Herbie run

Date:Tuesday, April 16th, 2024
Commit:97bdded0 on zane-regimes-8-iters
Hostname:nightly with Racket 8.11.1
Seed:2024107
Parameters:256 points for 8 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: 13.6min)

localize3.7min (26.9%)

Results
1.8min50650×0valid
10.6s2860×0invalid
3.3s2201×0unsamplable
40.1s1376×5exit
6.3s1280×1valid
1.0ms2valid
Compiler

Compiled 208279 to 60096 computations (71.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.4min
ival-mult: 34.1s (24% of total)
ival-pow: 30.5s (21.4% of total)
ival-div: 14.6s (10.2% of total)
backward-pass: 7.8s (5.5% of total)
ival-tan: 6.4s (4.5% of total)
ival-add: 6.3s (4.4% of total)
ival-sub: 5.2s (3.6% of total)
ival-sin: 5.0s (3.5% of total)
ival-sqrt: 4.2s (3% of total)
ival-fmax: 3.9s (2.7% of total)
ival-log: 3.8s (2.6% of total)
ival-fma: 3.3s (2.3% of total)
ival-exp: 3.1s (2.2% of total)
const: 2.7s (1.9% of total)
ival-atan: 2.1s (1.5% of total)
ival-cos: 2.1s (1.4% of total)
ival-log1p: 1.4s (1% of total)
ival-hypot: 1.2s (0.8% of total)
ival-if: 788.0ms (0.6% of total)
ival-neg: 774.0ms (0.5% of total)
ival-cbrt: 538.0ms (0.4% of total)
ival-expm1: 473.0ms (0.3% of total)
ival-log2: 469.0ms (0.3% of total)
ival->: 413.0ms (0.3% of total)
ival-floor: 290.0ms (0.2% of total)
ival-sinh: 251.0ms (0.2% of total)
ival->=: 170.0ms (0.1% of total)
ival-acos: 138.0ms (0.1% of total)
ival-pi: 128.0ms (0.1% of total)
ival-fabs: 85.0ms (0.1% of total)
ival-asin: 82.0ms (0.1% of total)
ival-<: 54.0ms (0% of total)
ival-e: 47.0ms (0% of total)

eval1.8min (13.3%)

Compiler

Compiled 16238446 to 4740482 computations (70.8% saved)

simplify1.7min (12.2%)

Algorithm
250×egg-herbie
Rules
206788×fma-define
134054×associate-*r*
131762×*-commutative
125594×distribute-lft-in
112258×distribute-rgt-in
Stop Event
30×saturated
220×node limit
Counts
119501 → 100022

sample1.5min (11.2%)

Results
1.1min247680×0valid
1.4s8343×0invalid
760.0ms2120×0precondition
22.0ms54×5exit
Precisions
Click to see histograms. Total time spent on operations: 54.8s
ival-mult: 13.8s (25.2% of total)
ival-<=: 10.4s (19.1% of total)
ival-div: 5.5s (10% of total)
ival-sub: 2.5s (4.5% of total)
ival-sin: 2.4s (4.4% of total)
ival-add: 2.4s (4.3% of total)
ival-fabs: 2.0s (3.6% of total)
ival-log: 1.8s (3.2% of total)
ival-tan: 1.7s (3% of total)
ival-cos: 1.6s (2.9% of total)
ival-sqrt: 1.6s (2.9% of total)
ival-and: 1.6s (2.9% of total)
const: 1.3s (2.4% of total)
ival-exp: 1.2s (2.1% of total)
ival-floor: 949.0ms (1.7% of total)
ival-atan: 693.0ms (1.3% of total)
ival-neg: 645.0ms (1.2% of total)
ival-pi: 622.0ms (1.1% of total)
ival-fmax: 406.0ms (0.7% of total)
ival-<: 390.0ms (0.7% of total)
ival->: 310.0ms (0.6% of total)
ival-==: 291.0ms (0.5% of total)
ival-if: 270.0ms (0.5% of total)
ival-log2: 233.0ms (0.4% of total)
ival-asin: 131.0ms (0.2% of total)
backward-pass: 130.0ms (0.2% of total)
ival->=: 96.0ms (0.2% of total)
ival-sinh: 95.0ms (0.2% of total)
Bogosity

soundness1.1min (7.9%)

Rules
132070×fma-define
85452×associate-*r*
75992×times-frac
73634×distribute-lft-in
73628×*-commutative
Stop Event
saturated
209×node limit
27×fuel
done
Compiler

Compiled 69331 to 30208 computations (56.4% saved)

prune1.0min (7.4%)

Counts
202183 → 9405
Compiler

Compiled 647977 to 369581 computations (43% saved)

regimes51.3s (6.3%)

Counts
14319 → 388
Calls

145 calls:

1.9s
cosTheta_i
1.5s
s
1.4s
dY.v
1.3s
dY.u
1.3s
dX.u
Compiler

Compiled 14606 to 10107 computations (30.8% saved)

rewrite41.7s (5.1%)

Algorithm
220×batch-egg-rewrite
Rules
105875×log1p-expm1-u
85303×expm1-log1p-u
67110×add-exp-log
66079×pow1
65581×add-log-exp
Stop Event
220×node limit
Counts
2460 → 57177

series29.9s (3.7%)

Counts
2460 → 62324
Calls

14682 calls:

TimeVariablePointExpression
1.1s
h
@-inf
(pow (pow (exp 2) (pow (cbrt (log (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)) (cbrt (log (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))))))))))
463.0ms
d
@inf
(pow (log2 (sqrt (fmax (pow (* (floor w) dX.u) 2) (pow (* (floor d) dY.w) 2)))) 3)
346.0ms
sinTheta_O
@inf
(/ 1 (/ v (* 1/2 (exp (- (/ (- (* cosTheta_i cosTheta_O) (* sinTheta_i sinTheta_O)) v) (- (/ 1 v) 6931/10000))))))
315.0ms
alpha
@inf
(* (+ (* alpha alpha) -1) (/ 1/2 (* (PI) (log alpha))))
293.0ms
h
@-inf
(pow (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 d) dY.w) 2)) 1/4)

analyze25.8s (3.2%)

Algorithm
30×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%2.6%97.4%0%0%0%0
0.2%0%2.6%97.4%0%0%0%1
9.2%0.2%2.4%97.4%0%0%0%2
10.8%0.3%2.3%97.4%0%0%0%3
15.5%0.4%2.2%97.4%0%0%0%4
48.8%1.3%1.3%97.4%0%0%0%5
53.6%1.4%1.2%97.4%0%0%0%6
70.7%1.8%0.8%97.4%0%0%0%7
72.6%1.9%0.7%97.4%0%0.1%0%8
81.8%2.1%0.5%97.4%0%0.1%0%9
83.3%2.1%0.4%97.4%0%0.1%0%10
88.8%2.2%0.3%97.4%0%0.1%0%11
89.5%2.2%0.3%97.4%0%0.1%0%12
Compiler

Compiled 2668 to 1267 computations (52.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 16.1s
ival-mult: 4.2s (26.2% of total)
ival-<=: 3.3s (20.7% of total)
ival-fabs: 1.4s (8.4% of total)
ival-add: 969.0ms (6% of total)
ival-div: 947.0ms (5.9% of total)
ival-floor: 750.0ms (4.7% of total)
ival-fmax: 649.0ms (4% of total)
ival-sqrt: 547.0ms (3.4% of total)
ival-and: 542.0ms (3.4% of total)
ival-if: 490.0ms (3% of total)
const: 322.0ms (2% of total)
ival-log2: 306.0ms (1.9% of total)
ival-sub: 264.0ms (1.6% of total)
ival-==: 228.0ms (1.4% of total)
ival-sin: 221.0ms (1.4% of total)
ival-tan: 198.0ms (1.2% of total)
ival-cos: 179.0ms (1.1% of total)
ival-log: 99.0ms (0.6% of total)
ival->: 93.0ms (0.6% of total)
ival->=: 88.0ms (0.5% of total)
ival-atan: 63.0ms (0.4% of total)
ival-exp: 58.0ms (0.4% of total)
ival-<: 47.0ms (0.3% of total)
ival-neg: 37.0ms (0.2% of total)
backward-pass: 28.0ms (0.2% of total)
ival-pi: 28.0ms (0.2% of total)
ival-asin: 17.0ms (0.1% of total)
ival-sinh: 16.0ms (0.1% of total)

explain14.2s (1.7%)

Results
10.2s15304×0valid
73.0ms56×5exit
Compiler

Compiled 16652 to 4502 computations (73% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.2s
ival-mult: 2.8s (34.8% of total)
ival-tan: 798.0ms (9.8% of total)
ival-div: 792.0ms (9.7% of total)
ival-sin: 721.0ms (8.8% of total)
ival-sub: 665.0ms (8.1% of total)
ival-cos: 530.0ms (6.5% of total)
ival-add: 461.0ms (5.6% of total)
ival-atan: 372.0ms (4.6% of total)
ival-log: 264.0ms (3.2% of total)
ival-sqrt: 226.0ms (2.8% of total)
const: 139.0ms (1.7% of total)
ival-exp: 84.0ms (1% of total)
ival-floor: 51.0ms (0.6% of total)
ival-neg: 44.0ms (0.5% of total)
ival-pi: 33.0ms (0.4% of total)
backward-pass: 29.0ms (0.4% of total)
ival-sinh: 29.0ms (0.4% of total)
ival-fmax: 22.0ms (0.3% of total)
ival-if: 19.0ms (0.2% of total)
ival-log2: 14.0ms (0.2% of total)
ival-fabs: 13.0ms (0.2% of total)
ival->=: 6.0ms (0.1% of total)
ival->: 6.0ms (0.1% of total)
ival-asin: 5.0ms (0.1% of total)
ival-<: 4.0ms (0% of total)

preprocess9.6s (1.2%)

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 52436 to 25002 computations (52.3% saved)

bsearch139.0ms (0%)

Algorithm
62×binary-search
24×left-value
Stop Event
62×narrow-enough
Compiler

Compiled 4083 to 1942 computations (52.4% saved)

end0.0ms (0%)

Profiling

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