0ms (9.1% of total)
ival-sub: 452.0ms (7.9% of total)
ival-tan: 408.0ms (7.2% of total)
ival-pow2: 237.0ms (4.2% of total)
ival-sqrt: 156.0ms (2.7% of total)
ival-neg: 123.0ms (2.2% of total)
ival-exp: 104.0ms (1.8% of total)
ival-cos: 65.0ms (1.1% of total)
adjust: 49.0ms (0.9% of total)
...in/eval/compile.rkt:77:19: 37.0ms (0.7% of total)
ival-true: 26.0ms (0.5% of total)
...in/eval/compile.rkt:76:19: 22.0ms (0.4% of total)
ival-assert: 15.0ms (0.3% of total)
ival-atan: 14.0ms (0.2% of total)
ival-hypot: 12.0ms (0.2% of total)
ival-fabs: 6.0ms (0.1% of total)
ival-log: 6.0ms (0.1% of total)
ival-asin: 2.0ms (0% of total)
ival-pi: 2.0ms (0% of total)

preprocess9.1s (2%)

Memory
-97.1MiB live, 8 992.4MiB allocated
Algorithm
32×egg-herbie
Rules
20 054×fma-define
13 409×fmm-def
8 518×times-frac
7 224×distribute-lft-in
7 153×unsub-neg
Stop Event
23×node limit
9×saturated
Compiler

Compiled 48 828 to 19 496 computations (60.1% saved)

end0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated

Profiling

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