Herbie run

Date:Saturday, May 11th, 2024
Commit:66dd3019 on main
Hostname:nightly with Racket 8.11.1
Seed:2024132
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)

sample23.5min (24.3%)

Results
9.0min3840628×0valid
3.5min62572×5exit
3.3min482929×1valid
1.5min129534×2valid
33.3s19417×3valid
32.9s145583×0precondition
32.5s171380×0invalid
15.3s60303×0unsamplable
11.4s2263×4valid
6.7s23110×1invalid
1.5s2224×2invalid
231.0ms11×5valid
180.0ms60×1unsamplable
17.0ms26×3invalid
Precisions
Click to see histograms. Total time spent on operations: 15.0min
ival-mult: 2.9min (19.3% of total)
ival-pow: 2.9min (19% of total)
ival-sin: 1.3min (8.5% of total)
ival-div: 1.2min (8.1% of total)
ival-add: 1.0min (6.8% of total)
ival-sub: 59.6s (6.6% of total)
...c/correct-round.rkt:119:19: 40.7s (4.5% of total)
ival-cos: 39.2s (4.3% of total)
ival-exp: 30.5s (3.4% of total)
ival-log: 30.5s (3.4% of total)
backward-pass: 29.4s (3.3% of total)
ival-sqrt: 21.9s (2.4% of total)
ival-<=: 20.9s (2.3% of total)
ival-tan: 19.1s (2.1% of total)
ival-neg: 8.6s (1% of total)
const: 7.7s (0.9% of total)
ival-<: 6.6s (0.7% of total)
ival-fabs: 5.8s (0.6% of total)
ival-and: 3.5s (0.4% of total)
ival-pi: 2.8s (0.3% of total)
ival-atan2: 2.3s (0.3% of total)
ival-acos: 2.1s (0.2% of total)
ival->: 1.9s (0.2% of total)
ival-asin: 1.9s (0.2% of total)
ival-atan: 1.2s (0.1% of total)
ival-cbrt: 1.1s (0.1% of total)
ival-floor: 1.1s (0.1% of total)
ival-fmod: 869.0ms (0.1% of total)
ival-sinh: 764.0ms (0.1% of total)
ival-fmin: 751.0ms (0.1% of total)
ival->=: 743.0ms (0.1% of total)
ival-==: 698.0ms (0.1% of total)
ival-if: 568.0ms (0.1% of total)
ival-fmax: 542.0ms (0.1% of total)
ival-cosh: 417.0ms (0% of total)
ival-hypot: 329.0ms (0% of total)
ival-acosh: 323.0ms (0% of total)
ival-fma: 319.0ms (0% of total)
ival-log2: 240.0ms (0% of total)
ival-asinh: 233.0ms (0% of total)
ival-atanh: 180.0ms (0% of total)
ival-tanh: 90.0ms (0% of total)
ival-or: 63.0ms (0% of total)
Bogosity

simplify18.5min (19.1%)

Algorithm
4350×egg-herbie
Rules
1646767×fma-define
1237444×fma-neg
893943×distribute-lft-in
843854×times-frac
806156×associate-*r*
Stop Event
1463×saturated
2858×node limit
29×unsound
Counts
1134375 → 984660

soundness11.6min (12%)

Rules
664552×fma-define
488171×fma-neg
477735×log1p-expm1-u
402088×associate-*r*
383615×distribute-lft-in
Stop Event
157×saturated
362×fuel
1946×node limit
29×unsound
179×done
Compiler

Compiled 428450 to 129549 computations (69.8% saved)

rewrite7.9min (8.2%)

Algorithm
1878×batch-egg-rewrite
Rules
1181943×log1p-expm1-u
897058×expm1-log1p-u
420303×pow1
403444×add-exp-log
386801×add-log-exp
Stop Event
saturated
1861×node limit
16×unsound
Counts
21681 → 649808

localize7.7min (8%)

Results
2.7min393732×0valid
1.2min47347×1valid
46.7s7829×5exit
29.5s13715×2valid
16.9s26472×0invalid
8.3s1929×3valid
1.9s829×1invalid
1.2s2351×0unsamplable
1.1s125×4valid
29.0ms5valid
2.0ms2invalid
Compiler

Compiled 460768 to 49340 computations (89.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.3min
ival-mult: 44.5s (22.2% of total)
ival-div: 23.8s (11.9% of total)
ival-pow: 23.1s (11.5% of total)
ival-add: 13.4s (6.7% of total)
backward-pass: 13.3s (6.6% of total)
ival-sin: 12.4s (6.2% of total)
ival-cos: 10.0s (5% of total)
ival-sub: 9.2s (4.6% of total)
...c/correct-round.rkt:119:19: 7.6s (3.8% of total)
ival-log: 6.4s (3.2% of total)
ival-fma: 5.6s (2.8% of total)
ival-tan: 5.4s (2.7% of total)
ival-sqrt: 4.8s (2.4% of total)
ival-exp: 3.8s (1.9% of total)
ival-neg: 2.8s (1.4% of total)
ival-hypot: 2.0s (1% of total)
ival-log1p: 1.9s (0.9% of total)
ival-cbrt: 1.6s (0.8% of total)
const: 1.4s (0.7% of total)
ival-expm1: 1.2s (0.6% of total)
ival-fmod: 991.0ms (0.5% of total)
ival-asin: 697.0ms (0.3% of total)
ival-atan2: 670.0ms (0.3% of total)
ival-atan: 660.0ms (0.3% of total)
ival-fabs: 642.0ms (0.3% of total)
ival-acos: 541.0ms (0.3% of total)
ival-if: 335.0ms (0.2% of total)
ival-pi: 258.0ms (0.1% of total)
ival-cosh: 208.0ms (0.1% of total)
ival-log2: 177.0ms (0.1% of total)
ival-fmax: 176.0ms (0.1% of total)
ival-sinh: 127.0ms (0.1% of total)
ival->: 127.0ms (0.1% of total)
ival-floor: 102.0ms (0.1% of total)
ival-copysign: 91.0ms (0% of total)
ival-e: 65.0ms (0% of total)
ival->=: 51.0ms (0% of total)
ival-<: 18.0ms (0% of total)
ival-tanh: 17.0ms (0% of total)

prune6.7min (6.9%)

Counts
1450145 → 39911
Compiler

Compiled 1906961 to 974245 computations (48.9% saved)

eval5.2min (5.4%)

Compiler

Compiled 49368883 to 5571818 computations (88.7% saved)

regimes3.7min (3.8%)

Counts
107191 → 9075
Calls

1211 calls:

18.8s
x
13.7s
z
13.0s
y
9.6s
t
8.6s
a
Compiler

Compiled 97297 to 70983 computations (27% saved)

series3.2min (3.3%)

Counts
21681 → 484567
Calls

117942 calls:

TimeVariablePointExpression
569.0ms
b
@-inf
(+ (* -1/2 (/ c b)) (* -3/8 (/ (* a (pow c 2)) (pow b 3))))
558.0ms
x-scale
@-inf
(/ (sqrt (* (* b (* (pow a 2) (neg b))) (* (* 8 (* b (/ (* (pow a 2) (neg b)) (pow (* x-scale y-scale) 2)))) (+ (/ (+ (pow (* a (sin (* angle (/ (PI) 180)))) 2) (pow (* b (cos (* angle (/ (PI) 180)))) 2)) (pow x-scale 2)) (- (/ (+ (pow (* a (cos (* angle (/ (PI) 180)))) 2) (pow (* b (sin (* angle (/ (PI) 180)))) 2)) (pow y-scale 2)) (sqrt (+ (* (- (/ (+ (pow (* a (sin (* angle (/ (PI) 180)))) 2) (pow (* b (cos (* angle (/ (PI) 180)))) 2)) (pow x-scale 2)) (/ (+ (pow (* a (cos (* angle (/ (PI) 180)))) 2) (pow (* b (sin (* angle (/ (PI) 180)))) 2)) (pow y-scale 2))) (- (/ (+ (pow (* a (sin (* angle (/ (PI) 180)))) 2) (pow (* b (cos (* angle (/ (PI) 180)))) 2)) (pow x-scale 2)) (/ (+ (pow (* a (cos (* angle (/ (PI) 180)))) 2) (pow (* b (sin (* angle (/ (PI) 180)))) 2)) (pow y-scale 2)))) (* (* (* 2 (- (pow b 2) (pow a 2))) (/ (* (sin (* angle (/ (PI) 180))) (cos (* angle (/ (PI) 180)))) (* x-scale y-scale))) (* (* 2 (- (pow b 2) (pow a 2))) (/ (* (sin (* angle (/ (PI) 180))) (cos (* angle (/ (PI) 180)))) (* x-scale y-scale))))))))))) (* b (/ (* (pow a 2) (neg b)) (pow (* x-scale y-scale) 2))))
493.0ms
y
@-inf
(- x (/ y (* y x)))
441.0ms
h
@0
(+ (cbrt (* (/ 1/2 a) (- (sqrt (- (* g g) (* h h))) g))) (cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a))))
431.0ms
y-scale
@-inf
(+ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) (pow x-scale 2)) (+ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) (pow y-scale 2)) (sqrt (+ (pow (- (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) (pow x-scale 2)) (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) (pow y-scale 2))) 2) (pow (/ (* (* 2 (- (pow b 2) (pow a 2))) (* (sin (* (/ angle 180) (PI))) (cos (* (/ angle 180) (PI))))) (* x-scale y-scale)) 2)))))

bsearch2.4min (2.5%)

Algorithm
4078×binary-search
568×left-value
Stop Event
94×predicate-same
3984×narrow-enough
Results
1.3min448940×0valid
18.0s36432×1valid
4.2s5609×2valid
4.0s1745×3valid
3.2s19683×0invalid
863.0ms234×4valid
350.0ms218×1invalid
103.0ms387×0unsamplable
65.0ms164×2invalid
Compiler

Compiled 921065 to 664306 computations (27.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.2min
ival-mult: 23.6s (31.7% of total)
ival-sub: 10.3s (13.9% of total)
ival-add: 8.7s (11.7% of total)
ival-div: 6.1s (8.2% of total)
ival-sin: 4.9s (6.6% of total)
ival-cos: 4.1s (5.5% of total)
ival-pow: 4.0s (5.3% of total)
ival-log: 2.3s (3.1% of total)
ival-sqrt: 2.1s (2.8% of total)
...c/correct-round.rkt:119:19: 2.0s (2.7% of total)
backward-pass: 2.0s (2.7% of total)
ival-exp: 1.0s (1.4% of total)
ival-tan: 775.0ms (1% of total)
const: 730.0ms (1% of total)
ival-neg: 692.0ms (0.9% of total)
ival-atan2: 425.0ms (0.6% of total)
ival-atan: 161.0ms (0.2% of total)
ival-acos: 135.0ms (0.2% of total)
ival-pi: 94.0ms (0.1% of total)
ival-fabs: 89.0ms (0.1% of total)
ival-copysign: 58.0ms (0.1% of total)
ival-asin: 31.0ms (0% of total)
ival-cbrt: 27.0ms (0% of total)
ival-hypot: 11.0ms (0% of total)
ival->=: 10.0ms (0% of total)
ival-if: 10.0ms (0% of total)
ival-cosh: 9.0ms (0% of total)
ival-fmod: 9.0ms (0% of total)
ival-tanh: 7.0ms (0% of total)
ival-sinh: 6.0ms (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 368104 to 141636 computations (61.5% saved)

analyze2.0min (2%)

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: 1.1min
ival-mult: 17.9s (25.9% of total)
...c/correct-round.rkt:119:19: 6.9s (10% of total)
ival-div: 6.1s (8.8% of total)
ival-<=: 5.2s (7.5% of total)
ival-pow: 5.1s (7.4% of total)
ival-add: 4.7s (6.8% of total)
ival-sub: 4.2s (6.1% of total)
ival-sqrt: 2.4s (3.5% of total)
ival-cos: 2.3s (3.3% of total)
ival-sin: 2.2s (3.2% of total)
ival-fabs: 2.0s (2.9% of total)
ival-floor: 1.5s (2.1% of total)
ival-log: 1.4s (2% of total)
ival-and: 847.0ms (1.2% of total)
ival-exp: 746.0ms (1.1% of total)
ival-neg: 746.0ms (1.1% of total)
ival-==: 727.0ms (1.1% of total)
ival-tan: 659.0ms (1% of total)
const: 560.0ms (0.8% of total)
ival-if: 514.0ms (0.7% of total)
ival-<: 390.0ms (0.6% of total)
ival-fmax: 375.0ms (0.5% of total)
ival-log2: 265.0ms (0.4% of total)
ival-atan2: 213.0ms (0.3% of total)
ival-pi: 196.0ms (0.3% of total)
backward-pass: 176.0ms (0.3% of total)
ival->: 155.0ms (0.2% of total)
ival->=: 130.0ms (0.2% of total)
ival-acos: 116.0ms (0.2% of total)
ival-fmod: 115.0ms (0.2% of total)
ival-atan: 97.0ms (0.1% of total)
ival-asin: 73.0ms (0.1% of total)
ival-sinh: 51.0ms (0.1% of total)
ival-or: 30.0ms (0% of total)
ival-cosh: 18.0ms (0% of total)
ival-cbrt: 17.0ms (0% of total)
ival-tanh: 8.0ms (0% of total)
ival-fmin: 7.0ms (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)

explain1.9min (2%)

Results
38.2s230430×0valid
22.6s34780×1valid
9.1s10566×2valid
3.3s1400×3valid
1.1s156×4valid
575.0ms172×5exit
Compiler

Compiled 97157 to 18586 computations (80.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 45.4s
ival-mult: 15.2s (33.4% of total)
ival-div: 4.0s (8.8% of total)
ival-sub: 3.2s (7.1% of total)
ival-add: 3.1s (6.8% of total)
ival-sin: 3.0s (6.6% of total)
ival-cos: 2.9s (6.5% of total)
ival-pow: 2.4s (5.4% of total)
backward-pass: 2.0s (4.4% of total)
ival-log: 1.8s (4.1% of total)
ival-sqrt: 1.6s (3.5% of total)
ival-exp: 1.6s (3.5% of total)
ival-tan: 1.4s (3.1% of total)
...c/correct-round.rkt:119:19: 1.0s (2.2% of total)
const: 494.0ms (1.1% of total)
ival-neg: 391.0ms (0.9% of total)
ival-atan: 136.0ms (0.3% of total)
ival-acos: 136.0ms (0.3% of total)
ival-atan2: 131.0ms (0.3% of total)
ival-cbrt: 122.0ms (0.3% of total)
ival-asin: 116.0ms (0.3% of total)
ival-pi: 107.0ms (0.2% of total)
ival-if: 93.0ms (0.2% of total)
ival-fabs: 77.0ms (0.2% of total)
ival-sinh: 73.0ms (0.2% of total)
ival-floor: 46.0ms (0.1% of total)
ival-fmod: 41.0ms (0.1% of total)
ival-fmax: 24.0ms (0.1% of total)
ival-log2: 24.0ms (0.1% of total)
ival-hypot: 21.0ms (0% of total)
ival-fma: 17.0ms (0% of total)
ival-copysign: 17.0ms (0% of total)
ival-cosh: 14.0ms (0% of total)
ival->=: 12.0ms (0% of total)
ival-log1p: 8.0ms (0% of total)
ival-tanh: 8.0ms (0% of total)
ival->: 8.0ms (0% of total)
ival-<: 2.0ms (0% of total)

end3.0ms (0%)

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