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: 10.7min)

simplify2.4min (22.2%)

Algorithm
268×egg-herbie
Rules
215708×fma-define
120276×times-frac
120022×distribute-lft-in
118514×*-commutative
113718×fma-neg
Stop Event
65×saturated
203×node limit
Counts
102538 → 73426

sample1.5min (14.2%)

Results
1.2min247632×0valid
1.5s8365×0invalid
618.0ms2120×0precondition
11.0ms48×1valid
Precisions
Click to see histograms. Total time spent on operations: 58.6s
ival-mult: 11.9s (20.3% of total)
ival-<=: 10.4s (17.7% of total)
...c/correct-round.rkt:121:19: 9.0s (15.4% of total)
ival-div: 4.6s (7.9% of total)
ival-sin: 2.6s (4.4% of total)
ival-add: 2.3s (3.9% of total)
ival-sqrt: 2.3s (3.9% of total)
ival-sub: 2.3s (3.9% of total)
ival-fabs: 1.8s (3.2% of total)
ival-log: 1.6s (2.8% of total)
ival-and: 1.6s (2.8% of total)
ival-cos: 1.0s (1.8% of total)
ival-exp: 914.0ms (1.6% of total)
ival-neg: 884.0ms (1.5% of total)
ival-floor: 790.0ms (1.3% of total)
ival-==: 620.0ms (1.1% of total)
ival-pi: 548.0ms (0.9% of total)
ival-if: 529.0ms (0.9% of total)
const: 441.0ms (0.8% of total)
ival-fmax: 364.0ms (0.6% of total)
ival-tan: 358.0ms (0.6% of total)
ival-<: 351.0ms (0.6% of total)
ival-log2: 341.0ms (0.6% of total)
ival->: 323.0ms (0.6% of total)
ival-sinh: 221.0ms (0.4% of total)
ival-asin: 165.0ms (0.3% of total)
ival-atan: 145.0ms (0.2% of total)
ival->=: 85.0ms (0.1% of total)
backward-pass: 74.0ms (0.1% of total)
Bogosity

soundness1.5min (14.1%)

Rules
107976×fma-define
70784×times-frac
69616×*-commutative
65470×associate-*r*
56456×distribute-lft-in
Stop Event
7×saturated
164×node limit
29×fuel
1×done
Compiler

Compiled 62999 to 12855 computations (79.6% saved)

prune58.3s (9.1%)

Counts
152282 → 4062
Compiler

Compiled 362196 to 132286 computations (63.5% saved)

end45.1s (7%)

localize44.0s (6.9%)

Results
17.3s26010×0valid
7.5s784×5exit
1.9s1993×0invalid
1.2s518×1valid
787.0ms1159×0unsamplable
Compiler

Compiled 103174 to 5501 computations (94.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.8s
ival-mult: 4.1s (23.3% of total)
ival-div: 2.2s (12.3% of total)
ival-pow: 1.6s (9% of total)
ival-expm1: 1.5s (8.6% of total)
backward-pass: 836.0ms (4.7% of total)
ival-add: 783.0ms (4.4% of total)
ival-exp: 646.0ms (3.6% of total)
ival-sqrt: 626.0ms (3.5% of total)
ival-tan: 593.0ms (3.3% of total)
ival-sin: 500.0ms (2.8% of total)
ival-cos: 491.0ms (2.8% of total)
ival-log1p: 473.0ms (2.7% of total)
ival-sub: 465.0ms (2.6% of total)
...c/correct-round.rkt:121:19: 457.0ms (2.6% of total)
ival-fma: 423.0ms (2.4% of total)
ival-log: 352.0ms (2% of total)
ival-hypot: 309.0ms (1.7% of total)
ival-neg: 192.0ms (1.1% of total)
ival-fmax: 176.0ms (1% of total)
ival-if: 158.0ms (0.9% of total)
ival-atan: 150.0ms (0.8% of total)
ival-log2: 106.0ms (0.6% of total)
ival-floor: 97.0ms (0.5% of total)
const: 96.0ms (0.5% of total)
ival->: 72.0ms (0.4% of total)
ival-pi: 71.0ms (0.4% of total)
ival-fabs: 61.0ms (0.3% of total)
ival-cbrt: 49.0ms (0.3% of total)
ival->=: 43.0ms (0.2% of total)
ival-asin: 41.0ms (0.2% of total)
ival-sinh: 12.0ms (0.1% of total)
ival-<: 12.0ms (0.1% of total)
ival-e: 2.0ms (0% of total)

eval34.0s (5.3%)

Compiler

Compiled 17062972 to 625865 computations (96.3% saved)

analyze32.5s (5.1%)

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: 21.4s
ival-mult: 5.2s (24.5% of total)
ival-<=: 3.4s (15.7% of total)
...c/correct-round.rkt:121:19: 2.4s (11% of total)
ival-div: 1.7s (7.8% of total)
ival-fabs: 1.5s (7.1% of total)
ival-floor: 1.0s (4.9% of total)
ival-add: 887.0ms (4.1% of total)
ival-and: 653.0ms (3.1% of total)
ival-sqrt: 644.0ms (3% of total)
ival-==: 636.0ms (3% of total)
ival-if: 510.0ms (2.4% of total)
ival-sub: 475.0ms (2.2% of total)
ival-fmax: 378.0ms (1.8% of total)
ival-cos: 322.0ms (1.5% of total)
ival-sin: 320.0ms (1.5% of total)
ival-log2: 238.0ms (1.1% of total)
ival-log: 199.0ms (0.9% of total)
ival-neg: 139.0ms (0.6% of total)
ival->: 138.0ms (0.6% of total)
const: 128.0ms (0.6% of total)
ival-tan: 126.0ms (0.6% of total)
ival->=: 93.0ms (0.4% of total)
ival-exp: 82.0ms (0.4% of total)
ival-pi: 73.0ms (0.3% of total)
ival-<: 59.0ms (0.3% of total)
ival-atan: 38.0ms (0.2% of total)
ival-sinh: 30.0ms (0.1% of total)
backward-pass: 22.0ms (0.1% of total)
ival-asin: 18.0ms (0.1% of total)

rewrite32.2s (5%)

Algorithm
119×batch-egg-rewrite
Rules
60454×log1p-expm1-u
48868×expm1-log1p-u
37013×pow1
36414×log-prod
35796×add-exp-log
Stop Event
119×node limit
Counts
2012 → 46024

regimes29.6s (4.6%)

Counts
9655 → 401
Calls

145 calls:

1.1s
cosTheta_i
959.0ms
dY.u
823.0ms
maxCos
698.0ms
ux
692.0ms
uy
Compiler

Compiled 14799 to 10226 computations (30.9% saved)

series26.8s (4.2%)

Counts
2012 → 56514
Calls

14022 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)))
234.0ms
cosTheta_O
@inf
(/ (* cosTheta_i cosTheta_O) (* (* (sinh (/ 1 v)) (* (* v 2) v)) (pow (+ 1 sinTheta_i) (/ sinTheta_O v))))
176.0ms
s
@inf
(+ (* (* s 8) (pow u 2)) (* s (* u 4)))
158.0ms
dY.u
@0
(* (* (floor h) dY.v) (/ 1 (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (floor h) (* dY.v (* (floor h) dY.v))))))))
156.0ms
alphay
@-inf
(/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay))))

preprocess8.8s (1.4%)

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 51400 to 15380 computations (70.1% saved)

explain6.6s (1%)

Results
3.4s15286×0valid
58.0ms74×1valid
Compiler

Compiled 16652 to 1662 computations (90% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.8s
ival-mult: 676.0ms (37.6% of total)
ival-div: 210.0ms (11.7% of total)
ival-add: 153.0ms (8.5% of total)
ival-sub: 107.0ms (6% of total)
ival-log: 93.0ms (5.2% of total)
ival-sin: 82.0ms (4.6% of total)
ival-sqrt: 79.0ms (4.4% of total)
ival-pi: 54.0ms (3% of total)
ival-floor: 48.0ms (2.7% of total)
ival-cos: 48.0ms (2.7% of total)
ival-exp: 39.0ms (2.2% of total)
ival-neg: 35.0ms (1.9% of total)
const: 27.0ms (1.5% of total)
...c/correct-round.rkt:121:19: 26.0ms (1.4% of total)
ival-tan: 21.0ms (1.2% of total)
ival-fmax: 19.0ms (1.1% of total)
ival-if: 16.0ms (0.9% of total)
ival-log2: 15.0ms (0.8% of total)
ival-fabs: 10.0ms (0.6% of total)
backward-pass: 8.0ms (0.4% of total)
ival-atan: 8.0ms (0.4% of total)
ival->=: 7.0ms (0.4% of total)
ival-sinh: 6.0ms (0.3% of total)
ival->: 5.0ms (0.3% of total)
ival-asin: 5.0ms (0.3% of total)
ival-<: 2.0ms (0.1% of total)

bsearch39.0ms (0%)

Algorithm
70×binary-search
12×left-value
Stop Event
70×narrow-enough
Compiler

Compiled 3881 to 1847 computations (52.4% saved)

Profiling

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