Metrics for Herbie run

Date:	Thursday, May 16th, 2024
Commit:	9db37a23 on report-cost-multi-alts
Hostname:	nightly with Racket 8.11.1
Seed:	2024137
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

simplify2.1min (22.8%)

Algorithm

149×	egg-herbie

Rules

95830×	`fma-define`
80362×	`times-frac`
80306×	`*-commutative`
67472×	`distribute-lft-in`
63552×	`associate-r`

Stop Event

30×	saturated
119×	node limit

Counts

99175 → 71551

sample1.4min (15.3%)

Results

1.0min	247680×	0	valid
1.9s	8373×	0	invalid
557.0ms	1973×	0	precondition
20.0ms	68×	5	exit

Precisions

Click to see histograms. Total time spent on operations: 52.0s

ival-mult: 12.4s (23.8% of total)

ival-<=: 10.0s (19.3% of total)

ival-div: 5.8s (11.1% of total)

ival-sub: 2.6s (5.1% of total)

ival-add: 2.6s (4.9% of total)

ival-sqrt: 2.3s (4.5% of total)

ival-fabs: 2.2s (4.2% of total)

ival-sin: 1.9s (3.7% of total)

ival-log: 1.8s (3.5% of total)

ival-and: 1.5s (3% of total)

ival-floor: 1.1s (2.2% of total)

ival-cos: 992.0ms (1.9% of total)

ival-exp: 941.0ms (1.8% of total)

ival-neg: 863.0ms (1.7% of total)

ival-if: 751.0ms (1.4% of total)

const: 656.0ms (1.3% of total)

ival-pi: 602.0ms (1.2% of total)

ival-fmax: 521.0ms (1% of total)

ival-tan: 471.0ms (0.9% of total)

ival-<: 407.0ms (0.8% of total)

ival->: 383.0ms (0.7% of total)

ival-log2: 309.0ms (0.6% of total)

ival-==: 170.0ms (0.3% of total)

ival-asin: 141.0ms (0.3% of total)

ival-atan: 125.0ms (0.2% of total)

backward-pass: 115.0ms (0.2% of total)

ival-sinh: 91.0ms (0.2% of total)

ival->=: 89.0ms (0.2% of total)

Bogosity

soundness1.4min (14.9%)

Rules

103164×	`fma-define`
67550×	`times-frac`
64646×	`associate-r`
63894×	`*-commutative`
54910×	`distribute-lft-in`

Stop Event

8×	saturated
158×	node limit
29×	fuel
1×	done

Compiler

Compiled 52504 to 12096 computations (77% saved)

localize1.0min (11%)

Algorithm

119×	egg-herbie

Rules

117600×	`fma-define`
72318×	`fma-neg`
50848×	`distribute-lft-in`
48138×	`unsub-neg`
46334×	`sub-neg`

Stop Event

34×	saturated
85×	node limit

Results

18.6s	26175×	0	valid
1.7s	1908×	0	invalid
1.6s	1097×	1	valid
3.5s	786×	5	exit
163.0ms	498×	0	unsamplable

Compiler

Compiled 103017 to 5431 computations (94.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.3s

ival-mult: 4.0s (25.9% of total)

ival-div: 1.9s (12.3% of total)

ival-pow: 1.6s (10.2% of total)

ival-sin: 719.0ms (4.7% of total)

ival-add: 686.0ms (4.5% of total)

ival-log: 652.0ms (4.3% of total)

backward-pass: 623.0ms (4.1% of total)

ival-log1p: 617.0ms (4% of total)

ival-sub: 598.0ms (3.9% of total)

ival-exp: 582.0ms (3.8% of total)

ival-sqrt: 542.0ms (3.6% of total)

ival-fma: 439.0ms (2.9% of total)

ival-cos: 410.0ms (2.7% of total)

ival-hypot: 329.0ms (2.2% of total)

ival-neg: 286.0ms (1.9% of total)

ival-tan: 233.0ms (1.5% of total)

ival-fmax: 174.0ms (1.1% of total)

ival-if: 172.0ms (1.1% of total)

ival-expm1: 115.0ms (0.8% of total)

const: 107.0ms (0.7% of total)

ival-log2: 103.0ms (0.7% of total)

ival-floor: 100.0ms (0.7% of total)

ival-pi: 75.0ms (0.5% of total)

ival-atan: 65.0ms (0.4% of total)

ival->=: 52.0ms (0.3% of total)

ival->: 37.0ms (0.2% of total)

ival-asin: 36.0ms (0.2% of total)

ival-fabs: 35.0ms (0.2% of total)

ival-cbrt: 35.0ms (0.2% of total)

ival-sinh: 12.0ms (0.1% of total)

ival-<: 12.0ms (0.1% of total)

ival-e: 11.0ms (0.1% of total)

ival-acos: 3.0ms (0% of total)

prune42.2s (7.6%)

Counts: 142303 → 4029
Compiler: Compiled 376468 to 131732 computations (65% saved)

rewrite31.2s (5.6%)

Algorithm

119×	batch-egg-rewrite

Rules

59387×	`log1p-expm1-u`
51327×	`expm1-log1p-u`
38156×	`log-prod`
36744×	`pow1`
36330×	`add-exp-log`

Stop Event

119×	node limit

Counts

1975 → 44048

eval30.5s (5.5%)

Compiler: Compiled 13536741 to 601376 computations (95.6% saved)

series28.6s (5.1%)

Counts

1975 → 55127

Calls

13338 calls:

Time	Variable		Point	Expression
405.0ms	dX.v	@	inf	(if (< (if (> (/ (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)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (/ (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))))) (floor maxAniso)) (/ (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))) (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))))))) 1) (fmax 1 (* (if (> (/ (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)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (floor maxAniso) (/ (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)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))))) (if (> (/ (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)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (/ (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))))) (floor maxAniso)) (/ (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))) (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))))))))) (if (> (/ (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)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (floor maxAniso) (/ (fmax (+ (* (pow dX.u 2) (pow (floor w) 2)) (* (pow dX.v 2) (pow (floor h) 2))) (+ (* (pow dY.u 2) (pow (floor w) 2)) (* (pow dY.v 2) (pow (floor h) 2)))) (fabs (- (* dX.u (* dY.v (* (floor h) (floor w)))) (* dX.v (* dY.u (* (floor h) (floor w)))))))))
286.0ms	d	@	-inf	(log (log2 (sqrt (fmax (pow (sqrt (+ (* (* dX.w (floor d)) (* dX.w (floor d))) (* (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* dX.v (floor h)) (* dX.v (floor h))))) (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* dX.v (floor h)) (* dX.v (floor h)))))))) 2) (pow (* (floor d) dY.w) 2)))))
266.0ms	dY.u	@	-inf	(/ 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)) (exp (* (log (* (floor h) dY.v)) 2))))))
215.0ms	eta	@	0	(sqrt (- (* eta eta) (/ (* sinTheta_O sinTheta_O) (sqrt (- 1 (* sinTheta_O sinTheta_O))))))
179.0ms	cosTheta_i	@	0	(/ (* (exp (* sinTheta_i (/ sinTheta_O (neg v)))) (* cosTheta_i (/ cosTheta_O v))) (* v (* (- (exp (log (+ 1 (sinh (/ 1 v))))) 1) 2)))

regimes27.2s (4.9%)

Counts

9722 → 406

Calls

145 calls:

782.0ms	cosTheta_i
732.0ms	s
627.0ms	dY.u
610.0ms	u2
554.0ms	u

Compiler

Compiled 13625 to 9450 computations (30.6% saved)

analyze24.6s (4.4%)

Algorithm

30×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
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 1046 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.4s

ival-mult: 4.3s (27.8% of total)

ival-<=: 3.1s (20% of total)

ival-fabs: 1.7s (11% of total)

ival-div: 1.0s (6.5% of total)

ival-floor: 876.0ms (5.7% of total)

ival-add: 577.0ms (3.8% of total)

ival-and: 552.0ms (3.6% of total)

ival-if: 540.0ms (3.5% of total)

ival-sqrt: 487.0ms (3.2% of total)

ival-fmax: 440.0ms (2.9% of total)

ival-sub: 225.0ms (1.5% of total)

ival-==: 224.0ms (1.5% of total)

ival-exp: 183.0ms (1.2% of total)

ival-sin: 175.0ms (1.1% of total)

ival-log2: 166.0ms (1.1% of total)

ival->: 145.0ms (0.9% of total)

const: 138.0ms (0.9% of total)

ival-cos: 129.0ms (0.8% of total)

ival->=: 90.0ms (0.6% of total)

ival-tan: 86.0ms (0.6% of total)

ival-log: 76.0ms (0.5% of total)

ival-<: 66.0ms (0.4% of total)

ival-neg: 37.0ms (0.2% of total)

ival-pi: 33.0ms (0.2% of total)

backward-pass: 27.0ms (0.2% of total)

ival-sinh: 23.0ms (0.1% of total)

ival-asin: 18.0ms (0.1% of total)

ival-atan: 13.0ms (0.1% of total)

preprocess9.6s (1.7%)

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 47326 to 14904 computations (68.5% saved)

explain6.6s (1.2%)

Results

3.8s	15296×	0	valid
59.0ms	64×	5	exit

Compiler

Compiled 16652 to 1662 computations (90% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.2s

ival-mult: 930.0ms (43.1% of total)

ival-div: 245.0ms (11.4% of total)

ival-log: 154.0ms (7.1% of total)

ival-add: 145.0ms (6.7% of total)

ival-sqrt: 131.0ms (6.1% of total)

ival-sub: 100.0ms (4.6% of total)

ival-sin: 82.0ms (3.8% of total)

ival-floor: 49.0ms (2.3% of total)

ival-cos: 49.0ms (2.3% of total)

ival-exp: 43.0ms (2% of total)

ival-neg: 33.0ms (1.5% of total)

ival-pi: 31.0ms (1.4% of total)

const: 29.0ms (1.3% of total)

ival-log2: 21.0ms (1% of total)

ival-fmax: 19.0ms (0.9% of total)

backward-pass: 19.0ms (0.9% of total)

ival-tan: 19.0ms (0.9% of total)

ival-if: 16.0ms (0.7% of total)

ival-fabs: 10.0ms (0.5% of total)

ival->: 8.0ms (0.4% of total)

ival-atan: 7.0ms (0.3% of total)

ival->=: 6.0ms (0.3% of total)

ival-sinh: 6.0ms (0.3% of total)

ival-asin: 5.0ms (0.2% of total)

ival-<: 2.0ms (0.1% of total)

bsearch72.0ms (0%)

Algorithm

51×	binary-search
28×	left-value

Stop Event

51×	narrow-enough

Compiler

Compiled 3674 to 1751 computations (52.3% saved)

Herbie run

simplify2.1min (22.8%)

sample1.4min (15.3%)

soundness1.4min (14.9%)

localize1.0min (11%)

prune42.2s (7.6%)

rewrite31.2s (5.6%)

eval30.5s (5.5%)

series28.6s (5.1%)

regimes27.2s (4.9%)

analyze24.6s (4.4%)

preprocess9.6s (1.7%)

explain6.6s (1.2%)

bsearch72.0ms (0%)

end0.0ms (0%)

Profiling