Herbie run

Date:Saturday, May 18th, 2024
Commit:c2f4097e on main
Hostname:nightly with Racket 8.11.1
Seed:2024139
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: 5.8min)

sample2.8min (47.1%)

Results
42.6s55410×2valid
32.7s142346×0precondition
29.0s116188×1valid
28.0s7062×5exit
6.6s56965×0valid
3.5s2605×3valid
470.0ms4122×0invalid
465.0ms4250×0unsamplable
Precisions
Click to see histograms. Total time spent on operations: 2.0min
ival-pow: 25.7s (21.3% of total)
ival-tan: 12.1s (10% of total)
ival-exp: 11.4s (9.4% of total)
ival-sub: 8.8s (7.2% of total)
ival-mult: 8.6s (7.1% of total)
...c/correct-round.rkt:121:19: 7.3s (6% of total)
backward-pass: 6.4s (5.3% of total)
ival-add: 6.3s (5.2% of total)
ival-log: 5.3s (4.4% of total)
ival-div: 5.2s (4.3% of total)
ival-cos: 4.4s (3.7% of total)
ival-sin: 4.3s (3.6% of total)
ival-<=: 4.0s (3.3% of total)
ival-fabs: 2.9s (2.4% of total)
ival-<: 2.0s (1.6% of total)
ival-sqrt: 1.7s (1.4% of total)
ival->: 963.0ms (0.8% of total)
ival-and: 737.0ms (0.6% of total)
ival-neg: 707.0ms (0.6% of total)
const: 638.0ms (0.5% of total)
ival-fmin: 623.0ms (0.5% of total)
ival-atan: 601.0ms (0.5% of total)
ival-cbrt: 306.0ms (0.3% of total)
Bogosity

simplify48.9s (13.9%)

Algorithm
245×egg-herbie
Rules
89304×fma-define
74842×fma-neg
48799×distribute-lft-in
43356×distribute-rgt-in
42966×times-frac
Stop Event
83×saturated
161×node limit
1×unsound
Counts
58284 → 59683

soundness27.8s (7.9%)

Rules
31302×log1p-expm1-u
30148×fma-define
25731×fma-neg
23963×expm1-log1p-u
18948×associate-*r*
Stop Event
9×saturated
109×node limit
22×fuel
6×done
Compiler

Compiled 19745 to 6182 computations (68.7% saved)

rewrite25.6s (7.3%)

Algorithm
108×batch-egg-rewrite
Rules
68186×log1p-expm1-u
49833×expm1-log1p-u
22182×pow1
21886×add-exp-log
21499×add-log-exp
Stop Event
108×node limit
Counts
1234 → 39696

localize24.1s (6.9%)

Results
7.1s8234×1valid
4.5s3851×2valid
4.0s13667×0valid
1.0s445×3valid
584.0ms1417×0invalid
551.0ms203×5exit
36.0ms87×0unsamplable
Compiler

Compiled 17085 to 2482 computations (85.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.4s
ival-pow: 2.1s (18% of total)
ival-mult: 1.8s (15.5% of total)
backward-pass: 1.2s (10.6% of total)
ival-div: 1.1s (10% of total)
ival-sub: 690.0ms (6% of total)
ival-log: 612.0ms (5.4% of total)
ival-add: 602.0ms (5.3% of total)
ival-tan: 534.0ms (4.7% of total)
...c/correct-round.rkt:121:19: 510.0ms (4.5% of total)
ival-sqrt: 427.0ms (3.7% of total)
ival-exp: 414.0ms (3.6% of total)
ival-cos: 328.0ms (2.9% of total)
ival-fma: 281.0ms (2.5% of total)
ival-sin: 201.0ms (1.8% of total)
ival-log1p: 147.0ms (1.3% of total)
ival-cbrt: 122.0ms (1.1% of total)
ival-neg: 108.0ms (0.9% of total)
const: 99.0ms (0.9% of total)
ival-cosh: 53.0ms (0.5% of total)
ival-hypot: 40.0ms (0.3% of total)
ival-expm1: 32.0ms (0.3% of total)
ival-atan: 28.0ms (0.2% of total)
ival-atan2: 18.0ms (0.2% of total)
ival-e: 14.0ms (0.1% of total)

prune15.8s (4.5%)

Counts
81553 → 2129
Compiler

Compiled 65319 to 36996 computations (43.4% saved)

eval13.8s (3.9%)

Compiler

Compiled 1884855 to 302892 computations (83.9% saved)

series7.2s (2.1%)

Counts
1234 → 18588
Calls

4995 calls:

TimeVariablePointExpression
350.0ms
x
@inf
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))))
324.0ms
eps
@inf
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
195.0ms
eps
@-inf
(log (- (tan (+ x eps)) (tan x)))
169.0ms
x
@inf
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
121.0ms
b
@-inf
(sqrt (+ (* (* a c) -4) (pow b 2)))

explain7.2s (2%)

Results
2.8s3486×2valid
2.1s7218×1valid
431.0ms3476×0valid
169.0ms156×3valid
Compiler

Compiled 2227 to 707 computations (68.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.8s
ival-exp: 694.0ms (18.3% of total)
ival-tan: 640.0ms (16.9% of total)
ival-log: 540.0ms (14.2% of total)
backward-pass: 336.0ms (8.9% of total)
ival-add: 307.0ms (8.1% of total)
ival-sub: 222.0ms (5.8% of total)
ival-sin: 221.0ms (5.8% of total)
ival-cos: 213.0ms (5.6% of total)
ival-div: 173.0ms (4.6% of total)
ival-mult: 155.0ms (4.1% of total)
ival-pow: 111.0ms (2.9% of total)
ival-sqrt: 81.0ms (2.1% of total)
ival-neg: 32.0ms (0.8% of total)
const: 30.0ms (0.8% of total)
ival-atan: 23.0ms (0.6% of total)
ival-cbrt: 18.0ms (0.5% of total)

preprocess5.3s (1.5%)

Algorithm
28×egg-herbie
Rules
8308×fma-neg
6663×fma-define
4279×div-sub
2669×sub-neg
2621×times-frac
Stop Event
23×saturated
5×node limit
Compiler

Compiled 9428 to 3838 computations (59.3% saved)

regimes3.6s (1%)

Counts
4086 → 318
Calls

43 calls:

1.1s
x
449.0ms
b
372.0ms
eps
142.0ms
(-.f64 (cbrt.f64 (+.f64 x #s(literal 1 binary64))) (cbrt.f64 x))
131.0ms
a
Compiler

Compiled 1578 to 1057 computations (33% saved)

analyze3.3s (0.9%)

Algorithm
28×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%61.1%38.9%0%0%0%0
6.1%3.7%57.4%38.9%0%0%0%1
16.5%10.1%51%38.9%0%0%0%2
35.3%20.6%37.8%41.6%0%0%0%3
46.1%26.9%31.4%41.7%0%0%0%4
54.8%31.5%26%42.4%0%0%0%5
57.1%32.5%24.4%43.1%0%0%0%6
61.5%33.9%21.3%44%0%0.8%0.1%7
64.6%35.3%19.3%44.5%0%0.8%0.1%8
67.1%36%17.6%44.9%0%1.2%0.3%9
69.1%36.5%16.3%45.2%0%1.7%0.3%10
71.7%37.5%14.8%45.4%0%1.9%0.4%11
72.8%37.8%14.1%45.6%0%2.2%0.4%12
Compiler

Compiled 498 to 322 computations (35.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.7s
ival-mult: 210.0ms (12.7% of total)
ival-sub: 209.0ms (12.6% of total)
ival-pow: 171.0ms (10.3% of total)
...c/correct-round.rkt:121:19: 170.0ms (10.3% of total)
ival-sqrt: 133.0ms (8% of total)
ival-div: 127.0ms (7.7% of total)
ival-log: 106.0ms (6.4% of total)
ival-<=: 85.0ms (5.1% of total)
ival-sin: 81.0ms (4.9% of total)
ival-exp: 73.0ms (4.4% of total)
ival-add: 69.0ms (4.2% of total)
ival-fabs: 50.0ms (3% of total)
ival-tan: 41.0ms (2.5% of total)
ival-neg: 32.0ms (1.9% of total)
ival-cos: 23.0ms (1.4% of total)
const: 22.0ms (1.3% of total)
ival->: 14.0ms (0.8% of total)
ival-and: 13.0ms (0.8% of total)
ival-<: 10.0ms (0.6% of total)
backward-pass: 7.0ms (0.4% of total)
ival-fmin: 6.0ms (0.4% of total)
ival-atan: 0.0ms (0% of total)
ival-cbrt: 0.0ms (0% of total)

bsearch2.9s (0.8%)

Algorithm
83×binary-search
33×left-value
Stop Event
7×predicate-same
76×narrow-enough
Results
1.1s8370×0valid
432.0ms2354×1valid
382.0ms1794×0invalid
327.0ms620×2valid
9.0ms71×0unsamplable
Compiler

Compiled 17986 to 13115 computations (27.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.6s
ival-neg: 355.0ms (22.5% of total)
ival-mult: 304.0ms (19.3% of total)
ival-sub: 204.0ms (13% of total)
ival-pow: 175.0ms (11.1% of total)
ival-div: 151.0ms (9.6% of total)
ival-exp: 135.0ms (8.6% of total)
ival-sqrt: 82.0ms (5.2% of total)
backward-pass: 52.0ms (3.3% of total)
ival-add: 50.0ms (3.2% of total)
const: 21.0ms (1.3% of total)
ival-cos: 20.0ms (1.3% of total)
ival-cbrt: 19.0ms (1.2% of total)
ival-sin: 4.0ms (0.3% of total)
ival-log: 2.0ms (0.1% of total)

end0.0ms (0%)

Profiling

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