Metrics for Herbie run

Date:	Thursday, June 13th, 2024
Commit:	63d27371 on web-cleanup
Hostname:	nightly with Racket 8.11.1
Seed:	2024165
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

simplify2.5min (25.9%)

Algorithm

268×	egg-herbie

Rules

232 544×	`fma-define`
118 052×	`distribute-lft-in`
117 306×	`fmm-def`
111 380×	`*-commutative`
110 456×	`times-frac`

Stop Event

197×	node limit
71×	saturated

Counts

100 703 → 73 288

soundness1.6min (16.4%)

Rules

107 290×	`fma-define`
69 284×	`associate-r`
62 616×	`*-commutative`
60 514×	`times-frac`
54 886×	`distribute-lft-in`

Stop Event

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

Compiler

Compiled 69 486 to 12 181 computations (82.5% saved)

sample1.4min (15.1%)

Samples

1.1min	247 627×	0	valid
2.0s	10 306×	0	invalid
8.0ms	53×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 52.4s

ival-mult: 10.5s (20% of total)

...in/eval/compile.rkt:71:19: 8.9s (16.9% of total)

ival-<=: 7.8s (14.9% of total)

ival-div: 5.3s (10.1% of total)

ival-add: 2.6s (5% of total)

ival-sub: 2.2s (4.3% of total)

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

ival-log: 1.6s (3.1% of total)

ival-sqrt: 1.5s (2.8% of total)

ival-and: 1.4s (2.6% of total)

ival-neg: 1.3s (2.4% of total)

ival-fabs: 1.3s (2.4% of total)

ival-floor: 1.1s (2.1% of total)

ival-cos: 790.0ms (1.5% of total)

ival-pi: 710.0ms (1.4% of total)

ival-exp: 659.0ms (1.3% of total)

ival-log2: 558.0ms (1.1% of total)

ival-tan: 401.0ms (0.8% of total)

...in/eval/compile.rkt:70:19: 328.0ms (0.6% of total)

ival-fmax: 311.0ms (0.6% of total)

ival-<: 248.0ms (0.5% of total)

ival->: 246.0ms (0.5% of total)

ival-if: 236.0ms (0.5% of total)

ival-==: 153.0ms (0.3% of total)

ival-asin: 140.0ms (0.3% of total)

ival-assert: 135.0ms (0.3% of total)

ival-sinh: 128.0ms (0.2% of total)

ival-atan: 123.0ms (0.2% of total)

ival->=: 60.0ms (0.1% of total)

adjust: 1.0ms (0% of total)

Bogosity

prune43.5s (7.6%)

Counts: 140 468 → 4 057
Compiler: Compiled 344 970 to 127 656 computations (63% saved)

localize36.1s (6.3%)

Samples

14.8s	26 941×	0	valid
4.6s	655×	5	exit
1.7s	2 303×	0	invalid
1.2s	565×	1	valid

Compiler

Compiled 101 022 to 5 552 computations (94.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0s

ival-mult: 3.8s (27.5% of total)

ival-div: 1.8s (13% of total)

ival-pow: 1.1s (8.2% of total)

ival-add: 841.0ms (6% of total)

ival-sqrt: 824.0ms (5.9% of total)

adjust: 671.0ms (4.8% of total)

ival-sin: 624.0ms (4.5% of total)

ival-sub: 535.0ms (3.8% of total)

ival-tan: 499.0ms (3.6% of total)

ival-hypot: 429.0ms (3.1% of total)

ival-fma: 336.0ms (2.4% of total)

ival-log: 332.0ms (2.4% of total)

ival-exp: 271.0ms (1.9% of total)

...in/eval/compile.rkt:71:19: 221.0ms (1.6% of total)

ival-log1p: 214.0ms (1.5% of total)

ival-fmax: 171.0ms (1.2% of total)

ival-atan: 146.0ms (1% of total)

ival-neg: 138.0ms (1% of total)

ival-cos: 131.0ms (0.9% of total)

ival-if: 131.0ms (0.9% of total)

ival-pi: 126.0ms (0.9% of total)

ival-log2: 98.0ms (0.7% of total)

ival-floor: 93.0ms (0.7% of total)

ival-expm1: 55.0ms (0.4% of total)

...in/eval/compile.rkt:70:19: 42.0ms (0.3% of total)

ival-asin: 41.0ms (0.3% of total)

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

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

ival-true: 32.0ms (0.2% of total)

ival->=: 30.0ms (0.2% of total)

ival->: 21.0ms (0.2% of total)

ival-assert: 20.0ms (0.1% of total)

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

ival-<: 10.0ms (0.1% of total)

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

rewrite34.5s (6%)

Algorithm

119×	batch-egg-rewrite

Rules

65 149×	`log1p-expm1-u`
50 043×	`expm1-log1p-u`
37 171×	`pow1`
35 626×	`log-prod`
35 277×	`add-exp-log`

Stop Event

119×	node limit

Counts

1 990 → 44 265

series31.1s (5.4%)

Counts

1 990 → 56 438

Calls

13572 calls:

Time	Variable		Point	Expression
715.0ms	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 (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)) 1/4)
429.0ms	dX.w	@	inf	(log (log2 (sqrt (fmax (pow (sqrt (+ (* (* dX.w (floor d)) (* dX.w (floor d))) (* (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* (floor h) dX.v) (* (floor h) dX.v)))) (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* (floor h) dX.v) (* (floor h) dX.v))))))) 2) (pow (* (floor d) dY.w) 2)))))
415.0ms	dY.u	@	inf	(if (>= (+ (* (* dX.v dX.v) (* (floor h) (floor h))) (* (floor w) (* (floor w) (* dX.u dX.u)))) (+ (* (floor w) (* (floor w) (* dY.u dY.u))) (* (floor h) (* (floor h) (* dY.v dY.v))))) (* dX.v (/ (floor h) (sqrt (fmax (+ (* (* dX.v dX.v) (* (floor h) (floor h))) (* (floor w) (* (floor w) (* dX.u dX.u)))) (+ (* (floor w) (* (floor w) (* dY.u dY.u))) (* (floor h) (* (floor h) (* dY.v dY.v)))))))) (* (floor h) (/ dY.v (sqrt (fmax (+ (* (* dX.v dX.v) (* (floor h) (floor h))) (* (floor w) (* (floor w) (* dX.u dX.u)))) (+ (* (floor w) (* (floor w) (* dY.u dY.u))) (* (floor h) (* (floor h) (* dY.v dY.v)))))))))
402.0ms	w	@	inf	(> (/ (fmax (+ (* (floor w) (* (* dX.u dX.u) (floor w))) (* (floor h) (* (* dX.v dX.v) (floor h)))) (+ (* (floor w) (* (* dY.u dY.u) (floor w))) (* (floor h) (* (* dY.v dY.v) (floor h))))) (fabs (* (floor h) (- (* dX.u (* (floor w) dY.v)) (* (* dY.u dX.v) (floor w)))))) (floor maxAniso))
380.0ms	cosTheta_i	@	-inf	(exp (- (log (/ (* cosTheta_O cosTheta_i) (* (sinh (/ 1 v)) (* v (* v 2))))) (* sinTheta_i (/ sinTheta_O v))))

regimes28.7s (5%)

Counts

9 504 → 395

Calls

145 calls:

1.4s	s
1.1s	cosTheta_i
689.0ms	dX.v
672.0ms	x
656.0ms	ux

Compiler

Compiled 13 320 to 9 241 computations (30.6% saved)

eval27.7s (4.8%)

Compiler: Compiled 14 001 445 to 594 859 computations (95.8% saved)

analyze22.9s (4%)

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 2 586 to 1 076 computations (58.4% saved)

explain10.2s (1.8%)

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f32`	`#f`	sensitivity	1020	71
`-.f32`	`#f`	cancellation	395	33
`sqrt.f32`	`#f`	oflow-rescue	353	0
`cos.f32`	`#f`	sensitivity	194	19
`tan.f32`	`(tan.f32 (+.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))`	cancellation	189	16
`/.f32`	`#f`	o/n	130	0
`exp.f32`	`#f`	sensitivity	37	14
`/.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	18	0
↳	`(*.f32 sinTheta_O sinTheta_O)`	underflow	276
↳	`(-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O)))))`	underflow	18
↳	`(/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_O))))`	underflow	138
↳	`(*.f32 eta eta)`	underflow	18
`/.f32`	`#f`	o/o	14	0
`/.f32`	`#f`	n/o	6	0
`*.f32`	`(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*nu**	4	0
`sin.f32`	`(sin.f32 (.f32 (.f32 uy #s(literal 2 binary32)) (PI.f32)))`	cancellation	1	0
`*.f32`	`(.f32 (sin.f32 (.f32 (-.f32 #s(literal 1 binary32) u) normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*no**	1	0
`*.f32`	`(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*uo**	1	0
↳	`(*.f32 u normAngle)`	underflow	5
↳	`(sin.f32 (*.f32 u normAngle))`	underflow	5
↳	`(/.f32 #s(literal 1 binary32) (sin.f32 normAngle))`	overflow	1

Confusion

	Predicted +	Predicted -
+	1669	62
-	391	5558

Precision

0.8101941747572815

Recall

0.9641825534373195

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1669	34	28
-	391	101	5457

Precision?

0.7758542141230068

Recall?

0.9838243789716926

Freqs

test

number	freq
0	5620
1	1749
2	296
3	15

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	22	0	2
-	3	1	2

Precision?

0.8461538461538461

Recall?

0.9166666666666666

Samples

3.4s	15 274×	0	valid
36.0ms	86×	1	valid

Compiler

Compiled 18 280 to 2 256 computations (87.7% saved)

Precisions

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

ival-mult: 653.0ms (34.4% of total)

ival-div: 269.0ms (14.2% of total)

ival-sin: 178.0ms (9.4% of total)

ival-add: 150.0ms (7.9% of total)

ival-floor: 111.0ms (5.8% of total)

ival-log: 83.0ms (4.4% of total)

ival-sub: 80.0ms (4.2% of total)

ival-sqrt: 67.0ms (3.5% of total)

ival-cos: 43.0ms (2.3% of total)

ival-exp: 41.0ms (2.2% of total)

ival-neg: 33.0ms (1.7% of total)

ival-pi: 26.0ms (1.4% of total)

...in/eval/compile.rkt:71:19: 26.0ms (1.4% of total)

ival-if: 19.0ms (1% of total)

ival-tan: 19.0ms (1% of total)

ival-fmax: 18.0ms (0.9% of total)

ival-log2: 16.0ms (0.8% of total)

ival-true: 16.0ms (0.8% of total)

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

ival-fabs: 9.0ms (0.5% of total)

...in/eval/compile.rkt:70:19: 8.0ms (0.4% of total)

ival-atan: 7.0ms (0.4% of total)

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

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

ival->=: 4.0ms (0.2% of total)

ival->: 3.0ms (0.2% of total)

adjust: 3.0ms (0.2% of total)

ival-<: 1.0ms (0.1% of total)

preprocess9.6s (1.7%)

Algorithm

30×	egg-herbie

Rules

30 620×	`fma-define`
21 784×	`fmm-def`
14 698×	`distribute-lft-neg-in`
14 266×	`unsub-neg`
11 858×	`distribute-rgt-neg-in`

Stop Event

19×	node limit
11×	saturated

Compiler

Compiled 49 944 to 15 844 computations (68.3% saved)

bsearch40.0ms (0%)

Algorithm

58×	binary-search
20×	left-value

Stop Event

58×	narrow-enough

Compiler

Compiled 3 847 to 1 948 computations (49.4% saved)

Herbie run

simplify2.5min (25.9%)

soundness1.6min (16.4%)

sample1.4min (15.1%)

prune43.5s (7.6%)

localize36.1s (6.3%)

rewrite34.5s (6%)

series31.1s (5.4%)

regimes28.7s (5%)

eval27.7s (4.8%)

analyze22.9s (4%)

explain10.2s (1.8%)

preprocess9.6s (1.7%)

bsearch40.0ms (0%)

end0.0ms (0%)

Profiling