Metrics for Herbie run

Date:	Wednesday, June 5th, 2024
Commit:	8a54fd57 on main
Hostname:	nightly with Racket 8.11.1
Seed:	2024157
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

simplify2.2min (23.5%)

Algorithm

268×	egg-herbie

Rules

213074×	`fma-define`
113926×	`distribute-lft-in`
112704×	`times-frac`
108902×	`*-commutative`
103116×	`associate-r`

Stop Event

69×	saturated
199×	node limit

Counts

100243 → 71536

sample1.6min (16.5%)

Results

1.2min	247640×	0	valid
2.6s	10625×	0	invalid
7.0ms	40×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 58.3s

ival-mult: 12.2s (21% of total)

ival-<=: 10.7s (18.3% of total)

...c/correct-round.rkt:168:19: 8.6s (14.8% of total)

ival-div: 5.3s (9.2% of total)

ival-add: 2.4s (4% of total)

ival-sin: 2.1s (3.5% of total)

ival-sub: 2.0s (3.5% of total)

ival-fabs: 2.0s (3.5% of total)

ival-sqrt: 1.6s (2.7% of total)

ival-and: 1.6s (2.7% of total)

ival-log: 1.5s (2.6% of total)

ival-floor: 1.2s (2% of total)

ival-cos: 997.0ms (1.7% of total)

ival-neg: 965.0ms (1.7% of total)

ival-exp: 830.0ms (1.4% of total)

ival-pi: 748.0ms (1.3% of total)

const: 611.0ms (1% of total)

ival-<: 409.0ms (0.7% of total)

ival-tan: 389.0ms (0.7% of total)

ival-if: 348.0ms (0.6% of total)

ival-fmax: 326.0ms (0.6% of total)

ival->: 304.0ms (0.5% of total)

ival-log2: 283.0ms (0.5% of total)

ival-assert: 255.0ms (0.4% of total)

ival-asin: 180.0ms (0.3% of total)

ival-==: 171.0ms (0.3% of total)

ival-atan: 122.0ms (0.2% of total)

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

ival->=: 80.0ms (0.1% of total)

adjust: 1.0ms (0% of total)

Bogosity

soundness1.3min (13.9%)

Rules

86274×	`fma-define`
62240×	`associate-r`
58126×	`*-commutative`
57768×	`times-frac`
48162×	`distribute-lft-in`

Stop Event

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

Compiler

Compiled 69120 to 12049 computations (82.6% saved)

prune48.1s (8.5%)

Counts: 142561 → 3955
Compiler: Compiled 368049 to 132120 computations (64.1% saved)

localize47.7s (8.4%)

Results

24.5s	26405×	0	valid
4.1s	554×	5	exit
3.6s	2825×	0	invalid
2.3s	680×	1	valid

Compiler

Compiled 103228 to 5581 computations (94.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.6s

ival-mult: 3.8s (25.8% of total)

ival-div: 1.7s (11.5% of total)

ival-pow: 1.5s (10.3% of total)

ival-add: 786.0ms (5.4% of total)

ival-fma: 691.0ms (4.7% of total)

ival-exp: 686.0ms (4.7% of total)

ival-sqrt: 620.0ms (4.2% of total)

adjust: 529.0ms (3.6% of total)

ival-sin: 512.0ms (3.5% of total)

...c/correct-round.rkt:168:19: 453.0ms (3.1% of total)

ival-log: 411.0ms (2.8% of total)

ival-hypot: 334.0ms (2.3% of total)

ival-sub: 294.0ms (2% of total)

ival-fmax: 286.0ms (2% of total)

ival-log1p: 274.0ms (1.9% of total)

ival-tan: 232.0ms (1.6% of total)

ival-floor: 216.0ms (1.5% of total)

ival-log2: 189.0ms (1.3% of total)

ival-neg: 172.0ms (1.2% of total)

ival-if: 153.0ms (1% of total)

ival-cos: 150.0ms (1% of total)

ival-pi: 119.0ms (0.8% of total)

const: 81.0ms (0.6% of total)

ival-atan: 70.0ms (0.5% of total)

ival-cbrt: 59.0ms (0.4% of total)

ival-true: 58.0ms (0.4% of total)

ival-expm1: 47.0ms (0.3% of total)

ival->=: 46.0ms (0.3% of total)

ival->: 39.0ms (0.3% of total)

ival-assert: 39.0ms (0.3% of total)

ival-asin: 34.0ms (0.2% of total)

ival-fabs: 31.0ms (0.2% of total)

ival-<: 14.0ms (0.1% of total)

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

ival-e: 8.0ms (0.1% of total)

ival-acos: 2.0ms (0% of total)

rewrite32.9s (5.8%)

Algorithm

119×	batch-egg-rewrite

Rules

61141×	`log1p-expm1-u`
49945×	`expm1-log1p-u`
37209×	`pow1`
35224×	`add-exp-log`
35204×	`log-prod`

Stop Event

119×	node limit

Counts

1957 → 44735

series30.6s (5.4%)

Counts

1957 → 55508

Calls

13494 calls:

Time	Variable		Point	Expression
526.0ms	d	@	0	(* (log (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 (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) 2))) 1/2)
425.0ms	w	@	-inf	(if (< (if (> (/ (fmax (pow (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* (floor h) dX.v) (* (floor h) dX.v)))) 2) (pow (sqrt (+ (* (* dY.v (floor h)) (* dY.v (floor h))) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2)) (* (* (floor h) (floor w)) (- (* dX.u dY.v) (* dX.v 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 (+ (* (* (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)))))))
414.0ms	dX.u	@	0	(/ (* 1 (* (floor h) dX.v)) (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)))))))
318.0ms	w	@	-inf	(log (log2 (sqrt (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 (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)))))
304.0ms	maxAniso	@	-inf	(* (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))))))))

eval27.5s (4.9%)

Compiler: Compiled 13642992 to 592838 computations (95.7% saved)

regimes27.0s (4.8%)

Counts

9412 → 387

Calls

145 calls:

839.0ms	(floor.f32 h)
670.0ms	dY.v
621.0ms	uy
598.0ms	dY.u
585.0ms	cosTheta_i

Compiler

Compiled 13047 to 9120 computations (30.1% saved)

analyze26.8s (4.7%)

Algorithm

30×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
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%	0.1%	0%	6
69.5%	1.8%	0.8%	97.4%	0%	0.1%	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 2586 to 1076 computations (58.4% saved)

explain10.9s (1.9%)

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f32`	`#f`	sensitivity	1059	68
`-.f32`	`#f`	cancellation	402	35
`sqrt.f32`	`#f`	oflow-rescue	357	0
`cos.f32`	`(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) u1) (.f32 #s(literal 1/2 binary32) (PI.f32)))))))`	sensitivity	201	20
`tan.f32`	`(tan.f32 (+.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))`	cancellation	196	15
`/.f32`	`#f`	o/n	126	0
`exp.f32`	`#f`	sensitivity	34	21
`/.f32`	`#f`	u/n	23	0
`sqrt.f32`	`(sqrt.f32 (-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O))))))`	uflow-rescue	17	0
↳	`(*.f32 sinTheta_O sinTheta_O)`	underflow	286
↳	`(-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O)))))`	underflow	17
↳	`(/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_O))))`	underflow	143
↳	`(*.f32 eta eta)`	underflow	17
`/.f32`	`#f`	o/o	10	0
`*.f32`	`#f`	*no**	4	0
`sin.f32`	`#f`	cancellation	2	0
`/.f32`	`(/.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))`	n/o	2	0
↳	`(/.f32 sin2phi (*.f32 alphay alphay))`	overflow	12
↳	`(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))`	overflow	12
`*.f32`	`(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*nu**	1	0

Confusion

	Predicted +	Predicted -
+	1687	58
-	417	5518

Precision

0.8018060836501901

Recall

0.9667621776504298

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1687	34	24
-	417	112	5406

Precision?

0.7648888888888888

Recall?

0.9862464183381089

Freqs

test

number	freq
0	5576
1	1784
2	310
3	10

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	21	1	0
-	3	1	4

Precision?

0.8461538461538461

Recall?

1.0

Results

4.3s	15282×	0	valid
68.0ms	78×	1	valid

Compiler

Compiled 18280 to 2256 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-mult: 691.0ms (37.1% of total)

ival-div: 238.0ms (12.8% of total)

ival-sub: 146.0ms (7.8% of total)

ival-add: 109.0ms (5.8% of total)

ival-sin: 96.0ms (5.2% of total)

ival-log: 88.0ms (4.7% of total)

ival-sqrt: 83.0ms (4.5% of total)

ival-floor: 47.0ms (2.5% of total)

ival-cos: 47.0ms (2.5% of total)

ival-exp: 46.0ms (2.5% of total)

ival-neg: 31.0ms (1.7% of total)

ival-pi: 28.0ms (1.5% of total)

...c/correct-round.rkt:168:19: 28.0ms (1.5% of total)

ival-true: 27.0ms (1.4% of total)

ival-tan: 20.0ms (1.1% of total)

ival-fmax: 18.0ms (1% of total)

ival-if: 18.0ms (1% of total)

ival-assert: 18.0ms (1% of total)

const: 17.0ms (0.9% of total)

ival-log2: 16.0ms (0.9% of total)

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

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

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

ival->=: 7.0ms (0.4% of total)

ival->: 5.0ms (0.3% of total)

ival-asin: 5.0ms (0.3% of total)

adjust: 4.0ms (0.2% of total)

ival-<: 4.0ms (0.2% of total)

preprocess9.0s (1.6%)

Algorithm

30×	egg-herbie

Rules

30620×	`fma-define`
21784×	`fmm-def`
14698×	`distribute-lft-neg-in`
14266×	`unsub-neg`
11858×	`distribute-rgt-neg-in`

Stop Event

11×	saturated
19×	node limit

Compiler

Compiled 51492 to 17310 computations (66.4% saved)

bsearch46.0ms (0%)

Algorithm

60×	binary-search
15×	left-value

Stop Event

60×	narrow-enough

Compiler

Compiled 3883 to 1916 computations (50.7% saved)

Herbie run

simplify2.2min (23.5%)

sample1.6min (16.5%)

soundness1.3min (13.9%)

prune48.1s (8.5%)

localize47.7s (8.4%)

rewrite32.9s (5.8%)

series30.6s (5.4%)

eval27.5s (4.9%)

regimes27.0s (4.8%)

analyze26.8s (4.7%)

explain10.9s (1.9%)

preprocess9.0s (1.6%)

bsearch46.0ms (0%)

end0.0ms (0%)

Profiling