Metrics for Herbie run

Date:	Wednesday, October 9th, 2024
Commit:	b5a8073d on reorg-report-page
Hostname:	nightly with Racket 8.10
Seed:	2024283
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

soundness3.2min (20.9%)

Memory

52.5MiB live, 36 075.3MiB allocated

Stop Event

346×	iter limit
218×	node limit
38×	fuel
18×	done
3×	saturated
3×	unsound

Compiler

Compiled 62 393 to 21 401 computations (65.7% saved)

sample2.8min (18.1%)

Memory

533.8MiB live, 111 229.7MiB allocated

Samples

1.8min	439 122×	0	valid
7.2s	21 985×	1	valid
4.1s	8 625×	2	valid
2.4s	4 381×	0	invalid
1.3s	9 036×	0	exit
441.0ms	902×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 1.1min

ival-mult: 28.6s (42.3% of total)

ival-add: 9.8s (14.5% of total)

ival-div: 4.8s (7% of total)

const: 3.8s (5.6% of total)

ival-exp: 2.8s (4.2% of total)

ival-hypot: 2.8s (4.2% of total)

ival-sub: 2.3s (3.4% of total)

ival-log: 2.2s (3.2% of total)

ival-asin: 1.3s (1.9% of total)

adjust: 1.2s (1.7% of total)

ival-sin: 1.2s (1.7% of total)

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

ival-cos: 907.0ms (1.3% of total)

ival-atan2: 903.0ms (1.3% of total)

ival->: 419.0ms (0.6% of total)

exact: 383.0ms (0.6% of total)

ival-pow: 351.0ms (0.5% of total)

ival-sinu: 337.0ms (0.5% of total)

ival-<=: 294.0ms (0.4% of total)

ival-pi: 284.0ms (0.4% of total)

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

ival-acosh: 247.0ms (0.4% of total)

ival-asinh: 230.0ms (0.3% of total)

ival-fabs: 230.0ms (0.3% of total)

ival-neg: 229.0ms (0.3% of total)

ival-atanh: 220.0ms (0.3% of total)

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

ival-cosu: 118.0ms (0.2% of total)

ival-and: 77.0ms (0.1% of total)

ival->=: 76.0ms (0.1% of total)

Bogosity

localize2.8min (17.9%)

Memory

-590.7MiB live, 41 737.2MiB allocated

Samples

49.7s	1 633×	2	valid
38.1s	4 221×	1	valid
18.0s	41 472×	0	valid
1.6s	3 448×	0	invalid
413.0ms	510×	1	exit
107.0ms	85×	3	valid
48.0ms	80×	0	exit
6.0ms	2×	2	exit
5.0ms	3×	5	exit
2.0ms	2×	4	valid

Compiler

Compiled 171 286 to 14 028 computations (91.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.4min

ival-mult: 21.4s (25.2% of total)

ival-pow: 17.8s (20.9% of total)

ival-div: 17.4s (20.4% of total)

ival-sqrt: 15.6s (18.4% of total)

ival-add: 6.1s (7.2% of total)

const: 1.4s (1.6% of total)

ival-sub: 884.0ms (1% of total)

adjust: 861.0ms (1% of total)

ival-log: 792.0ms (0.9% of total)

ival-exp: 527.0ms (0.6% of total)

ival-hypot: 442.0ms (0.5% of total)

ival-acos: 261.0ms (0.3% of total)

ival-neg: 210.0ms (0.2% of total)

ival-sin: 170.0ms (0.2% of total)

ival-cos: 153.0ms (0.2% of total)

ival-asin: 146.0ms (0.2% of total)

ival-pow2: 133.0ms (0.2% of total)

ival-cosh: 110.0ms (0.1% of total)

ival-atan2: 108.0ms (0.1% of total)

ival-log1p: 105.0ms (0.1% of total)

exact: 84.0ms (0.1% of total)

ival-fabs: 82.0ms (0.1% of total)

ival-copysign: 62.0ms (0.1% of total)

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

ival-pi: 35.0ms (0% of total)

ival-assert: 24.0ms (0% of total)

ival-sinu: 13.0ms (0% of total)

ival-cosu: 11.0ms (0% of total)

ival-cbrt: 10.0ms (0% of total)

rewrite2.7min (17.3%)

Memory

-473.0MiB live, 49 919.5MiB allocated

Stop Event

428×	iter limit
190×	node limit
6×	unsound
5×	saturated

Counts

2 900 → 105 659

simplify1.4min (9%)

Memory

195.5MiB live, 69 273.0MiB allocated

Algorithm

459×	egg-herbie

Stop Event

603×	iter limit
272×	node limit
187×	saturated

Counts

58 812 → 58 058

eval1.1min (7.1%)

Memory: 448.0MiB live, 69 149.7MiB allocated
Compiler: Compiled 16 465 215 to 622 020 computations (96.2% saved)

explain19.4s (2.1%)

Memory

-308.5MiB live, 18 829.9MiB allocated

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`#f`	oflow-rescue	1217	0
`-.f64`	`#f`	cancellation	743	0
`/.f64`	`#f`	o/o	590	0
`/.f64`	`#f`	o/n	218	0
`sqrt.f32`	`#f`	oflow-rescue	184	0
`sin.f64`	`#f`	sensitivity	169	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	169	0
`+.f64`	`#f`	cancellation	155	0
`sqrt.f64`	`#f`	uflow-rescue	137	0
`log.f32`	`(log.f32 (+.f32 (fabs.f32 x) (sqrt.f32 (+.f32 (*.f32 x x) #s(literal 1 binary32)))))`	sensitivity	131	2
`log.f64`	`(log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`	sensitivity	125	0
`-.f64`	`#f`	nan-rescue	93	0
`/.f64`	`#f`	n/o	74	0
`/.f64`	`#f`	u/u	74	0
`*.f64`	`#f`	*nu**	62	0
`+.f64`	`#f`	nan-rescue	41	0
`/.f64`	`#f`	u/n	38	0
`*.f64`	`#f`	*no**	30	0
`/.f64`	`#f`	n/u	10	0
`log.f32`	`#f`	oflow-rescue	6	0
`exp.f64`	`#f`	sensitivity	4	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)))`	oflow-rescue	2	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	2
↳	`(*.f64 (atan2.f64 x.im x.re) y.re)`	overflow	1
↳	`(*.f64 x.re x.re)`	overflow	72
↳	`(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))`	overflow	122
↳	`(.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	65
`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	2	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	2
↳	`(*.f64 (atan2.f64 x.im x.re) y.re)`	overflow	1
↳	`(*.f64 x.re x.re)`	overflow	72
↳	`(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))`	overflow	122
↳	`(.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	65
`log.f64`	`(log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`	oflow-rescue	1	0
↳	`(+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`	overflow	1
↳	`(*.f64 x x)`	overflow	68
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	68
`*.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**	1	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	1
↳	`(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	1
↳	`(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	1

Confusion

	Predicted +	Predicted -
+	3570	69
-	177	10776

Precision

0.9527622097678142

Recall

0.9810387469084914

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3570	1	68
-	177	5	10771

Precision?

0.9515054622968292

Recall?

0.9813135476779336

Freqs

test

number	freq
0	10845
1	3223
2	519
3	5

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	37	0	1
-	1	2	16

Precision?

0.925

Recall?

0.9736842105263158

Samples

3.7s	25 894×	0	valid
1.2s	2 406×	1	valid
509.0ms	832×	2	valid
17.0ms	50×	3	valid
1.0ms	2×	5	exit

Compiler

Compiled 19 577 to 2 968 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.8s

ival-mult: 1.4s (35.3% of total)

ival-add: 414.0ms (10.8% of total)

ival-div: 331.0ms (8.6% of total)

const: 273.0ms (7.1% of total)

ival-log: 229.0ms (6% of total)

ival-hypot: 221.0ms (5.8% of total)

ival-sub: 206.0ms (5.4% of total)

ival-exp: 205.0ms (5.3% of total)

adjust: 173.0ms (4.5% of total)

ival-asin: 69.0ms (1.8% of total)

ival-sin: 60.0ms (1.6% of total)

ival-cos: 47.0ms (1.2% of total)

ival-sqrt: 45.0ms (1.2% of total)

ival-atan2: 42.0ms (1.1% of total)

ival-true: 26.0ms (0.7% of total)

ival-pow: 22.0ms (0.6% of total)

exact: 20.0ms (0.5% of total)

ival-fabs: 18.0ms (0.5% of total)

ival-log1p: 15.0ms (0.4% of total)

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

ival-pi: 13.0ms (0.3% of total)

ival-assert: 13.0ms (0.3% of total)

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

ival-cosu: 6.0ms (0.2% of total)

ival-sinu: 6.0ms (0.2% of total)

regimes17.2s (1.9%)

Memory

171.6MiB live, 20 891.9MiB allocated

Counts

9 254 → 928

Calls

132 calls:

1.1s	re
1.0s	im
750.0ms	beta
698.0ms	x
637.0ms	y.re

Compiler

Compiled 14 275 to 10 152 computations (28.9% saved)

prune16.4s (1.8%)

Memory: -367.2MiB live, 26 285.8MiB allocated
Counts: 222 824 → 3 149
Compiler: Compiled 324 403 to 124 285 computations (61.7% saved)

preprocess15.2s (1.6%)

Memory

46.3MiB live, 15 082.1MiB allocated

Algorithm

57×	egg-herbie

Stop Event

114×	iter limit
76×	saturated
38×	node limit

Compiler

Compiled 77 374 to 15 043 computations (80.6% saved)

series14.5s (1.6%)

Memory

227.7MiB live, 18 707.0MiB allocated

Counts

2 900 → 58 812

Calls

1227 calls:

Time	Variable		Point	Expression
660.0ms	x	@	0	((+ (pow (+ (* (+ (* (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (/ (pow (exp x) (neg x)) (+ (* (fabs x) 3275911/10000000) 1))) 1) (/ (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (* (+ (* (fabs x) 3275911/10000000) 1) (pow (exp x) x)))) 1) -1) (* (pow (+ (* (+ (* (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (/ (pow (exp x) (neg x)) (+ (* (fabs x) 3275911/10000000) 1))) 1) (/ (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (* (+ (* (fabs x) 3275911/10000000) 1) (pow (exp x) x)))) 1) -1) (pow (/ (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (* (+ (* (fabs x) 3275911/10000000) 1) (pow (exp x) x))) 3))) (- (pow (+ (* (+ (* (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (/ (pow (exp x) (neg x)) (+ (* (fabs x) 3275911/10000000) 1))) 1) (/ (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (* (+ (* (fabs x) 3275911/10000000) 1) (pow (exp x) x)))) 1) -2) (pow (* (pow (/ (/ (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (pow (exp x) x)) (+ (* -3275911/10000000 (fabs x)) -1)) 3) (pow (+ (* (+ (* (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (/ (pow (exp x) (neg x)) (+ (* (fabs x) 3275911/10000000) 1))) 1) (/ (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (* (+ (* (fabs x) 3275911/10000000) 1) (pow (exp x) x)))) 1) -1)) 2)) (* (pow (/ (/ (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (pow (exp x) x)) (+ (* -3275911/10000000 (fabs x)) -1)) 3) (pow (+ (* (+ (* (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (/ (pow (exp x) (neg x)) (+ (* (fabs x) 3275911/10000000) 1))) 1) (/ (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (* (+ (* (fabs x) 3275911/10000000) 1) (pow (exp x) x)))) 1) -1)) (* (pow (+ (* (+ (* (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (/ (pow (exp x) (neg x)) (+ (* (fabs x) 3275911/10000000) 1))) 1) (/ (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (* (+ (* (fabs x) 3275911/10000000) 1) (pow (exp x) x)))) 1) -1) (pow (/ (+ 31853699/125000000 (/ (+ (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) -8890523/31250000) (+ (* (fabs x) 3275911/10000000) 1))) (* (+ (* (fabs x) 3275911/10000000) 1) (pow (exp x) x))) 3)) (- 1 (* (* (/ 1 (+ 1 (* 3275911/10000000 (fabs x)))) (+ 31853699/125000000 (* (/ 1 (+ 1 (* 3275911/10000000 (fabs x)))) (+ -8890523/31250000 (* (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (- 1 (* 10731592879921/100000000000000 (* x x)))) (- 1 (* (fabs x) 3275911/10000000))))))) (exp (neg (* (fabs x) (fabs x)))))) (* (* (/ 1 (+ 1 (* 3275911/10000000 (fabs x)))) (+ 31853699/125000000 (* (/ 1 (+ 1 (* 3275911/10000000 (fabs x)))) (+ -8890523/31250000 (* (/ (+ (/ (+ (/ 1061405429/1000000000 (+ (* (fabs x) 3275911/10000000) 1)) -1453152027/1000000000) (+ (* (fabs x) 3275911/10000000) 1)) 1421413741/1000000000) (- 1 (* 10731592879921/100000000000000 (* x x)))) (- 1 (* (fabs x) 3275911/10000000))))))) (exp (neg (* (fabs x) (fabs x))))) (* (exp (* (neg x) x)) (/ (- 31853699/125000000 (/ 8890523/31250000 (+ (* (fabs x) 3275911/10000000) 1))) (+ (* (fabs x) 3275911/10000000) 1))) (/ (- 31853699/125000000 (/ 8890523/31250000 (+ (* (fabs x) 3275911/10000000) 1))) (+ (* (fabs x) 3275911/10000000) 1)) (* (fabs x) (fabs x)) (- 1 (* (* (/ (+ (/ (+ (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ 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270.0ms	i	@	-inf	((* (neg beta) (+ (* (/ (+ (* i 2) 2) beta) -1) -1)) (+ (* (/ (+ (* i 2) 2) beta) -1) -1) (/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2) (* 1/2 (+ (* (/ beta (+ (+ (* 2 i) beta) 2)) (/ beta (+ (* 2 i) beta))) 1)) (/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2) (* (+ 1 (/ (- beta alpha) (+ (+ beta alpha) 2))) 1/2) (* (+ 1 (/ (- beta alpha) (+ (+ beta alpha) 2))) 1/2) (/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2) (+ 1 (/ (- beta alpha) (+ (+ beta alpha) 2))) (/ (- beta alpha) (+ (+ beta alpha) 2)) (* (+ (+ (* 4 i) (* 2 beta)) 2) 1/2) (+ (+ (* 4 i) (* 2 beta)) 2) (/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2) (/ (* 1/2 (+ (+ (+ (* 4 i) (* 2 beta)) 2) (/ (- (* beta beta) (+ (* (- -2 (+ (* 2 i) beta)) (+ (* 2 i) beta)) (* (+ (+ (* 4 i) (* 2 beta)) 2) (+ (+ (* 4 i) (* 2 beta)) 2)))) alpha))) alpha) (/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2) (* 1/2 (+ (* beta (/ beta (* (+ (+ (* i 2) beta) 2) (+ (* i 2) beta)))) 1)) (+ (* beta (/ beta (* (+ (+ (* i 2) beta) 2) (+ (* i 2) beta)))) 1) (* (+ (+ (* i 2) beta) 2) (+ (* i 2) beta)) (/ beta (+ (* 2 i) beta)) (/ beta (+ (+ (* 2 i) beta) 2)) (* 1/2 (+ (+ (+ (* 4 i) (* 2 beta)) 2) (/ (- (* beta beta) (+ (* (- -2 (+ (* 2 i) beta)) (+ (* 2 i) beta)) (* (+ (+ (* 4 i) (* 2 beta)) 2) (+ (+ (* 4 i) (* 2 beta)) 2)))) alpha))) (/ beta (* (+ (+ (* i 2) beta) 2) (+ (* i 2) beta))) (+ (+ (* i 2) beta) 2))
190.0ms	x	@	0	((copysign (log (+ (sqrt (+ (* x x) 1)) (fabs x))) x) (log (+ (sqrt (+ (* x x) 1)) (fabs x))) (+ (* (* (/ 1/2 (+ 1 (fabs x))) x) x) (log (+ 1 (fabs x)))) (* (/ 1/2 (+ 1 (fabs x))) x) (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1)))) x) (log (+ (fabs x) (sqrt (+ (* x x) 1)))) (+ (fabs x) (sqrt (+ (* x x) 1))) (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1)))) x) (log (+ (fabs x) (sqrt (+ (* x x) 1)))) (+ (fabs x) (sqrt (+ (* x x) 1))) (fabs x) (copysign (neg (log (- (sqrt (+ (* x x) 1)) (fabs x)))) x) (neg (log (- (sqrt (+ (* x x) 1)) (fabs x)))) (log (- (sqrt (+ (* x x) 1)) (fabs x))) (- (sqrt (+ (* x x) 1)) (fabs x)) (log (+ (* (neg x) x) (+ (* x x) 1))) (+ (* (neg x) x) (+ (* x x) 1)) (neg (- (fabs x) (sqrt (+ (* x x) 1)))) (- (log (+ (* (neg x) x) (+ (* x x) 1))) (log (neg (- (fabs x) (sqrt (+ (* x x) 1)))))) (/ 1/2 (+ 1 (fabs x))) (sqrt (+ (* x x) 1)) (sqrt (+ (* x x) 1)) (- (fabs x) (sqrt (+ (* x x) 1))) (log (neg (- (fabs x) (sqrt (+ (* x x) 1))))))
174.0ms	alpha	@	-inf	((/ (/ (+ (* (+ (+ beta alpha) i) i) (* beta alpha)) (+ (* 2 i) (+ beta alpha))) (- (+ (* 2 i) (+ beta alpha)) 1)) (+ (* (+ (+ beta alpha) i) i) (* beta alpha)) (* (/ (* (+ (+ beta alpha) i) (/ i (+ (* 2 i) (+ beta alpha)))) (+ (+ (* 2 i) (+ beta alpha)) 1)) (/ (/ (+ (* (+ (+ beta alpha) i) i) (* beta alpha)) (+ (* 2 i) (+ beta alpha))) (- (+ (* 2 i) (+ beta alpha)) 1))) (/ (* (+ (+ beta alpha) i) (/ i (+ (* 2 i) (+ beta alpha)))) (+ (+ (* 2 i) (+ beta alpha)) 1)) (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (* (/ (+ i alpha) beta) (/ i beta)) (* alpha (/ i (* beta beta))) (* beta beta) (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/ (* (/ (+ alpha i) beta) i) beta) (* (/ (+ alpha i) beta) i) (/ (+ alpha i) beta) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1) (+ (+ alpha beta) (* 2 i)) (/ (/ (* (* (+ (* (+ (+ alpha beta) i) i) (* alpha beta)) (+ (+ alpha beta) i)) i) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/ (* (* (+ (* (+ (+ alpha beta) i) i) (* alpha beta)) (+ (+ alpha beta) i)) i) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (/ (* (+ (+ beta alpha) i) (* (+ (* (+ (+ beta alpha) i) i) (* beta alpha)) i)) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (/ (+ (* (+ (+ beta alpha) i) i) (* beta alpha)) (+ (* 2 i) (+ beta alpha))) (* (+ (+ beta alpha) i) (/ i (+ (* 2 i) (+ beta alpha)))) (/ i (* beta beta)) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (* 1/4 (* i i)) (/ (/ (* (+ (+ beta alpha) i) (* (+ (* (+ (+ beta alpha) i) i) (* beta alpha)) i)) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (* (+ (* (+ (+ beta alpha) i) i) (* beta alpha)) i) (* (+ (+ beta alpha) i) (* (+ (* (+ (+ beta alpha) i) i) (* beta alpha)) i)))

bsearch4.5s (0.5%)

Memory

-96.7MiB live, 4 978.4MiB allocated

Algorithm

233×	left-value
226×	binary-search

Stop Event

218×	narrow-enough
8×	predicate-same

Samples

1.8s	14 104×	0	valid
641.0ms	1 515×	1	valid
35.0ms	100×	2	valid
11.0ms	41×	3	valid

Compiler

Compiled 136 672 to 77 189 computations (43.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.7s

ival-mult: 489.0ms (28.8% of total)

ival-hypot: 186.0ms (11% of total)

ival-sub: 167.0ms (9.8% of total)

ival-add: 153.0ms (9% of total)

ival-log: 138.0ms (8.1% of total)

adjust: 99.0ms (5.8% of total)

ival-sqrt: 83.0ms (4.9% of total)

ival-sin: 71.0ms (4.2% of total)

ival-div: 65.0ms (3.8% of total)

ival-exp: 65.0ms (3.8% of total)

ival-cos: 58.0ms (3.4% of total)

ival-atan2: 58.0ms (3.4% of total)

const: 40.0ms (2.4% of total)

ival-true: 12.0ms (0.7% of total)

ival-assert: 6.0ms (0.4% of total)

exact: 4.0ms (0.2% of total)

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

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

analyze2.6s (0.3%)

Memory

39.8MiB live, 3 360.8MiB 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 816 computations (45.5% saved)

start2.0ms (0%)

Memory: 5.8MiB live, 6.1MiB allocated

end0.0ms (0%)

Memory: 1.0MiB live, 0.9MiB allocated

soundness3.2min (20.9%)

sample2.8min (18.1%)

localize2.8min (17.9%)

rewrite2.7min (17.3%)

simplify1.4min (9%)

eval1.1min (7.1%)

explain19.4s (2.1%)

regimes17.2s (1.9%)

prune16.4s (1.8%)

preprocess15.2s (1.6%)

series14.5s (1.6%)

bsearch4.5s (0.5%)

analyze2.6s (0.3%)

start2.0ms (0%)

end0.0ms (0%)

Profiling