Herbie run

Date:Sunday, April 28th, 2024
Commit:49c7f308 on main
Hostname:nightly with Racket 8.11.1
Seed:2024119
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)

sample6.0min (33%)

Results
2.1min25780×5exit
1.2min129900×1valid
43.0s270647×0valid
26.1s8183×3valid
20.0s19168×2valid
14.3s49739×0unsamplable
9.9s1406×4valid
3.4s18959×0invalid
2.9s11367×1invalid
1.2s1801×2invalid
290.0ms8×5valid
184.0ms904×0precondition
137.0ms1×4unsamplable
63.0ms71×1unsamplable
25.0ms1×3unsamplable
10.0ms17×3invalid
2.0ms1×2unsamplable
Precisions
Click to see histograms. Total time spent on operations: 4.7min
ival-pow: 2.1min (43.6% of total)
ival-mult: 30.8s (10.9% of total)
ival-sin: 25.3s (9% of total)
ival-cos: 22.0s (7.8% of total)
ival-div: 19.2s (6.8% of total)
backward-pass: 9.8s (3.5% of total)
ival-sub: 9.5s (3.4% of total)
ival-add: 9.4s (3.3% of total)
ival-exp: 8.1s (2.9% of total)
ival-log: 6.6s (2.3% of total)
ival-sqrt: 5.2s (1.8% of total)
ival-neg: 4.4s (1.5% of total)
ival-<: 3.1s (1.1% of total)
const: 1.2s (0.4% of total)
ival-atan2: 1.2s (0.4% of total)
ival-pi: 678.0ms (0.2% of total)
ival-tan: 560.0ms (0.2% of total)
ival-atan: 527.0ms (0.2% of total)
ival-and: 427.0ms (0.2% of total)
ival-acos: 382.0ms (0.1% of total)
ival-cbrt: 375.0ms (0.1% of total)
ival-<=: 329.0ms (0.1% of total)
ival-fabs: 211.0ms (0.1% of total)
ival-asin: 160.0ms (0.1% of total)
ival-==: 2.0ms (0% of total)
ival-or: 0.0ms (0% of total)
Bogosity

simplify2.2min (12.4%)

Algorithm
248×egg-herbie
Rules
72241×fma-define
62099×*-commutative
61704×distribute-lft-in
58505×times-frac
56590×distribute-rgt-in
Stop Event
51×saturated
196×node limit
1×unsound
Counts
147734 → 122530

localize2.2min (12.3%)

Algorithm
200×egg-herbie
Rules
108648×fma-define
76428×fma-neg
47194×distribute-lft-in
42157×unsub-neg
42085×distribute-rgt-in
Stop Event
60×saturated
140×node limit
Results
37.4s4434×5exit
20.2s11944×1valid
13.1s28555×0valid
7.5s2141×2valid
2.8s375×3valid
2.5s3430×0invalid
686.0ms50×4valid
643.0ms170×1invalid
96.0ms21×2invalid
5.0ms1×5valid
1.0ms1×0unsamplable
Compiler

Compiled 96621 to 7746 computations (92% saved)

Precisions
Click to see histograms. Total time spent on operations: 57.8s
ival-mult: 10.1s (17.5% of total)
ival-sin: 9.0s (15.6% of total)
ival-pow: 9.0s (15.5% of total)
backward-pass: 6.0s (10.4% of total)
ival-cos: 5.3s (9.2% of total)
ival-div: 4.5s (7.8% of total)
ival-exp: 1.7s (3% of total)
ival-add: 1.7s (2.9% of total)
ival-log: 1.6s (2.8% of total)
ival-sub: 1.5s (2.6% of total)
ival-expm1: 1.4s (2.4% of total)
ival-sqrt: 983.0ms (1.7% of total)
ival-log1p: 846.0ms (1.5% of total)
ival-hypot: 688.0ms (1.2% of total)
ival-fma: 637.0ms (1.1% of total)
ival-neg: 486.0ms (0.8% of total)
ival-cbrt: 482.0ms (0.8% of total)
ival-tan: 452.0ms (0.8% of total)
ival-atan2: 444.0ms (0.8% of total)
ival-atan: 334.0ms (0.6% of total)
const: 254.0ms (0.4% of total)
ival-acos: 149.0ms (0.3% of total)
ival-pi: 124.0ms (0.2% of total)
ival-fabs: 119.0ms (0.2% of total)
ival-asin: 21.0ms (0% of total)
ival-e: 7.0ms (0% of total)
ival-cosh: 3.0ms (0% of total)

soundness2.0min (11.1%)

Rules
86656×fma-define
71398×log1p-expm1-u
56334×distribute-lft-in
53035×times-frac
52815×expm1-log1p-u
Stop Event
16×saturated
44×fuel
273×node limit
2×unsound
7×done
Compiler

Compiled 78989 to 22541 computations (71.5% saved)

regimes1.1min (5.8%)

Counts
28044 → 1040
Calls

143 calls:

4.7s
phi1
3.8s
lambda1
3.6s
lambda2
3.2s
phi2
2.9s
a
Compiler

Compiled 14415 to 9570 computations (33.6% saved)

prune56.3s (5.2%)

Counts
196141 → 8312
Compiler

Compiled 602351 to 293548 computations (51.3% saved)

rewrite53.3s (4.9%)

Algorithm
197×batch-egg-rewrite
Rules
121129×log1p-expm1-u
89183×expm1-log1p-u
55472×pow1
53294×add-exp-log
46730×add-log-exp
Stop Event
192×node limit
5×unsound
Counts
3019 → 78301

eval43.1s (4%)

Compiler

Compiled 9212882 to 896900 computations (90.3% saved)

series38.6s (3.5%)

Counts
3019 → 69433
Calls

17853 calls:

TimeVariablePointExpression
503.0ms
a
@0
(/ (neg (sqrt (* (* 2 (* (* 4 (/ (* a (* b (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* a (* b (* b (neg a)))))) (+ (/ (+ (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)))))))) (* 4 (* a (* b (* b (neg a))))))
360.0ms
b
@0
(* (/ (neg (sqrt (* (* 2 (* (* 4 (/ (* a (* b (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* a (* b (* b (neg a)))))) (+ (sqrt (+ (* (* (* 2 (* (- (pow b 2) (pow a 2)) (sin (* angle (* (PI) 1/180))))) (/ (/ (cos (* angle (* (PI) 1/180))) x-scale) y-scale)) (* (* 2 (* (- (pow b 2) (pow a 2)) (sin (* angle (* (PI) 1/180))))) (/ (/ (cos (* angle (* (PI) 1/180))) x-scale) y-scale))) (* (- (/ (+ (pow (* a (sin (* angle (* (PI) 1/180)))) 2) (pow (* b (cos (* angle (* (PI) 1/180)))) 2)) (pow x-scale 2)) (/ (+ (pow (* a (cos (* angle (* (PI) 1/180)))) 2) (pow (* b (sin (* angle (* (PI) 1/180)))) 2)) (pow y-scale 2))) (- (/ (+ (pow (* a (sin (* angle (* (PI) 1/180)))) 2) (pow (* b (cos (* angle (* (PI) 1/180)))) 2)) (pow x-scale 2)) (/ (+ (pow (* a (cos (* angle (* (PI) 1/180)))) 2) (pow (* b (sin (* angle (* (PI) 1/180)))) 2)) (pow y-scale 2)))))) (+ (/ (+ (pow (* a (sin (* angle (* (PI) 1/180)))) 2) (pow (* b (cos (* angle (* (PI) 1/180)))) 2)) (pow x-scale 2)) (/ (+ (pow (* a (cos (* angle (* (PI) 1/180)))) 2) (pow (* b (sin (* angle (* (PI) 1/180)))) 2)) (pow y-scale 2))))))) (* 4 (* a (* b (* b (neg a)))))) (pow (* x-scale y-scale) 2))
313.0ms
b
@0
(* (/ (neg (+ (* 1/2 (/ (+ (* -2 (* (+ (* (pow b 2) (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (pow x-scale 2))) (* (pow a 2) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (pow x-scale 2)))) (pow (sqrt (+ (* (* (cos (* 1/180 (* angle (PI)))) a) (* (cos (* 1/180 (* angle (PI)))) a)) (* (* b (sin (* 1/180 (* angle (PI))))) (* b (sin (* 1/180 (* angle (PI)))))))) 2))) (* 4 (* (pow (cos (* 1/180 (* angle (PI)))) 2) (/ (* (pow (sin (* 1/180 (* angle (PI)))) 2) (pow (- (pow b 2) (pow a 2)) 2)) (pow x-scale 2))))) (pow (sqrt (+ (* (* (cos (* 1/180 (* angle (PI)))) a) (* (cos (* 1/180 (* angle (PI)))) a)) (* (* b (sin (* 1/180 (* angle (PI))))) (* b (sin (* 1/180 (* angle (PI)))))))) 2))) (+ (* (pow b 2) (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (pow x-scale 2))) (* (pow a 2) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (pow x-scale 2)))))) (sin (* angle (/ (PI) 180)))) (/ y-scale (* (* 2 (- (pow b 2) (pow a 2))) (/ (cos (* angle (/ (PI) 180))) x-scale))))
294.0ms
ew
@-inf
(log (pow (exp (cos (atan (* eh (/ (tan t) (neg ew)))))) (cos t)))
280.0ms
a
@0
(* a x-scale)

bsearch26.8s (2.5%)

Algorithm
409×binary-search
66×left-value
Stop Event
8×predicate-same
401×narrow-enough
Results
11.6s15078×1valid
6.7s32060×0valid
1.7s1943×2valid
1.4s924×3valid
133.0ms1298×0invalid
59.0ms11×4valid
Compiler

Compiled 144192 to 95318 computations (33.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.9s
ival-sin: 3.9s (22% of total)
ival-cos: 3.9s (22% of total)
ival-mult: 3.1s (17.3% of total)
ival-pow: 1.4s (7.7% of total)
ival-div: 1.1s (6.1% of total)
ival-sub: 995.0ms (5.6% of total)
ival-add: 750.0ms (4.2% of total)
backward-pass: 606.0ms (3.4% of total)
ival-sqrt: 484.0ms (2.7% of total)
ival-atan2: 369.0ms (2.1% of total)
ival-acos: 221.0ms (1.2% of total)
ival-atan: 176.0ms (1% of total)
ival-exp: 157.0ms (0.9% of total)
ival-tan: 153.0ms (0.9% of total)
ival-log: 112.0ms (0.6% of total)
ival-neg: 97.0ms (0.5% of total)
const: 92.0ms (0.5% of total)
ival-fabs: 90.0ms (0.5% of total)
ival-pi: 79.0ms (0.4% of total)
ival-asin: 37.0ms (0.2% of total)
ival-cbrt: 9.0ms (0.1% of total)

analyze24.8s (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: 17.2s
ival-mult: 4.8s (28.1% of total)
ival-pow: 2.8s (16.4% of total)
ival-cos: 2.0s (11.9% of total)
ival-sin: 1.6s (9.6% of total)
ival-div: 1.5s (8.5% of total)
ival-sub: 1.0s (5.9% of total)
ival-add: 754.0ms (4.4% of total)
ival-sqrt: 662.0ms (3.8% of total)
ival-neg: 474.0ms (2.8% of total)
ival-<: 392.0ms (2.3% of total)
ival-exp: 195.0ms (1.1% of total)
ival-tan: 183.0ms (1.1% of total)
ival-atan2: 158.0ms (0.9% of total)
const: 103.0ms (0.6% of total)
ival-acos: 101.0ms (0.6% of total)
ival-pi: 92.0ms (0.5% of total)
ival-and: 53.0ms (0.3% of total)
ival-fabs: 50.0ms (0.3% of total)
ival-atan: 48.0ms (0.3% of total)
ival-log: 48.0ms (0.3% of total)
ival-asin: 34.0ms (0.2% of total)
backward-pass: 33.0ms (0.2% of total)
ival-cbrt: 20.0ms (0.1% of total)
ival-<=: 3.0ms (0% of total)
ival-or: 0.0ms (0% of total)
ival-==: 0.0ms (0% of total)

explain19.7s (1.8%)

Results
5.9s8374×1valid
3.2s15688×0valid
2.6s1882×2valid
1.7s582×3valid
572.0ms98×4valid
Compiler

Compiled 20263 to 2450 computations (87.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.5s
ival-sin: 2.2s (23.1% of total)
ival-cos: 1.4s (14.6% of total)
ival-mult: 1.3s (14.1% of total)
backward-pass: 788.0ms (8.3% of total)
ival-pow: 781.0ms (8.2% of total)
ival-div: 777.0ms (8.2% of total)
ival-add: 438.0ms (4.6% of total)
ival-log: 369.0ms (3.9% of total)
ival-sub: 344.0ms (3.6% of total)
ival-exp: 267.0ms (2.8% of total)
ival-sqrt: 220.0ms (2.3% of total)
ival-neg: 206.0ms (2.2% of total)
ival-tan: 128.0ms (1.3% of total)
ival-atan2: 68.0ms (0.7% of total)
const: 58.0ms (0.6% of total)
ival-pi: 39.0ms (0.4% of total)
ival-atan: 36.0ms (0.4% of total)
ival-fabs: 23.0ms (0.2% of total)
ival-acos: 22.0ms (0.2% of total)
ival-cbrt: 20.0ms (0.2% of total)
ival-asin: 9.0ms (0.1% of total)

preprocess14.5s (1.3%)

Algorithm
52×egg-herbie
Rules
32328×fma-define
19274×fma-neg
13234×div-sub
11584×unsub-neg
11427×sub-neg
Stop Event
22×saturated
30×node limit
Compiler

Compiled 67692 to 24116 computations (64.4% saved)

end0.0ms (0%)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-exp: 23.0ms (102.2% of total)

Profiling

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