Herbie run

Date:Thursday, May 23rd, 2024
Commit:7841f259 on main
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: 10.8min)

simplify2.4min (22.5%)

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

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)

sample1.5min (14%)

Results
1.2min247632×0valid
1.6s8365×0invalid
661.0ms2120×0precondition
14.0ms48×1valid
Precisions
Click to see histograms. Total time spent on operations: 58.4s
ival-mult: 13.7s (23.5% of total)
ival-<=: 9.7s (16.5% of total)
...c/correct-round.rkt:121:19: 8.4s (14.3% of total)
ival-div: 5.0s (8.6% of total)
ival-sub: 2.4s (4.1% of total)
ival-sqrt: 2.1s (3.5% of total)
ival-sin: 1.9s (3.3% of total)
ival-add: 1.9s (3.3% of total)
ival-log: 1.8s (3.2% of total)
ival-fabs: 1.6s (2.8% of total)
ival-and: 1.5s (2.6% of total)
ival-pi: 1.0s (1.8% of total)
ival-neg: 1.0s (1.7% of total)
ival-cos: 954.0ms (1.6% of total)
ival-exp: 786.0ms (1.3% of total)
ival-floor: 731.0ms (1.3% of total)
ival-tan: 520.0ms (0.9% of total)
ival-<: 456.0ms (0.8% of total)
const: 441.0ms (0.8% of total)
ival-==: 441.0ms (0.8% of total)
ival-if: 385.0ms (0.7% of total)
ival-fmax: 356.0ms (0.6% of total)
ival->: 307.0ms (0.5% of total)
ival-log2: 259.0ms (0.4% of total)
ival->=: 166.0ms (0.3% of total)
ival-asin: 158.0ms (0.3% of total)
ival-sinh: 137.0ms (0.2% of total)
ival-atan: 123.0ms (0.2% of total)
backward-pass: 74.0ms (0.1% of total)
Bogosity

prune57.3s (8.9%)

Counts
152282 → 4062
Compiler

Compiled 362196 to 132286 computations (63.5% saved)

end44.9s (7%)

localize43.6s (6.8%)

Results
18.6s26010×0valid
7.6s784×5exit
1.7s1993×0invalid
1.5s518×1valid
555.0ms1159×0unsamplable
Compiler

Compiled 103174 to 5501 computations (94.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.6s
ival-mult: 4.8s (25.8% of total)
ival-div: 2.2s (11.6% of total)
ival-expm1: 1.7s (9.3% of total)
ival-pow: 1.6s (8.4% of total)
ival-add: 1.1s (5.7% of total)
backward-pass: 745.0ms (4% of total)
ival-sin: 730.0ms (3.9% of total)
ival-exp: 643.0ms (3.5% of total)
ival-sqrt: 554.0ms (3% of total)
ival-cos: 473.0ms (2.5% of total)
ival-fma: 458.0ms (2.5% of total)
ival-tan: 389.0ms (2.1% of total)
ival-sub: 382.0ms (2.1% of total)
...c/correct-round.rkt:121:19: 379.0ms (2% of total)
ival-log: 371.0ms (2% of total)
ival-log1p: 362.0ms (1.9% of total)
ival-pi: 310.0ms (1.7% of total)
ival-neg: 274.0ms (1.5% of total)
ival-hypot: 220.0ms (1.2% of total)
ival-fmax: 160.0ms (0.9% of total)
ival-if: 158.0ms (0.8% of total)
ival-atan: 143.0ms (0.8% of total)
const: 99.0ms (0.5% of total)
ival-floor: 95.0ms (0.5% of total)
ival-log2: 90.0ms (0.5% of total)
ival-cbrt: 48.0ms (0.3% of total)
ival-asin: 47.0ms (0.3% of total)
ival->=: 44.0ms (0.2% of total)
ival->: 40.0ms (0.2% of total)
ival-fabs: 31.0ms (0.2% of total)
ival-sinh: 17.0ms (0.1% of total)
ival-<: 13.0ms (0.1% of total)
ival-e: 8.0ms (0% of total)

eval34.6s (5.4%)

Compiler

Compiled 17062972 to 625865 computations (96.3% saved)

analyze32.7s (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: 21.6s
ival-mult: 5.6s (25.7% of total)
ival-<=: 4.1s (19.2% of total)
...c/correct-round.rkt:121:19: 2.1s (9.6% of total)
ival-fabs: 1.7s (8% of total)
ival-div: 1.2s (5.6% of total)
ival-add: 1.0s (4.7% of total)
ival-floor: 822.0ms (3.8% of total)
ival-sqrt: 728.0ms (3.4% of total)
ival-and: 650.0ms (3% of total)
ival-sub: 507.0ms (2.4% of total)
ival-if: 454.0ms (2.1% of total)
ival-fmax: 405.0ms (1.9% of total)
ival-log: 405.0ms (1.9% of total)
ival-sin: 371.0ms (1.7% of total)
ival-cos: 237.0ms (1.1% of total)
ival-==: 203.0ms (0.9% of total)
ival-log2: 177.0ms (0.8% of total)
ival-exp: 137.0ms (0.6% of total)
ival->: 132.0ms (0.6% of total)
const: 126.0ms (0.6% of total)
ival-tan: 117.0ms (0.5% of total)
ival->=: 80.0ms (0.4% of total)
ival-pi: 73.0ms (0.3% of total)
ival-neg: 73.0ms (0.3% of total)
ival-<: 62.0ms (0.3% of total)
ival-atan: 36.0ms (0.2% of total)
ival-sinh: 31.0ms (0.1% of total)
backward-pass: 22.0ms (0.1% of total)
ival-asin: 17.0ms (0.1% of total)

rewrite31.8s (4.9%)

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

regimes29.8s (4.6%)

Counts
9655 → 401
Calls

145 calls:

853.0ms
s
835.0ms
ux
824.0ms
uy
736.0ms
maxCos
709.0ms
(*.f32 (*.f32 uy #s(literal 2 binary32)) (PI.f32))
Compiler

Compiled 14799 to 10226 computations (30.9% saved)

series27.1s (4.2%)

Counts
2012 → 56514
Calls

14022 calls:

TimeVariablePointExpression
714.0ms
cosTheta_O
@0
(* (pow (exp sinTheta_i) (/ sinTheta_O (neg v))) (/ (* cosTheta_O (/ (/ cosTheta_i v) v)) (* (sinh (/ 1 v)) 2)))
253.0ms
xi
@0
(+ (* (* (- 1 ux) maxCos) (* ux zi)) (* (sqrt (+ 1 (* maxCos (* (- 1 ux) (* (* ux ux) (* maxCos (+ ux -1))))))) (+ (* (cos (* uy (* 2 (PI)))) xi) (pow (cbrt (* (sin (* uy (* 2 (PI)))) yi)) 3))))
236.0ms
sinTheta_i
@0
(/ (* cosTheta_i cosTheta_O) (* (* (sinh (/ 1 v)) (* (* v 2) v)) (pow (+ 1 sinTheta_i) (/ sinTheta_O v))))
163.0ms
c
@-inf
(* (/ 1 c) (/ 1 (+ 1 (+ (/ (pow (PI) -1/2) (* cosTheta c)) (- (/ 1 c) (/ (pow (PI) -1/2) c))))))
162.0ms
alpha
@inf
(* (/ (/ (+ (* alpha alpha) -1) (PI)) (* 2 (log alpha))) (/ 1 (+ (* (+ (* alpha alpha) -1) (pow cosTheta 2)) 1)))

preprocess8.9s (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)

explain7.4s (1.2%)

Results
4.4s15286×0valid
41.0ms74×1valid
Compiler

Compiled 16652 to 1662 computations (90% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.7s
ival-mult: 815.0ms (30.6% of total)
ival-sqrt: 527.0ms (19.8% of total)
ival-floor: 258.0ms (9.7% of total)
ival-div: 256.0ms (9.6% of total)
ival-add: 101.0ms (3.8% of total)
ival-log: 94.0ms (3.5% of total)
ival-sin: 93.0ms (3.5% of total)
ival-sub: 88.0ms (3.3% of total)
ival-fabs: 84.0ms (3.2% of total)
ival-neg: 56.0ms (2.1% of total)
ival-cos: 46.0ms (1.7% of total)
ival-exp: 39.0ms (1.5% of total)
ival-if: 30.0ms (1.1% of total)
...c/correct-round.rkt:121:19: 30.0ms (1.1% of total)
ival-pi: 29.0ms (1.1% of total)
const: 27.0ms (1% of total)
ival-fmax: 19.0ms (0.7% of total)
ival-tan: 18.0ms (0.7% of total)
ival-log2: 17.0ms (0.6% of total)
backward-pass: 8.0ms (0.3% of total)
ival-atan: 7.0ms (0.3% of total)
ival->=: 6.0ms (0.2% of total)
ival->: 5.0ms (0.2% 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)

bsearch44.0ms (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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