Metrics for Herbie run

Date:	Monday, August 5th, 2024
Commit:	2.2 on release
Hostname:	nightly with Racket 8.11.1
Seed:	2024218
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

soundness5.7min (20.8%)

Memory

-298.6MiB live, 41 262.0MiB allocated

Rules

2 058 952×	`lower-fma.f32`
2 058 498×	`lower-fma.f64`
1 007 234×	`lower-*.f32`
1 005 864×	`lower-*.f64`
569 746×	`lower-+.f32`

Stop Event

344×	iter limit
217×	node limit
33×	fuel
21×	done
2×	unsound
1×	saturated

Compiler

Compiled 34 753 to 15 223 computations (56.2% saved)

rewrite4.9min (18%)

Memory

184.8MiB live, 98 419.1MiB allocated

Algorithm

190×	batch-egg-rewrite

Rules

985 276×	`lower-fma.f32`
984 430×	`lower-fma.f64`
746 140×	`lower-*.f32`
744 024×	`lower-*.f64`
597 908×	`lower-/.f32`

Stop Event

396×	iter limit
181×	node limit
8×	saturated
3×	unsound

Counts

2 463 → 129 195

prune4.0min (14.8%)

Memory: -221.9MiB live, 68 767.1MiB allocated
Counts: 216 778 → 3 198
Compiler: Compiled 148 174 to 66 956 computations (54.8% saved)

sample3.6min (13%)

Memory

1 505.9MiB live, 138 612.7MiB allocated

Samples

2.6min	438 625×	0	valid
25.9s	3 932×	5	exit
7.9s	22 358×	1	valid
4.1s	8 775×	2	valid
1.6s	9 883×	0	exit
309.0ms	896×	3	valid
45.0ms	459×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.2min

ival-sin: 20.4s (28.7% of total)

ival-mult: 13.6s (19.1% of total)

ival-add: 5.2s (7.3% of total)

const: 5.2s (7.3% of total)

adjust: 4.6s (6.4% of total)

ival-div: 3.9s (5.4% of total)

ival-exp: 3.3s (4.6% of total)

ival-sub: 2.7s (3.8% of total)

ival-hypot: 2.3s (3.2% of total)

ival-log: 2.3s (3.2% of total)

ival-cos: 1.3s (1.8% of total)

ival-asin: 1.1s (1.6% of total)

ival-sqrt: 1.0s (1.5% of total)

ival-atan2: 617.0ms (0.9% of total)

ival-pi: 517.0ms (0.7% of total)

ival-pow: 384.0ms (0.5% of total)

exact: 378.0ms (0.5% of total)

ival->: 300.0ms (0.4% of total)

ival-true: 285.0ms (0.4% of total)

ival-asinh: 280.0ms (0.4% of total)

ival-acosh: 279.0ms (0.4% of total)

ival-<=: 255.0ms (0.4% of total)

ival-neg: 250.0ms (0.4% of total)

ival-fabs: 197.0ms (0.3% of total)

ival-assert: 190.0ms (0.3% of total)

ival-atanh: 139.0ms (0.2% of total)

ival->=: 112.0ms (0.2% of total)

ival-and: 75.0ms (0.1% of total)

Bogosity

localize3.3min (12.2%)

Memory

209.6MiB live, 36 322.4MiB allocated

Samples

50.7s	3 104×	1	valid
34.4s	40 123×	0	valid
1.6s	1 313×	2	valid
1.5s	3 309×	0	invalid
233.0ms	284×	2	exit
164.0ms	292×	1	exit
92.0ms	182×	0	exit
87.0ms	113×	3	valid
16.0ms	25×	5	exit
1.0ms	2×	4	valid

Compiler

Compiled 50 692 to 5 225 computations (89.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.4s

ival-add: 29.5s (53.2% of total)

ival-mult: 19.9s (36% of total)

ival-div: 1.2s (2.2% of total)

const: 863.0ms (1.6% of total)

ival-log: 701.0ms (1.3% of total)

adjust: 472.0ms (0.9% of total)

ival-sub: 339.0ms (0.6% of total)

ival-sqrt: 337.0ms (0.6% of total)

ival-cos: 316.0ms (0.6% of total)

ival-hypot: 288.0ms (0.5% of total)

ival-sin: 212.0ms (0.4% of total)

ival-exp: 210.0ms (0.4% of total)

ival-pow: 193.0ms (0.3% of total)

ival-asin: 182.0ms (0.3% of total)

ival-neg: 116.0ms (0.2% of total)

ival-copysign: 96.0ms (0.2% of total)

ival-acos: 75.0ms (0.1% of total)

ival-pow2: 69.0ms (0.1% of total)

ival-atan2: 64.0ms (0.1% of total)

exact: 63.0ms (0.1% of total)

ival-fabs: 50.0ms (0.1% of total)

ival-true: 43.0ms (0.1% of total)

ival-log1p: 29.0ms (0.1% of total)

ival-pi: 25.0ms (0% of total)

ival-assert: 21.0ms (0% of total)

ival-cosh: 14.0ms (0% of total)

simplify2.6min (9.6%)

Memory

-799.3MiB live, 164 416.6MiB allocated

Algorithm

435×	egg-herbie

Rules

3 617 884×	`lower-fma.f32`
3 617 026×	`lower-fma.f64`
1 279 976×	`lower-*.f32`
1 277 688×	`lower-*.f64`
841 126×	`lower-+.f32`

Stop Event

569×	iter limit
265×	node limit
173×	saturated

Counts

45 612 → 44 920

eval1.9min (7%)

Memory: 1 211.3MiB live, 64 556.9MiB allocated
Compiler: Compiled 11 055 782 to 506 513 computations (95.4% saved)

preprocess19.9s (1.2%)

Memory

-15.7MiB live, 21 323.4MiB allocated

Algorithm

57×	egg-herbie

Rules

296 104×	`lower-fma.f64`
296 104×	`lower-fma.f32`
79 264×	`lower-*.f32`
78 898×	`lower-*.f64`
56 582×	`lower-+.f32`

Stop Event

114×	iter limit
76×	saturated
38×	node limit

Compiler

Compiled 38 928 to 10 198 computations (73.8% saved)

explain19.9s (1.2%)

Memory

-248.9MiB live, 19 792.2MiB allocated

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`#f`	oflow-rescue	1222	0
`-.f64`	`#f`	cancellation	736	2
`/.f64`	`#f`	o/o	659	0
`/.f64`	`#f`	o/n	203	0
`sqrt.f32`	`#f`	oflow-rescue	194	0
`sin.f64`	`#f`	sensitivity	181	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	180	0
`sqrt.f64`	`#f`	uflow-rescue	162	0
`+.f64`	`#f`	cancellation	162	0
`log.f64`	`(log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`	sensitivity	140	0
`-.f64`	`#f`	nan-rescue	114	0
`log.f32`	`(log.f32 (+.f32 (fabs.f32 x) (sqrt.f32 (+.f32 (*.f32 x x) #s(literal 1 binary32)))))`	sensitivity	103	0
`/.f64`	`#f`	n/o	81	0
`*.f64`	`#f`	*nu**	71	0
`/.f64`	`#f`	u/u	64	0
`/.f64`	`#f`	u/n	40	0
`+.f64`	`#f`	nan-rescue	37	0
`*.f64`	`#f`	*no**	33	0
`/.f64`	`#f`	n/u	15	0
`exp.f64`	`#f`	sensitivity	7	0
`log.f32`	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`	oflow-rescue	5	0
↳	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`	overflow	5
↳	`(*.f32 x x)`	overflow	117
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	117
`*.f64`	`(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1/2 binary64)))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)))))`	*ou**	2	0
↳	`(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1/2 binary64))))`	overflow	2
↳	`(pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1/2 binary64)))`	overflow	2
↳	`(exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64))))`	underflow	2
`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)))`	oflow-rescue	1	0
↳	`(+.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))`	overflow	1
↳	`(*.f64 x.re x.re)`	overflow	75
↳	`(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))`	overflow	119
↳	`(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.im)`	overflow	1
↳	`(*.f64 x.im x.im)`	overflow	56
`sin.f64`	`(sin.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)))`	oflow-rescue	1	0
↳	`(+.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))`	overflow	1
↳	`(*.f64 x.re x.re)`	overflow	75
↳	`(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))`	overflow	119
↳	`(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.im)`	overflow	1
↳	`(*.f64 x.im x.im)`	overflow	56

Confusion

	Predicted +	Predicted -
+	3648	50
-	185	10709

Precision

0.9517349334724758

Recall

0.9864791779340184

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3648	0	50
-	185	2	10707

Precision?

0.951238591916558

Recall?

0.9864791779340184

Freqs

test

number	freq
0	10759
1	3257
2	572
3	4

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	38	0	0
-	2	0	17

Precision?

0.95

Recall?

1.0

Samples

3.6s	25 910×	0	valid
1.2s	2 320×	1	valid
858.0ms	906×	2	valid
25.0ms	44×	3	valid
2.0ms	4×	5	exit

Compiler

Compiled 15 068 to 2 968 computations (80.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0s

ival-mult: 1.3s (33.4% of total)

ival-add: 518.0ms (13% of total)

const: 290.0ms (7.3% of total)

ival-div: 283.0ms (7.1% of total)

ival-log: 231.0ms (5.8% of total)

ival-exp: 210.0ms (5.3% of total)

ival-sub: 188.0ms (4.7% of total)

adjust: 181.0ms (4.5% of total)

ival-hypot: 174.0ms (4.4% of total)

ival-asin: 108.0ms (2.7% of total)

ival-sin: 81.0ms (2% of total)

ival-pow: 79.0ms (2% of total)

ival-atan2: 64.0ms (1.6% of total)

ival-cos: 57.0ms (1.4% of total)

ival-sqrt: 51.0ms (1.3% of total)

ival-true: 27.0ms (0.7% of total)

ival-neg: 27.0ms (0.7% of total)

exact: 20.0ms (0.5% of total)

ival-fabs: 17.0ms (0.4% of total)

ival-pi: 16.0ms (0.4% of total)

ival-copysign: 14.0ms (0.4% of total)

ival-assert: 12.0ms (0.3% of total)

ival-log1p: 7.0ms (0.2% of total)

regimes16.5s (1%)

Memory

-316.5MiB live, 20 056.6MiB allocated

Counts

10 491 → 972

Calls

122 calls:

1.0s	re
994.0ms	im
668.0ms	x
631.0ms	(cos.f64 re)
563.0ms	y.re

Compiler

Compiled 16 158 to 9 376 computations (42% saved)

series12.5s (0.8%)

Memory

-221.5MiB live, 13 413.7MiB allocated

Counts

2 463 → 45 612

Calls

8769 calls:

Time	Variable		Point	Expression
545.0ms	x	@	0	(/ (- (* 1 (+ (* (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))) (+ 1 (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))))) 1)) (* (+ (* (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))) (+ 1 (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))))) 1) (pow (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))) 3))) (* (+ (* (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))) (+ 1 (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))))) 1) (+ (* (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))) (+ 1 (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (+ (* 3275911/10000000 (fabs x)) 1))) (* (+ (* 3275911/10000000 (fabs x)) 1) (exp (* x x)))))) 1)))
241.0ms	im	@	-inf	(/ (* re 1/2) im)
227.0ms	y.re	@	inf	(- (* (log (sqrt (* x.im x.im))) y.re) (* (atan2 x.im x.re) y.im))
180.0ms	base	@	0	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
122.0ms	y.im	@	0	(+ (* (log (sqrt (* (/ (* (+ (* x.re x.re) (* x.im x.im)) (* (+ x.re x.im) (- x.re x.im))) (* (+ (* x.re (* x.re x.re)) (* x.im (* x.im x.im))) (- (* x.re (* x.re x.re)) (* x.im (* x.im x.im))))) (+ (* (* x.im x.im) (+ (* x.re x.re) (* x.im x.im))) (* x.re (* x.re (* x.re x.re))))))) y.im) (* (atan2 x.im x.re) y.re))

bsearch4.0s (0.2%)

Memory

49.4MiB live, 5 023.6MiB allocated

Algorithm

294×	left-value
214×	binary-search

Stop Event

212×	narrow-enough
2×	predicate-same

Samples

1.9s	13 570×	0	valid
671.0ms	1 387×	1	valid
35.0ms	95×	2	valid
5.0ms	20×	3	valid

Compiler

Compiled 57 259 to 37 141 computations (35.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0s

ival-mult: 682.0ms (33.6% of total)

ival-hypot: 440.0ms (21.7% of total)

ival-add: 196.0ms (9.7% of total)

ival-log: 157.0ms (7.7% of total)

ival-atan2: 88.0ms (4.3% of total)

ival-sin: 88.0ms (4.3% of total)

ival-sub: 74.0ms (3.6% of total)

const: 74.0ms (3.6% of total)

ival-exp: 53.0ms (2.6% of total)

ival-div: 51.0ms (2.5% of total)

adjust: 46.0ms (2.3% of total)

ival-cos: 46.0ms (2.3% of total)

ival-sqrt: 12.0ms (0.6% of total)

ival-true: 12.0ms (0.6% of total)

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

exact: 5.0ms (0.2% of total)

analyze2.7s (0.2%)

Memory

-81.2MiB live, 3 459.3MiB allocated

Algorithm

58×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	86.3%	13.7%	0%	0%	0%	0
55.4%	47.8%	38.5%	13.7%	0%	0%	0%	1
65.9%	55.7%	28.9%	13.7%	0%	1.7%	0%	2
71.2%	58.4%	23.6%	13.7%	0%	4.3%	0%	3
77.4%	62%	18.1%	13.7%	0%	6.2%	0%	4
83.5%	66.8%	13.2%	13.7%	0%	6.3%	0%	5
85.8%	68.3%	11.3%	13.7%	0%	6.6%	0%	6
88.3%	70.3%	9.4%	13.7%	0%	6.6%	0%	7
89.9%	71.5%	8%	13.7%	0%	6.8%	0%	8
91.1%	72.5%	7.1%	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 1 498 to 821 computations (45.2% saved)

end0.0ms (0%)

Memory: 1.3MiB live, 1.3MiB allocated

soundness5.7min (20.8%)

rewrite4.9min (18%)

prune4.0min (14.8%)

sample3.6min (13%)

localize3.3min (12.2%)

simplify2.6min (9.6%)

eval1.9min (7%)

preprocess19.9s (1.2%)

explain19.9s (1.2%)

regimes16.5s (1%)

series12.5s (0.8%)

bsearch4.0s (0.2%)

analyze2.7s (0.2%)

end0.0ms (0%)

Profiling