Herbie run

Date:Friday, May 24th, 2024
Commit:7841f259 on main
Hostname:nightly with Racket 8.11.1
Seed:2024145
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: 10.1min)

simplify2.6min (25.7%)

Algorithm
268×egg-herbie
Rules
211904×fma-define
120428×distribute-lft-in
116402×*-commutative
115944×times-frac
109948×fma-neg
Stop Event
63×saturated
205×node limit
Counts
106406 → 74700

sample1.5min (15.1%)

Results
1.2min247619×0valid
1.7s8335×0invalid
735.0ms2049×0precondition
11.0ms61×1valid
Precisions
Click to see histograms. Total time spent on operations: 58.8s
ival-mult: 12.3s (20.9% of total)
ival-<=: 9.7s (16.6% of total)
...c/correct-round.rkt:121:19: 9.3s (15.9% of total)
ival-div: 4.8s (8.2% of total)
ival-sin: 2.6s (4.4% of total)
ival-sub: 2.3s (4% of total)
ival-fabs: 2.0s (3.4% of total)
ival-add: 1.9s (3.3% of total)
ival-sqrt: 1.9s (3.2% of total)
ival-log: 1.5s (2.6% of total)
ival-and: 1.5s (2.6% of total)
ival-floor: 1.5s (2.5% of total)
ival-cos: 1.1s (1.9% of total)
ival-exp: 1.1s (1.8% of total)
ival-pi: 1.0s (1.7% of total)
ival-tan: 726.0ms (1.2% of total)
ival-neg: 638.0ms (1.1% of total)
const: 436.0ms (0.7% of total)
ival->: 407.0ms (0.7% of total)
ival-log2: 344.0ms (0.6% of total)
ival-<: 337.0ms (0.6% of total)
ival-fmax: 334.0ms (0.6% of total)
ival-if: 292.0ms (0.5% of total)
ival-==: 184.0ms (0.3% of total)
ival-asin: 143.0ms (0.2% of total)
ival-atan: 134.0ms (0.2% of total)
ival-sinh: 84.0ms (0.1% of total)
ival->=: 82.0ms (0.1% of total)
backward-pass: 75.0ms (0.1% of total)
Bogosity

soundness1.5min (15.1%)

Rules
98304×fma-define
67054×*-commutative
65614×times-frac
61184×associate-*r*
56408×distribute-lft-in
Stop Event
saturated
167×node limit
29×fuel
done
Compiler

Compiled 63515 to 12661 computations (80.1% saved)

prune44.7s (7.4%)

Counts
145593 → 4294
Compiler

Compiled 394856 to 142644 computations (63.9% saved)

localize42.5s (7%)

Results
19.3s26645×0valid
4.8s706×5exit
1.8s1940×0invalid
1.0s586×1valid
213.0ms587×0unsamplable
Compiler

Compiled 106809 to 5587 computations (94.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 16.1s
ival-mult: 4.0s (24.5% of total)
ival-pow: 1.9s (11.9% of total)
ival-div: 1.8s (11.2% of total)
...c/correct-round.rkt:121:19: 925.0ms (5.7% of total)
ival-add: 911.0ms (5.6% of total)
ival-sqrt: 617.0ms (3.8% of total)
ival-exp: 614.0ms (3.8% of total)
ival-hypot: 522.0ms (3.2% of total)
ival-tan: 515.0ms (3.2% of total)
backward-pass: 505.0ms (3.1% of total)
ival-sin: 426.0ms (2.6% of total)
ival-log1p: 418.0ms (2.6% of total)
ival-sub: 406.0ms (2.5% of total)
ival-fma: 383.0ms (2.4% of total)
ival-pi: 305.0ms (1.9% of total)
ival-log: 290.0ms (1.8% of total)
ival-cos: 225.0ms (1.4% of total)
ival-fmax: 199.0ms (1.2% of total)
ival-if: 196.0ms (1.2% of total)
ival-atan: 186.0ms (1.2% of total)
ival-neg: 159.0ms (1% of total)
ival-log2: 107.0ms (0.7% of total)
ival-floor: 96.0ms (0.6% of total)
const: 91.0ms (0.6% of total)
ival-cbrt: 86.0ms (0.5% of total)
ival-expm1: 70.0ms (0.4% of total)
ival-asin: 56.0ms (0.3% of total)
ival->=: 46.0ms (0.3% of total)
ival->: 35.0ms (0.2% of total)
ival-fabs: 33.0ms (0.2% of total)
ival-sinh: 11.0ms (0.1% of total)
ival-<: 10.0ms (0.1% of total)
ival-e: 4.0ms (0% of total)

series38.5s (6.4%)

Counts
2057 → 60576
Calls

14868 calls:

TimeVariablePointExpression
535.0ms
d
@0
(pow (cbrt (sqrt (fmax (pow (sqrt (+ (* (* (floor d) dX.w) (* (floor d) dX.w)) (* (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v)))) (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))))))) 2) (pow (sqrt (+ (* (* (floor d) dY.w) (* (floor d) dY.w)) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2)))) 3)
458.0ms
w
@-inf
(exp (* (log (fmax (pow (sqrt (+ (* (* dX.v (floor h)) (* dX.v (floor h))) (* (* dX.u (floor w)) (* dX.u (floor w))))) 2) (pow (sqrt (+ (* (* (floor h) dY.v) (* (floor h) dY.v)) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2))) 1/2))
324.0ms
d
@0
(log (+ 1 (sqrt (fmax (pow (sqrt (+ (* (* (floor d) dX.w) (* (floor d) dX.w)) (* (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v)))) (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))))))) 2) (pow (* (floor h) dY.v) 2)))))
311.0ms
w
@-inf
(log (+ 1 (sqrt (fmax (pow (sqrt (+ (* (* (floor d) dX.w) (* (floor d) dX.w)) (* (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v)))) (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))))))) 2) (pow (sqrt (+ (* (* (floor d) dY.w) (* (floor d) dY.w)) (* (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))))) 2)))))
290.0ms
dY.w
@0
(log (log2 (sqrt (fmax (pow (sqrt (+ (* (* dX.w (floor d)) (* dX.w (floor d))) (* (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* dX.v (floor h)) (* dX.v (floor h))))) (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* dX.v (floor h)) (* dX.v (floor h)))))))) 2) (pow (sqrt (+ (* (* (floor d) dY.w) (* (floor d) dY.w)) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2)))))

analyze33.1s (5.5%)

Algorithm
30×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%2.6%97.4%0%0%0%0
0%0%2.6%97.4%0%0%0%1
7.8%0.2%2.4%97.4%0%0%0%2
8.5%0.2%2.4%97.4%0%0%0%3
12.8%0.3%2.3%97.4%0%0%0%4
47%1.2%1.4%97.4%0%0%0%5
51.8%1.3%1.2%97.4%0%0%0%6
69.5%1.8%0.8%97.4%0%0%0%7
71.6%1.8%0.7%97.4%0%0.1%0%8
81.1%2.1%0.5%97.4%0%0.1%0%9
82.6%2.1%0.4%97.4%0%0.1%0%10
88.3%2.2%0.3%97.4%0%0.1%0%11
89.1%2.2%0.3%97.4%0%0.1%0%12
Compiler

Compiled 2668 to 1046 computations (60.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.7s
ival-mult: 5.5s (25.2% of total)
ival-<=: 3.8s (17.5% of total)
...c/correct-round.rkt:121:19: 2.3s (10.5% of total)
ival-fabs: 1.8s (8.5% of total)
ival-div: 1.2s (5.4% of total)
ival-sqrt: 981.0ms (4.5% of total)
ival-add: 920.0ms (4.2% of total)
ival-if: 716.0ms (3.3% of total)
ival-floor: 685.0ms (3.2% of total)
ival-and: 642.0ms (3% of total)
ival-sub: 527.0ms (2.4% of total)
ival-fmax: 414.0ms (1.9% of total)
ival-sin: 311.0ms (1.4% of total)
ival-==: 244.0ms (1.1% of total)
ival-cos: 241.0ms (1.1% of total)
ival-log: 180.0ms (0.8% of total)
ival-log2: 171.0ms (0.8% of total)
ival-neg: 161.0ms (0.7% of total)
ival-tan: 145.0ms (0.7% of total)
ival->=: 144.0ms (0.7% of total)
const: 126.0ms (0.6% of total)
ival->: 120.0ms (0.6% of total)
ival-sinh: 88.0ms (0.4% of total)
ival-exp: 74.0ms (0.3% of total)
ival-<: 71.0ms (0.3% of total)
ival-pi: 69.0ms (0.3% of total)
ival-atan: 39.0ms (0.2% of total)
ival-asin: 23.0ms (0.1% of total)
backward-pass: 22.0ms (0.1% of total)

rewrite32.3s (5.3%)

Algorithm
119×batch-egg-rewrite
Rules
62619×log1p-expm1-u
51140×expm1-log1p-u
37978×pow1
36666×log-prod
36517×add-exp-log
Stop Event
119×node limit
Counts
2057 → 45830

regimes30.5s (5%)

Counts
10173 → 399
Calls

145 calls:

824.0ms
maxCos
761.0ms
u1
712.0ms
cosTheta_i
697.0ms
ux
656.0ms
s
Compiler

Compiled 14154 to 9859 computations (30.3% saved)

eval29.7s (4.9%)

Compiler

Compiled 14089995 to 624935 computations (95.6% saved)

preprocess9.1s (1.5%)

Algorithm
30×egg-herbie
Rules
30630×fma-define
21782×fma-neg
15892×unsub-neg
14706×distribute-lft-neg-in
11858×distribute-rgt-neg-in
Stop Event
11×saturated
19×node limit
Compiler

Compiled 52656 to 15352 computations (70.8% saved)

explain6.6s (1.1%)

Results
3.7s15284×0valid
42.0ms76×1valid
Compiler

Compiled 16652 to 1662 computations (90% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.1s
ival-mult: 709.0ms (34.1% of total)
ival-div: 258.0ms (12.4% of total)
ival-exp: 247.0ms (11.9% of total)
ival-add: 156.0ms (7.5% of total)
ival-sin: 139.0ms (6.7% of total)
ival-sub: 84.0ms (4% of total)
ival-log: 79.0ms (3.8% of total)
ival-sqrt: 74.0ms (3.6% of total)
ival-floor: 59.0ms (2.8% of total)
ival-cos: 48.0ms (2.3% of total)
ival-neg: 30.0ms (1.4% of total)
const: 26.0ms (1.3% of total)
ival-pi: 26.0ms (1.3% of total)
...c/correct-round.rkt:121:19: 25.0ms (1.2% of total)
ival-tan: 19.0ms (0.9% of total)
ival-fmax: 18.0ms (0.9% of total)
ival-if: 15.0ms (0.7% of total)
ival-log2: 14.0ms (0.7% of total)
ival-fabs: 12.0ms (0.6% of total)
backward-pass: 8.0ms (0.4% of total)
ival->: 7.0ms (0.3% of total)
ival-atan: 7.0ms (0.3% of total)
ival->=: 6.0ms (0.3% of total)
ival-asin: 5.0ms (0.2% of total)
ival-sinh: 5.0ms (0.2% of total)
ival-<: 2.0ms (0.1% of total)

bsearch49.0ms (0%)

Algorithm
51×binary-search
23×left-value
Stop Event
51×narrow-enough
Compiler

Compiled 4787 to 1924 computations (59.8% saved)

end0.0ms (0%)

Profiling

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