Herbie run

Date:Monday, April 22nd, 2024
Commit:1ba62266 on faster-localize-cost
Hostname:nightly with Racket 8.11.1
Seed:2024113
Parameters:256 points for 4 iterations
Flags:
reduce: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: 18.2min)

sample5.8min (31.7%)

Results
47.1s289686×0valid
57.0s115626×1valid
13.1s47327×0unsamplable
4.1s27551×0invalid
2.3min24859×5exit
17.3s14968×2valid
21.1s7491×3valid
1.9s3761×1invalid
6.2s1041×4valid
93.0ms889×0precondition
518.0ms819×2invalid
33.0ms40×1unsamplable
221.0ms4×5valid
2.0ms1×2unsamplable
Precisions
Click to see histograms. Total time spent on operations: 4.5min
ival-pow: 2.2min (49% of total)
ival-mult: 27.6s (10.2% of total)
ival-div: 18.1s (6.7% of total)
ival-sin: 16.0s (5.9% of total)
ival-cos: 14.8s (5.4% of total)
backward-pass: 14.0s (5.2% of total)
ival-add: 9.2s (3.4% of total)
ival-sub: 8.8s (3.2% of total)
ival-exp: 6.6s (2.4% of total)
ival-sqrt: 5.0s (1.8% of total)
ival-log: 4.7s (1.7% of total)
ival-neg: 3.9s (1.4% of total)
ival-<: 3.0s (1.1% of total)
ival-pi: 1.1s (0.4% of total)
const: 1.1s (0.4% of total)
ival-atan2: 968.0ms (0.4% of total)
ival-tan: 887.0ms (0.3% of total)
ival-atan: 528.0ms (0.2% of total)
ival-acos: 513.0ms (0.2% of total)
ival-and: 415.0ms (0.2% of total)
ival-cbrt: 400.0ms (0.1% of total)
ival-fabs: 264.0ms (0.1% of total)
ival-asin: 244.0ms (0.1% of total)
ival-<=: 218.0ms (0.1% of total)
ival-==: 2.0ms (0% of total)
ival-or: 0.0ms (0% of total)
Bogosity

simplify2.4min (13.4%)

Algorithm
241×egg-herbie
Rules
73208×fma-define
59718×*-commutative
57070×times-frac
55956×distribute-lft-in
50988×distribute-rgt-in
Stop Event
51×saturated
189×node limit
1×unsound
Counts
140901 → 116936

localize2.2min (11.8%)

Algorithm
191×egg-herbie
Rules
85420×fma-define
79860×fma-neg
40911×unsub-neg
40241×associate-*r*
39734×distribute-lft-in
Stop Event
63×saturated
128×node limit
Results
14.4s28205×0valid
17.5s9788×1valid
38.5s4844×5exit
3.1s3673×0invalid
5.4s1719×2valid
2.3s420×3valid
571.0ms145×1invalid
21.0ms70×0unsamplable
387.0ms31×4valid
5.0ms1×2invalid
Compiler

Compiled 92971 to 7266 computations (92.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 56.5s
ival-mult: 10.1s (17.8% of total)
ival-pow: 9.5s (16.8% of total)
ival-sin: 8.1s (14.3% of total)
backward-pass: 6.4s (11.2% of total)
ival-cos: 5.5s (9.7% of total)
ival-div: 4.4s (7.8% of total)
ival-log: 1.7s (3.1% of total)
ival-add: 1.7s (2.9% of total)
ival-sub: 1.2s (2.2% of total)
ival-sqrt: 1.1s (1.9% of total)
ival-expm1: 1.0s (1.8% of total)
ival-fma: 846.0ms (1.5% of total)
ival-exp: 827.0ms (1.5% of total)
ival-log1p: 724.0ms (1.3% of total)
ival-cbrt: 603.0ms (1.1% of total)
ival-neg: 575.0ms (1% of total)
ival-hypot: 546.0ms (1% of total)
ival-atan2: 536.0ms (0.9% of total)
ival-atan: 311.0ms (0.6% of total)
const: 253.0ms (0.4% of total)
ival-tan: 250.0ms (0.4% of total)
ival-acos: 172.0ms (0.3% of total)
ival-pi: 140.0ms (0.2% of total)
ival-fabs: 66.0ms (0.1% of total)
ival-asin: 62.0ms (0.1% of total)

soundness2.0min (10.7%)

Rules
90409×fma-define
67988×log1p-expm1-u
56736×expm1-log1p-u
50790×times-frac
50587×distribute-lft-in
Stop Event
14×saturated
43×fuel
271×node limit
3×unsound
8×done
Compiler

Compiled 68080 to 20011 computations (70.6% saved)

prune1.4min (7.8%)

Counts
187579 → 8488
Compiler

Compiled 594528 to 292328 computations (50.8% saved)

rewrite55.3s (5.1%)

Algorithm
190×batch-egg-rewrite
Rules
113978×log1p-expm1-u
87618×expm1-log1p-u
51436×pow1
49861×add-exp-log
46651×add-log-exp
Stop Event
187×node limit
3×unsound
Counts
2861 → 73787

regimes53.9s (4.9%)

Counts
25129 → 957
Calls

143 calls:

3.8s
phi1
3.7s
lambda1
3.3s
phi2
2.7s
lambda2
2.2s
a
Compiler

Compiled 12588 to 8252 computations (34.4% saved)

eval43.0s (3.9%)

Compiler

Compiled 9007520 to 839421 computations (90.7% saved)

series37.9s (3.5%)

Counts
2861 → 67114
Calls

17184 calls:

TimeVariablePointExpression
674.0ms
x-scale
@inf
(* (* 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)) (neg (+ (* (pow a 2) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (pow x-scale 2))) (* (pow b 2) (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (pow x-scale 2))))))))
424.0ms
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))))
422.0ms
y-scale
@0
(exp (log (+ (/ (pow (* a (cos (* 1/180 (* (PI) angle)))) 2) (pow y-scale 2)) (- (/ (pow (* a (sin (* 1/180 (* (PI) angle)))) 2) (pow x-scale 2)) (sqrt (+ (* 4 (/ (* (pow a 4) (pow (* (cos (* 1/180 (* (PI) angle))) (sin (* 1/180 (* (PI) angle)))) 2)) (pow (* x-scale y-scale) 2))) (pow (- (/ (pow (* a (sin (* 1/180 (* (PI) angle)))) 2) (pow x-scale 2)) (/ (pow (* a (cos (* 1/180 (* (PI) angle)))) 2) (pow y-scale 2))) 2)))))))
411.0ms
y-scale
@0
(/ (* y-scale (* 2 (- (/ (pow a 2) (pow y-scale 2)) (/ (pow b 2) (pow x-scale 2))))) (* (* angle (PI)) (- (pow b 2) (pow a 2))))
355.0ms
y-scale
@inf
(/ (sqrt (* (* b (* (pow a 2) (neg b))) (* (* 8 (* (* a (pow b 2)) (/ (neg a) (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))))))))))) (* (* a (pow b 2)) (/ (neg a) (pow (* x-scale y-scale) 2))))

analyze25.0s (2.3%)

Algorithm
53×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%79.4%20.6%0%0%0%0
14.8%11.8%67.6%20.6%0%0%0%1
22.6%17.7%60.4%21%0%0.9%0%2
32.7%24.7%50.8%21.2%0%3.3%0%3
39.8%29.8%45%21.2%0%4%0%4
45.4%33.8%40.6%21.2%0%4.5%0%5
48.4%35.7%38%21.2%0%5.1%0%6
51.8%37.8%35.2%21.2%0%5.7%0.1%7
53.5%38.9%33.8%21.3%0%6%0.1%8
56.4%40.6%31.4%21.3%0%6.6%0.2%9
57.7%41.4%30.3%21.3%0%6.8%0.2%10
59.8%42.7%28.7%21.3%0%7.1%0.3%11
61.3%43.5%27.5%21.3%0%7.5%0.3%12
Compiler

Compiled 1919 to 947 computations (50.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 16.9s
ival-mult: 5.8s (34.4% of total)
ival-pow: 2.7s (16.1% of total)
ival-cos: 1.5s (9.1% of total)
ival-sin: 1.5s (8.7% of total)
ival-div: 1.3s (7.9% of total)
ival-sub: 1.0s (6.2% of total)
ival-add: 799.0ms (4.7% of total)
ival-<: 560.0ms (3.3% of total)
ival-sqrt: 493.0ms (2.9% of total)
ival-neg: 321.0ms (1.9% of total)
ival-atan2: 139.0ms (0.8% of total)
ival-atan: 103.0ms (0.6% of total)
const: 91.0ms (0.5% of total)
ival-exp: 74.0ms (0.4% of total)
ival-pi: 70.0ms (0.4% of total)
ival-asin: 62.0ms (0.4% of total)
ival-tan: 54.0ms (0.3% of total)
ival-and: 50.0ms (0.3% of total)
ival-log: 50.0ms (0.3% of total)
ival-acos: 40.0ms (0.2% of total)
backward-pass: 32.0ms (0.2% of total)
ival-fabs: 32.0ms (0.2% of total)
ival-cbrt: 17.0ms (0.1% of total)
ival-<=: 3.0ms (0% of total)
ival-or: 0.0ms (0% of total)
ival-==: 0.0ms (0% of total)

bsearch20.5s (1.9%)

Algorithm
364×binary-search
92×left-value
Stop Event
12×predicate-same
352×narrow-enough
Results
7.1s32479×0valid
7.4s10526×1valid
1.1s1415×2valid
149.0ms1073×0invalid
626.0ms578×3valid
47.0ms10×4valid
Compiler

Compiled 117120 to 80950 computations (30.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.9s
ival-sin: 2.5s (19.6% of total)
ival-mult: 2.4s (18.7% of total)
ival-cos: 2.2s (17.1% of total)
ival-pow: 1.0s (8.2% of total)
ival-sub: 879.0ms (6.8% of total)
ival-div: 863.0ms (6.7% of total)
backward-pass: 654.0ms (5.1% of total)
ival-add: 470.0ms (3.7% of total)
ival-sqrt: 463.0ms (3.6% of total)
ival-atan: 330.0ms (2.6% of total)
ival-atan2: 216.0ms (1.7% of total)
ival-tan: 182.0ms (1.4% of total)
ival-neg: 132.0ms (1% of total)
ival-acos: 132.0ms (1% of total)
ival-exp: 83.0ms (0.6% of total)
const: 79.0ms (0.6% of total)
ival-pi: 70.0ms (0.5% of total)
ival-log: 66.0ms (0.5% of total)
ival-fabs: 37.0ms (0.3% of total)
ival-asin: 31.0ms (0.2% of total)

explain18.2s (1.7%)

Results
2.9s16436×0valid
5.2s7624×1valid
2.8s1460×2valid
1.8s530×3valid
394.0ms62×4valid
Compiler

Compiled 19842 to 2382 computations (88% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.6s
ival-sin: 1.8s (21.3% of total)
ival-mult: 1.5s (17% of total)
backward-pass: 920.0ms (10.8% of total)
ival-cos: 840.0ms (9.8% of total)
ival-pow: 667.0ms (7.8% of total)
ival-div: 630.0ms (7.4% of total)
ival-exp: 485.0ms (5.7% of total)
ival-add: 365.0ms (4.3% of total)
ival-sub: 304.0ms (3.6% of total)
ival-log: 282.0ms (3.3% of total)
ival-sqrt: 224.0ms (2.6% of total)
ival-tan: 179.0ms (2.1% of total)
ival-neg: 91.0ms (1.1% of total)
ival-pi: 66.0ms (0.8% of total)
const: 60.0ms (0.7% of total)
ival-atan2: 51.0ms (0.6% of total)
ival-atan: 32.0ms (0.4% of total)
ival-fabs: 27.0ms (0.3% of total)
ival-acos: 27.0ms (0.3% of total)
ival-cbrt: 20.0ms (0.2% of total)
ival-asin: 12.0ms (0.1% of total)

preprocess14.4s (1.3%)

Algorithm
51×egg-herbie
Rules
31500×fma-define
18832×fma-neg
12964×div-sub
11458×unsub-neg
11133×sub-neg
Stop Event
21×saturated
30×node limit
Compiler

Compiled 59672 to 20358 computations (65.9% saved)

end0.0ms (0%)

Precisions
Click to see histograms. Total time spent on operations: 3.6s
backward-pass: 3.6s (100% of total)

Profiling

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