Herbie run

Date:Thursday, May 23rd, 2024
Commit:f940d267 on brett-blog-post
Hostname:nightly with Racket 8.11.1
Seed:2024144
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: 1.6hr)

sample23.0min (23.6%)

Results
8.7min3839934×0valid
3.5min59286×5exit
3.3min483026×1valid
1.4min130222×2valid
33.3s19315×3valid
30.9s143655×0precondition
28.0s170482×0invalid
14.8s60968×0unsamplable
8.8s26935×1invalid
8.3s2271×4valid
1.8s2694×2invalid
45.0ms64×1unsamplable
16.0ms20×3invalid
6.0ms5valid
Precisions
Click to see histograms. Total time spent on operations: 14.6min
ival-mult: 2.6min (18% of total)
ival-pow: 2.6min (17.9% of total)
ival-sin: 1.3min (8.6% of total)
ival-div: 1.2min (8.1% of total)
ival-add: 58.4s (6.7% of total)
ival-sub: 55.9s (6.4% of total)
...c/correct-round.rkt:121:19: 39.6s (4.5% of total)
backward-pass: 38.5s (4.4% of total)
ival-cos: 37.6s (4.3% of total)
ival-exp: 33.1s (3.8% of total)
ival-log: 30.7s (3.5% of total)
ival-sqrt: 24.4s (2.8% of total)
ival-<=: 20.4s (2.3% of total)
ival-tan: 19.6s (2.2% of total)
ival->: 8.6s (1% of total)
ival-neg: 7.7s (0.9% of total)
const: 7.5s (0.9% of total)
ival-fabs: 6.5s (0.7% of total)
ival-<: 4.9s (0.6% of total)
ival-and: 3.4s (0.4% of total)
ival-acos: 2.8s (0.3% of total)
ival-pi: 2.6s (0.3% of total)
ival-atan2: 2.0s (0.2% of total)
ival-asin: 1.7s (0.2% of total)
ival-atan: 1.4s (0.2% of total)
ival-==: 1.2s (0.1% of total)
ival-sinh: 959.0ms (0.1% of total)
ival-if: 926.0ms (0.1% of total)
ival-fmod: 873.0ms (0.1% of total)
ival-floor: 790.0ms (0.1% of total)
ival-cbrt: 605.0ms (0.1% of total)
ival->=: 550.0ms (0.1% of total)
ival-fmin: 543.0ms (0.1% of total)
ival-asinh: 458.0ms (0.1% of total)
ival-fmax: 364.0ms (0% of total)
ival-log2: 341.0ms (0% of total)
ival-fma: 320.0ms (0% of total)
ival-cosh: 291.0ms (0% of total)
ival-acosh: 283.0ms (0% of total)
ival-hypot: 281.0ms (0% of total)
ival-atanh: 267.0ms (0% of total)
ival-tanh: 91.0ms (0% of total)
ival-or: 62.0ms (0% of total)
Bogosity

simplify18.6min (19.1%)

Algorithm
4378×egg-herbie
Rules
1673056×fma-define
1265307×fma-neg
887554×distribute-lft-in
850409×times-frac
813530×associate-*r*
Stop Event
1483×saturated
2868×node limit
27×unsound
Counts
1140462 → 976754

soundness11.6min (12%)

Rules
654550×fma-define
485926×log1p-expm1-u
479199×fma-neg
399372×associate-*r*
382927×times-frac
Stop Event
161×saturated
364×fuel
1911×node limit
29×unsound
178×done
Compiler

Compiled 436576 to 129018 computations (70.4% saved)

rewrite8.3min (8.5%)

Algorithm
1897×batch-egg-rewrite
Rules
1199922×log1p-expm1-u
897831×expm1-log1p-u
423141×pow1
403871×add-exp-log
388984×add-log-exp
Stop Event
saturated
1876×node limit
18×unsound
Counts
21757 → 658454

localize7.7min (7.9%)

Results
2.6min393781×0valid
1.1min48431×1valid
50.7s8322×5exit
26.7s13763×2valid
19.8s27332×0invalid
7.1s1797×3valid
1.6s2035×0unsamplable
1.5s711×1invalid
1.4s175×4valid
69.0ms36×1unsamplable
3.0ms2unsamplable
Compiler

Compiled 459820 to 49379 computations (89.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.3min
ival-mult: 43.9s (22.3% of total)
ival-div: 24.1s (12.3% of total)
ival-pow: 23.9s (12.1% of total)
backward-pass: 13.9s (7.1% of total)
ival-add: 13.7s (6.9% of total)
ival-sin: 10.4s (5.3% of total)
ival-sub: 9.8s (5% of total)
ival-cos: 9.1s (4.6% of total)
...c/correct-round.rkt:121:19: 8.0s (4.1% of total)
ival-sqrt: 5.7s (2.9% of total)
ival-log: 5.7s (2.9% of total)
ival-fma: 5.3s (2.7% of total)
ival-expm1: 3.6s (1.8% of total)
ival-tan: 3.2s (1.6% of total)
ival-exp: 3.0s (1.5% of total)
ival-log1p: 2.5s (1.3% of total)
ival-hypot: 1.9s (1% of total)
ival-neg: 1.8s (0.9% of total)
ival-cbrt: 1.4s (0.7% of total)
const: 1.4s (0.7% of total)
ival-acos: 623.0ms (0.3% of total)
ival-asin: 581.0ms (0.3% of total)
ival-fmod: 494.0ms (0.3% of total)
ival-atan2: 482.0ms (0.2% of total)
ival-atan: 470.0ms (0.2% of total)
ival-fabs: 453.0ms (0.2% of total)
ival-pi: 280.0ms (0.1% of total)
ival-if: 236.0ms (0.1% of total)
ival-copysign: 190.0ms (0.1% of total)
ival-fmax: 176.0ms (0.1% of total)
ival-log2: 106.0ms (0.1% of total)
ival-floor: 97.0ms (0% of total)
ival-cosh: 92.0ms (0% of total)
ival-sinh: 80.0ms (0% of total)
ival->: 72.0ms (0% of total)
ival->=: 57.0ms (0% of total)
ival-e: 28.0ms (0% of total)
ival-tanh: 13.0ms (0% of total)
ival-<: 12.0ms (0% of total)

prune6.6min (6.8%)

Counts
1449149 → 39665
Compiler

Compiled 1934313 to 980359 computations (49.3% saved)

eval5.2min (5.3%)

Compiler

Compiled 52544495 to 5507953 computations (89.5% saved)

regimes3.8min (3.9%)

Counts
106086 → 9017
Calls

1224 calls:

19.2s
x
16.3s
y
11.7s
z
9.1s
t
8.9s
a
Compiler

Compiled 99337 to 72337 computations (27.2% saved)

series3.2min (3.3%)

Counts
21757 → 482008
Calls

117627 calls:

TimeVariablePointExpression
711.0ms
sinTheta_i
@inf
(* (pow (exp sinTheta_i) (/ sinTheta_O (neg v))) (/ (* cosTheta_O (/ (/ cosTheta_i v) v)) (* (sinh (/ 1 v)) 2)))
486.0ms
im
@-inf
(log (/ (atan2 im re) (log base)))
481.0ms
im
@-inf
(* -3 (/ (log (cbrt im)) (log 1/10)))
475.0ms
a
@inf
(log (+ 1 (* 180 (/ (atan (/ (- (* (pow (sqrt (+ (* (* a (cos (* angle (* (PI) 1/180)))) (* a (cos (* angle (* (PI) 1/180))))) (* (* b (sin (* angle (* (PI) 1/180)))) (* b (sin (* angle (* (PI) 1/180))))))) 2) (pow y-scale -2)) (+ (* (pow (sqrt (+ (* (* a (sin (* angle (* (PI) 1/180)))) (* a (sin (* angle (* (PI) 1/180))))) (* (* (cos (* angle (* (PI) 1/180))) b) (* (cos (* angle (* (PI) 1/180))) b)))) 2) (pow x-scale -2)) (sqrt (+ (* (- (* (pow (sqrt (+ (* (* a (sin (* angle (* (PI) 1/180)))) (* a (sin (* angle (* (PI) 1/180))))) (* (* (cos (* angle (* (PI) 1/180))) b) (* (cos (* angle (* (PI) 1/180))) b)))) 2) (pow x-scale -2)) (* (pow (sqrt (+ (* (* a (cos (* angle (* (PI) 1/180)))) (* a (cos (* angle (* (PI) 1/180))))) (* (* b (sin (* angle (* (PI) 1/180)))) (* b (sin (* angle (* (PI) 1/180))))))) 2) (pow y-scale -2))) (- (* (pow (sqrt (+ (* (* a (sin (* angle (* (PI) 1/180)))) (* a (sin (* angle (* (PI) 1/180))))) (* (* (cos (* angle (* (PI) 1/180))) b) (* (cos (* angle (* (PI) 1/180))) b)))) 2) (pow x-scale -2)) (* (pow (sqrt (+ (* (* a (cos (* angle (* (PI) 1/180)))) (* a (cos (* angle (* (PI) 1/180))))) (* (* b (sin (* angle (* (PI) 1/180)))) (* b (sin (* angle (* (PI) 1/180))))))) 2) (pow y-scale -2)))) (* (* 2 (/ (* (cos (* angle (* (PI) 1/180))) (* (sin (* angle (* (PI) 1/180))) (- (pow b 2) (pow a 2)))) (* y-scale x-scale))) (* 2 (/ (* (cos (* angle (* (PI) 1/180))) (* (sin (* angle (* (PI) 1/180))) (- (pow b 2) (pow a 2)))) (* y-scale x-scale)))))))) (* 2 (/ (* (cos (* angle (* (PI) 1/180))) (* (sin (* angle (* (PI) 1/180))) (- (pow b 2) (pow a 2)))) (* y-scale x-scale))))) (PI)))))
458.0ms
x
@0
(* x (- (log (neg x)) (log (neg y))))

bsearch2.5min (2.6%)

Algorithm
4047×binary-search
564×left-value
Stop Event
92×predicate-same
3955×narrow-enough
Results
1.4min454695×0valid
18.2s33530×1valid
3.4s21018×0invalid
2.8s4375×2valid
2.1s1380×3valid
255.0ms100×4valid
100.0ms572×1invalid
33.0ms83×2invalid
20.0ms141×0unsamplable
Compiler

Compiled 951990 to 686808 computations (27.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.3min
ival-mult: 27.0s (35.8% of total)
ival-sub: 9.5s (12.6% of total)
ival-div: 6.8s (9% of total)
ival-add: 6.7s (8.9% of total)
ival-sin: 4.2s (5.6% of total)
ival-cos: 4.1s (5.4% of total)
ival-pow: 3.9s (5.1% of total)
ival-sqrt: 2.4s (3.1% of total)
ival-log: 2.3s (3% of total)
...c/correct-round.rkt:121:19: 2.1s (2.8% of total)
backward-pass: 1.7s (2.3% of total)
ival-exp: 1.3s (1.8% of total)
const: 1.0s (1.3% of total)
ival-tan: 883.0ms (1.2% of total)
ival-neg: 441.0ms (0.6% of total)
ival-atan2: 355.0ms (0.5% of total)
ival-atan: 178.0ms (0.2% of total)
ival-acos: 148.0ms (0.2% of total)
ival-fabs: 77.0ms (0.1% of total)
ival-fmod: 74.0ms (0.1% of total)
ival-pi: 60.0ms (0.1% of total)
ival-asin: 17.0ms (0% of total)
ival-hypot: 15.0ms (0% of total)
ival->=: 15.0ms (0% of total)
ival-copysign: 15.0ms (0% of total)
ival-tanh: 13.0ms (0% of total)
ival-if: 12.0ms (0% of total)
ival-cbrt: 10.0ms (0% of total)
ival-cosh: 7.0ms (0% of total)
ival-sinh: 5.0ms (0% of total)

preprocess2.3min (2.4%)

Algorithm
542×egg-herbie
Rules
254384×fma-define
252110×fma-neg
118944×unsub-neg
101039×sub-neg
94642×distribute-lft-in
Stop Event
294×saturated
248×node limit
Compiler

Compiled 372788 to 142360 computations (61.8% saved)

analyze2.0min (2.1%)

Algorithm
545×search
random
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%84.4%15.6%0%0%0%0
38.9%32.9%51.6%15.6%0%0%0%1
44.8%37.5%46.2%15.6%0%0.7%0%2
54%44.1%37.5%15.7%0%2.6%0%3
60.9%49.1%31.6%15.8%0%3.6%0%4
67.1%53.8%26.4%15.8%0%4%0%5
71%56.7%23.1%15.8%0%4.3%0%6
75%59.4%19.8%15.9%0%4.8%0.1%7
77%60.7%18.1%15.9%0%5.2%0.1%8
79.6%62.5%16%15.9%0%5.4%0.1%9
81.1%63.5%14.8%16%0%5.7%0.1%10
83.4%65.1%13%16%0%5.8%0.1%11
84.5%65.8%12.1%16%0%6%0.1%12
Compiler

Compiled 13446 to 7366 computations (45.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.2min
ival-mult: 18.5s (24.8% of total)
...c/correct-round.rkt:121:19: 13.0s (17.4% of total)
ival-div: 6.2s (8.3% of total)
ival-sub: 4.8s (6.4% of total)
ival-<=: 4.6s (6.2% of total)
ival-add: 4.5s (6% of total)
ival-pow: 4.3s (5.7% of total)
ival-sqrt: 2.8s (3.7% of total)
ival-cos: 2.2s (2.9% of total)
ival-sin: 2.1s (2.9% of total)
ival-fabs: 1.7s (2.3% of total)
ival-floor: 1.0s (1.4% of total)
ival-exp: 892.0ms (1.2% of total)
ival-log: 865.0ms (1.2% of total)
ival-==: 809.0ms (1.1% of total)
ival-and: 806.0ms (1.1% of total)
ival-tan: 760.0ms (1% of total)
ival-if: 715.0ms (1% of total)
ival-neg: 699.0ms (0.9% of total)
ival-atan2: 667.0ms (0.9% of total)
const: 554.0ms (0.7% of total)
ival-<: 411.0ms (0.6% of total)
ival-fmax: 378.0ms (0.5% of total)
ival-log2: 238.0ms (0.3% of total)
ival-pi: 203.0ms (0.3% of total)
ival->: 173.0ms (0.2% of total)
ival-acos: 153.0ms (0.2% of total)
backward-pass: 125.0ms (0.2% of total)
ival->=: 108.0ms (0.1% of total)
ival-asin: 107.0ms (0.1% of total)
ival-atan: 96.0ms (0.1% of total)
ival-fmod: 50.0ms (0.1% of total)
ival-sinh: 44.0ms (0.1% of total)
ival-or: 30.0ms (0% of total)
ival-cbrt: 21.0ms (0% of total)
ival-cosh: 16.0ms (0% of total)
ival-fmin: 8.0ms (0% of total)
ival-tanh: 8.0ms (0% of total)
ival-atanh: 1.0ms (0% of total)
ival-asinh: 0.0ms (0% of total)
ival-hypot: 0.0ms (0% of total)
ival-fma: 0.0ms (0% of total)
ival-acosh: 0.0ms (0% of total)

explain1.7min (1.7%)

Results
36.7s230846×0valid
16.1s34488×1valid
8.5s10460×2valid
2.9s1438×3valid
444.0ms146×4valid
294.0ms126×5exit
Compiler

Compiled 97157 to 18586 computations (80.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.1s
ival-mult: 8.3s (23.1% of total)
ival-div: 3.2s (8.8% of total)
ival-sub: 3.1s (8.7% of total)
ival-add: 3.1s (8.5% of total)
backward-pass: 2.9s (8% of total)
ival-sin: 2.8s (7.9% of total)
ival-cos: 2.2s (6.2% of total)
ival-pow: 2.0s (5.4% of total)
ival-log: 1.9s (5.2% of total)
ival-sqrt: 1.3s (3.5% of total)
ival-tan: 1.2s (3.3% of total)
ival-exp: 1.2s (3.2% of total)
...c/correct-round.rkt:121:19: 976.0ms (2.7% of total)
ival-neg: 549.0ms (1.5% of total)
const: 466.0ms (1.3% of total)
ival-pi: 149.0ms (0.4% of total)
ival-atan2: 103.0ms (0.3% of total)
ival-log1p: 86.0ms (0.2% of total)
ival-asin: 84.0ms (0.2% of total)
ival-atan: 79.0ms (0.2% of total)
ival-acos: 79.0ms (0.2% of total)
ival-fabs: 73.0ms (0.2% of total)
ival-floor: 48.0ms (0.1% of total)
ival-cbrt: 40.0ms (0.1% of total)
ival-fmod: 38.0ms (0.1% of total)
ival-sinh: 35.0ms (0.1% of total)
ival-if: 28.0ms (0.1% of total)
ival-fma: 19.0ms (0.1% of total)
ival-hypot: 19.0ms (0.1% of total)
ival-fmax: 19.0ms (0.1% of total)
ival-cosh: 16.0ms (0% of total)
ival-log2: 15.0ms (0% of total)
ival-copysign: 15.0ms (0% of total)
ival->=: 13.0ms (0% of total)
ival-tanh: 13.0ms (0% of total)
ival->: 5.0ms (0% of total)
ival-<: 2.0ms (0% of total)

end45.1s (0.8%)

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