Metrics for Herbie run

Date:	Friday, April 5th, 2024
Commit:	9a443234 on explanations-eval-top3
Hostname:	nightly with Racket 8.11.1
Seed:	2024096
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

sample3.3min (29.7%)

Results

1.3min	371644×	256	valid
14.6s	73602×	256	infinite
6.2s	10624×	1024	valid
1.2min	7872×	8192	exit
2.6s	7082×	512	valid
3.6s	4597×	512	infinite
695.0ms	4472×	256	unsamplable
1.0s	1875×	2048	valid
832.0ms	1099×	4096	valid
74.0ms	520×	256	invalid
103.0ms	87×	1024	infinite

Precisions

Click to see histograms. Total time spent on operations: 2.1min

Operation ival-sin, time spent: 48.6s, 39.0% of total-time

Operation ival-mult, time spent: 21.4s, 17.0% of total-time

Operation ival-add, time spent: 11.7s, 9.0% of total-time

Operation ival-sub, time spent: 9.1s, 7.0% of total-time

Operation ival-div, time spent: 8.8s, 7.0% of total-time

Operation ival-pow, time spent: 6.0s, 5.0% of total-time

Operation ival-log, time spent: 3.0s, 2.0% of total-time

Operation ival-sqrt, time spent: 2.8s, 2.0% of total-time

Operation ival-exp, time spent: 2.6s, 2.0% of total-time

Operation const, time spent: 2.1s, 2.0% of total-time

Operation ival-asin, time spent: 2.1s, 2.0% of total-time

Operation ival-cos, time spent: 1.4s, 1.0% of total-time

Operation ival-atan2, time spent: 1.3s, 1.0% of total-time

Operation ival-<=, time spent: 1.1s, 1.0% of total-time

Operation ival->, time spent: 911.0ms, 1.0% of total-time

Operation ival-pi, time spent: 615.0ms, 0.0% of total-time

Operation ival-acosh, time spent: 562.0ms, 0.0% of total-time

Operation ival-asinh, time spent: 536.0ms, 0.0% of total-time

Operation ival-fabs, time spent: 504.0ms, 0.0% of total-time

Operation ival-neg, time spent: 492.0ms, 0.0% of total-time

Operation ival-atanh, time spent: 382.0ms, 0.0% of total-time

Operation ival->=, time spent: 147.0ms, 0.0% of total-time

Operation ival-and, time spent: 106.0ms, 0.0% of total-time

Bogosity

localize2.7min (24.5%)

Compiler: Compiled 49722 to 28629 computations (42.4% saved)
Precisions: Click to see histograms. Total time spent on operations: 1.9min
Operation ival-mult, time spent: 22.0s, 19.0% of total-time
Operation ival-pow, time spent: 19.2s, 17.0% of total-time
Operation ival-add, time spent: 13.5s, 12.0% of total-time
Operation ival-div, time spent: 11.2s, 10.0% of total-time
Operation composed, time spent: 9.3s, 8.0% of total-time
Operation ival-log, time spent: 8.8s, 8.0% of total-time
Operation ival-sub, time spent: 7.8s, 7.0% of total-time
Operation ival-asin, time spent: 5.7s, 5.0% of total-time
Operation ival-sqrt, time spent: 3.2s, 3.0% of total-time
Operation ival-exp, time spent: 3.1s, 3.0% of total-time
Operation const, time spent: 3.0s, 3.0% of total-time
Operation ival-acos, time spent: 2.1s, 2.0% of total-time
Operation ival-sin, time spent: 1.3s, 1.0% of total-time
Operation ival-cos, time spent: 843.0ms, 1.0% of total-time
Operation ival-cbrt, time spent: 733.0ms, 1.0% of total-time
Operation ival-atan2, time spent: 395.0ms, 0.0% of total-time
Operation ival-neg, time spent: 343.0ms, 0.0% of total-time
Operation ival-fabs, time spent: 200.0ms, 0.0% of total-time
Operation ival-copysign, time spent: 96.0ms, 0.0% of total-time
Operation ival-pi, time spent: 85.0ms, 0.0% of total-time
Operation ival-e, time spent: 16.0ms, 0.0% of total-time

eval1.0min (9.5%)

Compiler: Compiled 2956951 to 1916863 computations (35.2% saved)

simplify48.2s (7.3%)

Algorithm

220×	egg-herbie

Rules

110113×	`fma-define`
89112×	`distribute-lft-in`
86708×	`fma-neg`
83413×	`*-commutative`
80168×	`associate-r`

Stop Event

57×	saturated
153×	node limit
35×	fuel
10×	unsound
22×	done

Counts

67809 → 62672

Compiler

Compiled 10931 to 6991 computations (36% saved)

preprocess42.4s (6.4%)

Algorithm

57×	egg-herbie

Rules

40033×	`fma-neg`
38663×	`fma-define`
19396×	`unsub-neg`
17401×	`distribute-lft-in`
16736×	`sub-neg`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`#f`	oflow-rescue	1169	0
`-.f64`	`#f`	cancellation	996	4
`/.f64`	`#f`	o/o	611	0
`sqrt.f32`	`#f`	oflow-rescue	205	0
`sin.f64`	`#f`	sensitivity	176	0
`cos.f64`	`(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))`	sensitivity	172	0
`+.f64`	`#f`	cancellation	166	0
`/.f64`	`#f`	o/n	165	0
`log.f64`	`(log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) 1))))`	sensitivity	138	1
`log.f32`	`(log.f32 (+.f32 (fabs.f32 x) (sqrt.f32 (+.f32 (*.f32 x x) 1))))`	sensitivity	115	1
`sqrt.f64`	`#f`	uflow-rescue	103	0
`-.f64`	`#f`	nan-rescue	95	0
`+.f64`	`#f`	nan-rescue	81	0
`/.f64`	`#f`	n/o	73	0
`/.f64`	`(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))`	u/u	67	0
↳	`(.f64 (.f64 i i) (*.f64 i i))`	underflow	95
↳	`(*.f64 i i)`	underflow	134
↳	`(.f64 (.f64 2 i) (*.f64 2 i))`	underflow	67
`*.f64`	`#f`	*nu**	58	0
`*.f64`	`#f`	*no**	32	0
`log.f32`	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))`	oflow-rescue	5	0
↳	`(-.f32 (*.f32 x x) 1)`	overflow	136
↳	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1)))`	overflow	5
↳	`(*.f32 x x)`	overflow	136
`exp.f64`	`#f`	sensitivity	5	0
`*.f64`	`(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2))))`	*ou**	4	0
↳	`(pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))`	overflow	4
↳	`(.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2)))`	overflow	4
↳	`(exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))`	underflow	4

Confusion

	Predicted +	Predicted -
+	3514	143
-	436	10499

Precision

0.889620253164557

Recall

0.9608969100355482

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3514	1	142
-	436	8	10491

Precision?

0.8878504672897196

Recall?

0.9611703582171178

Stop Event

32×	saturated
25×	node limit

Compiler

Compiled 49336 to 26890 computations (45.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.8s

Operation ival-mult, time spent: 3.2s, 25.0% of total-time

Operation ival-add, time spent: 2.3s, 18.0% of total-time

Operation ival-div, time spent: 2.1s, 16.0% of total-time

Operation ival-sub, time spent: 2.1s, 16.0% of total-time

Operation ival-log, time spent: 594.0ms, 5.0% of total-time

Operation const, time spent: 474.0ms, 4.0% of total-time

Operation ival-sqrt, time spent: 469.0ms, 4.0% of total-time

Operation ival-exp, time spent: 402.0ms, 3.0% of total-time

Operation ival-pow, time spent: 351.0ms, 3.0% of total-time

Operation composed, time spent: 223.0ms, 2.0% of total-time

Operation ival-asin, time spent: 218.0ms, 2.0% of total-time

Operation ival-cos, time spent: 138.0ms, 1.0% of total-time

Operation ival-sin, time spent: 107.0ms, 1.0% of total-time

Operation ival-atan2, time spent: 77.0ms, 1.0% of total-time

Operation ival-neg, time spent: 45.0ms, 0.0% of total-time

Operation ival-pi, time spent: 28.0ms, 0.0% of total-time

Operation ival-fabs, time spent: 28.0ms, 0.0% of total-time

Operation ival-copysign, time spent: 13.0ms, 0.0% of total-time

soundness42.3s (6.4%)

Rules

102525×	`fma-define`
84520×	`fma-neg`
70426×	`associate-r`
68575×	`distribute-lft-in`
61196×	`distribute-rgt-in`

Stop Event

19×	saturated
173×	node limit
7×	unsound

Compiler

Compiled 38337 to 24300 computations (36.6% saved)

rewrite33.2s (5%)

Algorithm

163×	batch-egg-rewrite

Rules

112837×	`log1p-expm1-u`
82429×	`expm1-log1p-u`
54613×	`prod-diff`
44183×	`log-prod`
42659×	`unpow-prod-down`

Stop Event

158×	node limit
5×	unsound

Counts

1326 → 41453

regimes22.6s (3.4%)

Counts

6326 → 734

Calls

132 calls:

2.1s	y.re
2.0s	y.im
1.7s	im
1.6s	x.re
1.6s	re

Compiler

Compiled 5831 to 3965 computations (32% saved)

prune22.3s (3.4%)

Counts: 88825 → 2785
Compiler: Compiled 133625 to 93749 computations (29.8% saved)

bsearch13.9s (2.1%)

Algorithm

325×	binary-search
32×	left-value

Stop Event

23×	predicate-same
302×	narrow-enough

Results

8.9s	31514×	256	valid
1.0s	5278×	256	infinite
1.4s	2071×	512	infinite
283.0ms	554×	512	valid
61.0ms	190×	1024	valid
43.0ms	98×	2048	valid
38.0ms	36×	1024	infinite
12.0ms	19×	4096	valid

Compiler

Compiled 79606 to 55102 computations (30.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.4s

Operation ival-mult, time spent: 2.3s, 36.0% of total-time

Operation ival-add, time spent: 880.0ms, 14.0% of total-time

Operation ival-log, time spent: 716.0ms, 11.0% of total-time

Operation ival-div, time spent: 649.0ms, 10.0% of total-time

Operation ival-sin, time spent: 362.0ms, 6.0% of total-time

Operation ival-sub, time spent: 313.0ms, 5.0% of total-time

Operation ival-atan2, time spent: 285.0ms, 4.0% of total-time

Operation ival-sqrt, time spent: 267.0ms, 4.0% of total-time

Operation ival-exp, time spent: 244.0ms, 4.0% of total-time

Operation ival-cos, time spent: 199.0ms, 3.0% of total-time

Operation const, time spent: 102.0ms, 2.0% of total-time

Operation ival-copysign, time spent: 21.0ms, 0.0% of total-time

Operation ival-fabs, time spent: 21.0ms, 0.0% of total-time

Operation ival-neg, time spent: 19.0ms, 0.0% of total-time

Operation ival-pow, time spent: 15.0ms, 0.0% of total-time

Operation ival-pi, time spent: 4.0ms, 0.0% of total-time

series11.6s (1.8%)

Counts

1326 → 26356

Calls

6879 calls:

Time	Variable		Point	Expression
296.0ms	im	@	-inf	(log (/ (log im) (log base)))
167.0ms	x.re	@	0	(* (pow (sqrt (+ (* x.im x.im) (* x.re x.re))) y.re) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re)))))
167.0ms	u1	@	-inf	(pow (* -2 (log u1)) 1/4)
140.0ms	base	@	inf	(exp (neg (log (log base))))
130.0ms	x.im	@	-inf	(/ (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (pow (exp y.im) (atan2 x.im x.re)))

analyze4.4s (0.7%)

Algorithm

58×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	86.3%	13.7%	0%	0%	0%	0
55.6%	48%	38.3%	13.7%	0%	0%	0%	1
64.1%	54.2%	30.4%	13.7%	0%	1.7%	0%	2
72%	59%	23%	13.7%	0%	4.3%	0%	3
77.8%	62.3%	17.8%	13.7%	0%	6.2%	0%	4
83.7%	67%	13%	13.7%	0%	6.3%	0%	5
85.9%	68.4%	11.2%	13.7%	0%	6.6%	0%	6
88.3%	70.3%	9.3%	13.7%	0%	6.6%	0%	7
90%	71.6%	8%	13.7%	0%	6.8%	0%	8
91.2%	72.5%	7%	13.7%	0%	6.8%	0%	9
92.6%	73.6%	5.9%	13.7%	0%	6.8%	0%	10
94%	74.7%	4.8%	13.7%	0%	6.8%	0%	11
94.5%	75.1%	4.4%	13.7%	0%	6.9%	0%	12

Compiler

Compiled 1558 to 1007 computations (35.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.8s

Operation ival-mult, time spent: 748.0ms, 27.0% of total-time

Operation ival-add, time spent: 394.0ms, 14.0% of total-time

Operation ival-log, time spent: 325.0ms, 12.0% of total-time

Operation ival-sub, time spent: 294.0ms, 11.0% of total-time

Operation ival-div, time spent: 252.0ms, 9.0% of total-time

Operation ival-atan2, time spent: 203.0ms, 7.0% of total-time

Operation ival-sqrt, time spent: 166.0ms, 6.0% of total-time

Operation ival-pow, time spent: 138.0ms, 5.0% of total-time

Operation ival-sin, time spent: 65.0ms, 2.0% of total-time

Operation ival-exp, time spent: 63.0ms, 2.0% of total-time

Operation const, time spent: 61.0ms, 2.0% of total-time

Operation ival-cos, time spent: 22.0ms, 1.0% of total-time

Operation ival-pi, time spent: 20.0ms, 1.0% of total-time

Operation ival->, time spent: 16.0ms, 1.0% of total-time

Operation ival-<=, time spent: 15.0ms, 1.0% of total-time

Operation ival-neg, time spent: 10.0ms, 0.0% of total-time

Operation ival-and, time spent: 2.0ms, 0.0% of total-time

Operation ival-asin, time spent: 1.0ms, 0.0% of total-time

Operation ival-atanh, time spent: 1.0ms, 0.0% of total-time

Operation ival-asinh, time spent: 0.0ms, 0.0% of total-time

Operation ival->=, time spent: 0.0ms, 0.0% of total-time

Operation ival-fabs, time spent: 0.0ms, 0.0% of total-time

Operation ival-acosh, time spent: 0.0ms, 0.0% of total-time

Herbie run

sample3.3min (29.7%)

localize2.7min (24.5%)

eval1.0min (9.5%)

simplify48.2s (7.3%)

preprocess42.4s (6.4%)

soundness42.3s (6.4%)

rewrite33.2s (5%)

regimes22.6s (3.4%)

prune22.3s (3.4%)

bsearch13.9s (2.1%)

series11.6s (1.8%)

analyze4.4s (0.7%)

end20.0ms (0%)

Profiling