Herbie run

Date:Tuesday, August 20th, 2024
Commit:fce740b4 on ffi-types
Hostname:nightly with Racket 8.11.1
Seed:2024233
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: 5.3min)

sample1.9min (36.4%)

Memory
226.4MiB live, 123 963.1MiB allocated
Samples
29.8s41 818×2valid
25.1s145 639×0invalid
19.5s91 985×1valid
8.9s4 839×5exit
8.2s94 458×0valid
2.3s2 904×3valid
642.0ms2 295×1exit
443.0ms4 152×0exit
11.0ms6×4exit
3.0ms3×4valid
2.0ms4×2exit
0.0ms1×3exit
Precisions
Click to see histograms. Total time spent on operations: 1.3min
ival-tan: 14.7s (18.9% of total)
ival-pow: 8.9s (11.5% of total)
ival-mult: 6.8s (8.7% of total)
ival-cos: 5.2s (6.7% of total)
adjust: 5.1s (6.5% of total)
const: 4.9s (6.4% of total)
ival-log: 3.9s (5% of total)
ival-div: 3.8s (5% of total)
ival-sin: 3.5s (4.5% of total)
ival-add: 3.4s (4.4% of total)
ival-sub: 3.4s (4.3% of total)
ival-fabs: 2.1s (2.7% of total)
ival-exp: 2.0s (2.5% of total)
ival-<=: 2.0s (2.5% of total)
ival-expm1: 1.8s (2.4% of total)
ival-sqrt: 1.4s (1.8% of total)
ival-log1p: 1.1s (1.5% of total)
ival-<: 880.0ms (1.1% of total)
ival-fmin: 652.0ms (0.8% of total)
ival-and: 597.0ms (0.8% of total)
ival-atan: 359.0ms (0.5% of total)
exact: 326.0ms (0.4% of total)
ival-cbrt: 261.0ms (0.3% of total)
ival-neg: 233.0ms (0.3% of total)
ival->: 223.0ms (0.3% of total)
ival-assert: 147.0ms (0.2% of total)
ival-true: 69.0ms (0.1% of total)
Bogosity

simplify53.0s (16.8%)

Memory
-30.5MiB live, 53 485.6MiB allocated
Algorithm
242×egg-herbie
Rules
2 110 014×lower-fma.f32
2 109 434×lower-fma.f64
745 516×lower-*.f32
744 524×lower-*.f64
464 454×lower-+.f32
Stop Event
321×iter limit
167×node limit
75×saturated
Counts
29 628 → 29 223

rewrite33.9s (10.7%)

Memory
-250.6MiB live, 37 379.0MiB allocated
Rules
492 964×lower-fma.f32
492 384×lower-fma.f64
425 608×lower-*.f32
424 628×lower-*.f64
390 850×lower-/.f32
Stop Event
221×iter limit
107×node limit
Counts
1 687 → 66 127

soundness28.0s (8.9%)

Memory
70.4MiB live, 17 525.5MiB allocated
Rules
1 037 530×lower-fma.f32
1 037 270×lower-fma.f64
552 360×lower-*.f32
551 918×lower-*.f64
302 802×lower-+.f32
Stop Event
183×iter limit
121×node limit
24×fuel
4×done
2×saturated
Compiler

Compiled 10 895 to 5 267 computations (51.7% saved)

localize22.8s (7.2%)

Memory
-69.9MiB live, 26 772.2MiB allocated
Samples
7.1s5 869×2valid
6.3s10 564×1valid
2.7s10 370×0valid
482.0ms356×3valid
83.0ms47×5exit
30.0ms40×0exit
16.0ms144×0invalid
3.0ms2×4valid
Compiler

Compiled 25 387 to 3 377 computations (86.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.2s
ival-mult: 2.6s (19.6% of total)
adjust: 1.8s (14% of total)
ival-div: 1.5s (11.2% of total)
ival-tan: 1.4s (10.3% of total)
ival-add: 1.2s (9.2% of total)
const: 822.0ms (6.2% of total)
ival-pow: 631.0ms (4.8% of total)
ival-sub: 602.0ms (4.6% of total)
ival-cos: 572.0ms (4.3% of total)
ival-log: 532.0ms (4% of total)
ival-exp: 436.0ms (3.3% of total)
ival-sqrt: 234.0ms (1.8% of total)
ival-sin: 219.0ms (1.7% of total)
ival-log1p: 142.0ms (1.1% of total)
ival-neg: 125.0ms (0.9% of total)
ival-pow2: 98.0ms (0.7% of total)
ival-expm1: 67.0ms (0.5% of total)
ival-atan: 48.0ms (0.4% of total)
ival-cbrt: 46.0ms (0.3% of total)
exact: 40.0ms (0.3% of total)
ival-true: 36.0ms (0.3% of total)
ival-cosh: 30.0ms (0.2% of total)
ival-atan2: 24.0ms (0.2% of total)
ival-assert: 12.0ms (0.1% of total)
ival-fabs: 1.0ms (0% of total)

prune21.3s (6.7%)

Memory
-230.7MiB live, 30 255.6MiB allocated
Counts
113 878 → 1 939
Compiler

Compiled 79 864 to 35 359 computations (55.7% saved)

eval19.8s (6.3%)

Memory
462.7MiB live, 26 119.4MiB allocated
Compiler

Compiled 3 345 549 to 267 043 computations (92% saved)

explain5.6s (1.8%)

Memory
49.5MiB live, 6 898.0MiB allocated
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation414735
log.f64#fsensitivity7641
/.f64#fu/u4420
sqrt.f64#foflow-rescue4120
+.f64#fcancellation3420
/.f64#fu/n1140
pow.f64#fsensitivity733
/.f64(/.f64 (*.f64 eps (-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))n/u220
↳(*.f64 b eps)underflow142
↳(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))underflow135
↳(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))underflow142
↳(*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))underflow231
↳(*.f64 a eps)underflow135
sqrt.f64#fuflow-rescue200
-.f64#fnan-rescue150
/.f64(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))n/o50
↳(*.f64 x x)overflow61
/.f64(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))o/o20
↳(exp.f64 (*.f64 #s(literal 2 binary64) x))overflow2
↳(*.f64 #s(literal 2 binary64) x)overflow1
↳(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))overflow2
↳(exp.f64 x)overflow2
↳(-.f64 (exp.f64 x) #s(literal 1 binary64))overflow2
exp.f64(exp.f64 (neg.f64 x))sensitivity10
sin.f64(sin.f64 (+.f64 x eps))sensitivity10
tan.f64(tan.f64 (+.f64 x eps))sensitivity10
Confusion
Predicted +Predicted -
+519418
-1491807
Precision
0.9721130451057458
Recall
0.9965464313123561
Confusion?
Predicted +Predicted MaybePredicted -
+5194135
-149251782
Precision?
0.967664002973425
Recall?
0.9990406753645433
Freqs
test
numberfreq
01825
14542
2642
3101
458
Total Confusion?
Predicted +Predicted MaybePredicted -
+2800
-000
Precision?
1.0
Recall?
1.0
Samples
1.6s2 638×2valid
1.0s5 712×1valid
521.0ms5 830×0valid
114.0ms154×3valid
2.0ms2×4valid
Compiler

Compiled 2 197 to 763 computations (65.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.6s
ival-tan: 880.0ms (33.4% of total)
adjust: 289.0ms (11% of total)
ival-cos: 216.0ms (8.2% of total)
ival-log: 191.0ms (7.3% of total)
ival-div: 182.0ms (6.9% of total)
ival-exp: 146.0ms (5.5% of total)
ival-sub: 136.0ms (5.2% of total)
ival-sin: 128.0ms (4.9% of total)
ival-pow: 88.0ms (3.3% of total)
ival-add: 86.0ms (3.3% of total)
ival-mult: 83.0ms (3.2% of total)
ival-sqrt: 55.0ms (2.1% of total)
ival-log1p: 55.0ms (2.1% of total)
ival-expm1: 28.0ms (1.1% of total)
ival-atan: 19.0ms (0.7% of total)
ival-cbrt: 15.0ms (0.6% of total)
ival-true: 12.0ms (0.5% of total)
ival-neg: 11.0ms (0.4% of total)
exact: 8.0ms (0.3% of total)
ival-assert: 6.0ms (0.2% of total)

preprocess4.9s (1.5%)

Memory
104.5MiB live, 5 600.9MiB allocated
Algorithm
28×egg-herbie
Rules
27 478×lower-fma.f64
27 478×lower-fma.f32
10 768×div-sub
10 444×sub-neg
9 190×lower-*.f32
Stop Event
56×iter limit
50×saturated
6×node limit
Compiler

Compiled 11 441 to 3 885 computations (66% saved)

series4.9s (1.5%)

Memory
161.3MiB live, 5 275.0MiB allocated
Counts
1 687 → 29 628
Calls

3807 calls:

TimeVariablePointExpression
377.0ms
n
@inf
(- (exp (/ (log x) n)) (pow (exp 1/2) (* 2 (/ (log x) n))))
304.0ms
x
@0
(- (exp (/ (log x) n)) (pow (exp 1/2) (* 2 (/ (log x) n))))
105.0ms
x
@-inf
(- (exp (/ (log x) n)) (pow (exp 1/2) (* 2 (/ (log x) n))))
88.0ms
x
@inf
(- (exp (/ (log x) n)) (pow (exp 1/2) (* 2 (/ (log x) n))))
44.0ms
x
@-inf
(/ (- (/ 1 (/ (+ (* (log x) (log (* x (+ x 1)))) (pow (log (+ 1 x)) 2)) (- (pow (log x) 3) (pow (log (+ 1 x)) 3)))) (/ (- (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) (/ (+ (* -1/24 (/ (- (pow (log (+ 1 x)) 4) (pow (log x) 4)) n)) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n)) n)) (neg n))

regimes4.1s (1.3%)

Memory
59.0MiB live, 5 131.6MiB allocated
Counts
4 115 → 337
Calls

43 calls:

1.0s
x
367.0ms
eps
225.0ms
b
157.0ms
N
154.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 3 122 to 2 083 computations (33.3% saved)

analyze1.6s (0.5%)

Memory
34.1MiB live, 1 979.3MiB allocated
Algorithm
28×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%61.1%38.9%0%0%0%0
7.4%4.5%56.6%38.9%0%0%0%1
22.3%13.6%47.5%38.9%0%0%0%2
40.2%23.5%34.9%38.9%0%2.7%0%3
53.4%31.1%27.2%38.9%0%2.8%0%4
63%36.3%21.3%38.9%0%3.6%0%5
65.9%37.5%19.4%38.9%0%4.2%0%6
70.4%38.8%16.3%38.9%0%6%0%7
73.6%40.2%14.4%38.9%0%6.5%0%8
76.3%40.9%12.7%38.9%0%7.5%0%9
78.4%41.4%11.4%38.9%0%8.3%0%10
81.1%42.4%9.9%38.9%0%8.8%0%11
82.3%42.7%9.2%38.9%0%9.3%0%12
Compiler

Compiled 483 to 337 computations (30.2% saved)

bsearch966.0ms (0.3%)

Memory
-23.1MiB live, 1 342.9MiB allocated
Algorithm
72×binary-search
47×left-value
Stop Event
67×narrow-enough
5×predicate-same
Samples
345.0ms4 194×0valid
115.0ms439×2valid
78.0ms492×1valid
47.0ms663×0invalid
3.0ms31×0exit
2.0ms11×3valid
0.0ms1×1exit
Compiler

Compiled 17 682 to 11 618 computations (34.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 426.0ms
ival-mult: 98.0ms (23% of total)
ival-pow: 60.0ms (14.1% of total)
ival-div: 53.0ms (12.4% of total)
ival-sub: 46.0ms (10.8% of total)
ival-sqrt: 42.0ms (9.8% of total)
adjust: 30.0ms (7% of total)
ival-cos: 29.0ms (6.8% of total)
ival-neg: 24.0ms (5.6% of total)
ival-add: 22.0ms (5.2% of total)
ival-expm1: 5.0ms (1.2% of total)
ival-sin: 5.0ms (1.2% of total)
ival-exp: 4.0ms (0.9% of total)
ival-true: 4.0ms (0.9% of total)
exact: 3.0ms (0.7% of total)
ival-assert: 2.0ms (0.5% of total)

start0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated

end0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated

Profiling

Loading profile data...