Metrics for Herbie run

Date:	Thursday, November 21st, 2024
Commit:	d1b0bfd6 on main
Hostname:	nightly with Racket 8.10
Seed:	2024326
Parameters:	256 points for 4 iterations
Flags:	`localize:costslocalize:errorsreduce:regimesreduce:binary-searchreduce:branch-expressionssetup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:proofs` default

sample1.8min (29%)

Memory

793.5MiB live, 90 355.5MiB allocated

Samples

1.0min	438 943×	0	valid
10.5s	22 346×	1	valid
4.0s	8 402×	2	valid
2.4s	4 423×	0	invalid
763.0ms	8 011×	0	exit
254.0ms	901×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 59.1s

ival-mult: 25.5s (43.1% of total)

ival-add: 5.9s (10% of total)

const: 3.9s (6.5% of total)

ival-div: 3.7s (6.3% of total)

ival-exp: 2.6s (4.3% of total)

ival-hypot: 2.3s (3.9% of total)

ival-sub: 2.1s (3.6% of total)

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

ival-asin: 1.5s (2.5% of total)

ival-sin: 1.3s (2.2% of total)

adjust: 1.2s (2% of total)

ival-cos: 985.0ms (1.7% of total)

ival-sqrt: 851.0ms (1.4% of total)

ival-atan2: 742.0ms (1.3% of total)

ival->: 699.0ms (1.2% of total)

ival-atanh: 396.0ms (0.7% of total)

ival-acosh: 379.0ms (0.6% of total)

exact: 370.0ms (0.6% of total)

ival-sinu: 332.0ms (0.6% of total)

ival-pi: 331.0ms (0.6% of total)

ival-pow: 323.0ms (0.5% of total)

ival->=: 294.0ms (0.5% of total)

ival-true: 278.0ms (0.5% of total)

ival-<=: 212.0ms (0.4% of total)

ival-asinh: 205.0ms (0.3% of total)

ival-assert: 200.0ms (0.3% of total)

ival-neg: 178.0ms (0.3% of total)

ival-fabs: 178.0ms (0.3% of total)

ival-cosu: 85.0ms (0.1% of total)

ival-and: 81.0ms (0.1% of total)

Bogosity

simplify1.0min (16.1%)

Memory

891.6MiB live, 56 712.5MiB allocated

Algorithm

461×	egg-herbie

Stop Event

609×	iter limit
341×	node limit
118×	saturated
2×	unsound

Counts

14 898 → 14 737

soundness57.5s (15.1%)

Memory

-76.4MiB live, 30 022.4MiB allocated

Stop Event

349×	iter limit
224×	node limit
34×	fuel
23×	done
2×	saturated
1×	unsound

Compiler

Compiled 62 638 to 23 190 computations (63% saved)

rewrite37.8s (9.9%)

Memory

545.5MiB live, 37 640.9MiB allocated

Stop Event

442×	iter limit
191×	node limit
6×	unsound
5×	saturated

Counts

2 704 → 86 468

localize28.3s (7.5%)

Memory

-633.8MiB live, 31 230.5MiB allocated

Samples

12.2s	42 220×	0	valid
4.7s	4 543×	1	valid
2.6s	1 598×	2	valid
1.4s	2 618×	0	invalid
315.0ms	602×	0	exit
102.0ms	113×	3	valid
11.0ms	12×	4	valid
7.0ms	6×	5	exit

Compiler

Compiled 66 636 to 6 011 computations (91% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.5s

ival-mult: 4.8s (31.2% of total)

ival-add: 1.8s (11.6% of total)

ival-div: 1.6s (10.3% of total)

const: 1.1s (7% of total)

adjust: 984.0ms (6.4% of total)

ival-log: 764.0ms (4.9% of total)

ival-sub: 644.0ms (4.2% of total)

ival-pow: 589.0ms (3.8% of total)

ival-hypot: 501.0ms (3.2% of total)

ival-exp: 497.0ms (3.2% of total)

ival-cos: 388.0ms (2.5% of total)

ival-sin: 331.0ms (2.1% of total)

ival-asin: 279.0ms (1.8% of total)

ival-sqrt: 265.0ms (1.7% of total)

ival-neg: 227.0ms (1.5% of total)

ival-log1p: 82.0ms (0.5% of total)

exact: 76.0ms (0.5% of total)

ival-acos: 73.0ms (0.5% of total)

ival-copysign: 67.0ms (0.4% of total)

ival-atan2: 61.0ms (0.4% of total)

ival-pow2: 55.0ms (0.4% of total)

ival-fabs: 51.0ms (0.3% of total)

ival-pi: 48.0ms (0.3% of total)

ival-true: 44.0ms (0.3% of total)

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

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

ival-sinu: 30.0ms (0.2% of total)

ival-cbrt: 16.0ms (0.1% of total)

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

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

ival-asinh: 7.0ms (0% of total)

ival-acosh: 6.0ms (0% of total)

eval22.7s (6%)

Memory: -274.7MiB live, 26 920.7MiB allocated
Compiler: Compiled 5 676 978 to 429 535 computations (92.4% saved)

explain13.9s (3.7%)

Memory

-332.2MiB live, 16 473.3MiB allocated

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`#f`	oflow-rescue	1113	0
`-.f64`	`#f`	cancellation	767	5
`/.f64`	`#f`	o/o	658	0
`sqrt.f32`	`#f`	oflow-rescue	198	0
`sin.f64`	`#f`	sensitivity	191	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	190	0
`/.f64`	`#f`	o/n	188	0
`+.f64`	`#f`	cancellation	171	0
`sqrt.f64`	`#f`	uflow-rescue	142	0
`log.f64`	`(log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`	sensitivity	133	0
`log.f32`	`(log.f32 (+.f32 (fabs.f32 x) (sqrt.f32 (+.f32 (*.f32 x x) #s(literal 1 binary32)))))`	sensitivity	108	2
`/.f64`	`#f`	n/o	96	0
`-.f64`	`#f`	nan-rescue	94	0
`*.f64`	`#f`	*nu**	65	0
`/.f64`	`#f`	u/u	62	0
`+.f64`	`#f`	nan-rescue	58	0
`/.f64`	`#f`	u/n	41	0
`*.f64`	`#f`	*no**	36	0
`/.f64`	`#f`	n/u	19	0
`log.f32`	`#f`	oflow-rescue	3	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	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	65
↳	`(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))`	overflow	101
↳	`(.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
`exp.f64`	`(exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))`	sensitivity	1	0
`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	65
↳	`(+.f64 (.f64 x.re x.re) (.f64 x.im x.im))`	overflow	101
↳	`(.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
`*.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 -
+	3558	71
-	221	10742

Precision

0.9415189203492987

Recall

0.9804353816478368

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3558	3	68
-	221	5	10737

Precision?

0.9403221547398997

Recall?

0.981262055662717

Freqs

test

number	freq
0	10813
1	3223
2	554
3	2

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	36	0	1
-	1	0	19

Precision?

0.972972972972973

Recall?

0.972972972972973

Samples

3.1s	25 826×	0	valid
1.1s	2 460×	1	valid
665.0ms	842×	2	valid
19.0ms	54×	3	valid
1.0ms	2×	5	exit

Compiler

Compiled 13 558 to 2 283 computations (83.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.4s

ival-mult: 846.0ms (25.2% of total)

ival-add: 372.0ms (11.1% of total)

ival-div: 331.0ms (9.9% of total)

ival-log: 319.0ms (9.5% of total)

adjust: 264.0ms (7.9% of total)

const: 226.0ms (6.7% of total)

ival-hypot: 198.0ms (5.9% of total)

ival-exp: 164.0ms (4.9% of total)

ival-sub: 126.0ms (3.8% of total)

ival-sqrt: 95.0ms (2.8% of total)

ival-asin: 75.0ms (2.2% of total)

ival-cos: 68.0ms (2% of total)

ival-sin: 63.0ms (1.9% of total)

ival-atan2: 54.0ms (1.6% of total)

ival-true: 27.0ms (0.8% of total)

ival-pow: 21.0ms (0.6% of total)

exact: 21.0ms (0.6% of total)

ival-fabs: 19.0ms (0.6% of total)

ival-pi: 16.0ms (0.5% of total)

ival-assert: 13.0ms (0.4% of total)

ival-neg: 12.0ms (0.4% of total)

ival-copysign: 12.0ms (0.4% of total)

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

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

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

regimes12.4s (3.3%)

Memory

-348.8MiB live, 13 934.0MiB allocated

Counts

6 790 → 792

Calls

132 calls:

789.0ms	y.re
617.0ms	im
575.0ms	(-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
561.0ms	re
494.0ms	(*.f64 im im)

Compiler

Compiled 13 310 to 9 316 computations (30% saved)

preprocess11.7s (3.1%)

Memory

276.0MiB live, 12 039.1MiB allocated

Algorithm

57×	egg-herbie

Stop Event

114×	iter limit
60×	saturated
54×	node limit

Compiler

Compiled 73 220 to 14 365 computations (80.4% saved)

series9.4s (2.5%)

Memory

137.1MiB live, 11 059.2MiB allocated

Counts

2 704 → 14 898

Calls

1266 calls:

Time	Variable		Point	Expression
266.0ms	alpha	@	0	((/ (/ (* (* 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)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1) (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* i (+ (+ alpha beta) i)))
142.0ms	x	@	-inf	((* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (* (* (* (* x x) (* x x)) (fabs x)) (fabs x)) (* (* x x) (* x x)) (* (/ 1 (sqrt (PI))) (+ (+ (* (+ (* (* x x) 2/3) 2) x) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* x x) (* x x)) (fabs x)) (fabs x)) (fabs x))))) (* (/ 1 (sqrt (PI))) (+ (* (pow x 5) 1/5) (+ (* x (+ (* 2/3 (* x x)) 2)) (* (pow x 7) 1/21)))) (* (/ 2 (sqrt (PI))) x) (/ 2 (sqrt (PI))) (sqrt (PI)) (fabs (* (/ 1 (sqrt (PI))) (+ (* (pow x 5) 1/5) (+ (* x (+ (* 2/3 (* x x)) 2)) (* (pow x 7) 1/21))))) (* (/ 1 (sqrt (PI))) (+ (* (pow x 5) 1/5) (+ (* x (+ (* 2/3 (* x x)) 2)) (* (pow x 7) 1/21)))) (* (* (+ (* (* x x) 2/3) 2) x) (sqrt (/ 1 (PI)))) (* (+ (* (* x x) 2/3) 2) x) (* (* (pow x 7) 1/21) 1) (fabs (* (/ 1 (sqrt (PI))) (+ (* (pow x 5) 1/5) (+ (* x (+ (* 2/3 (* x x)) 2)) (* (pow x 7) 1/21))))) (* (/ 1 (sqrt (PI))) (+ (* (pow x 5) 1/5) (+ (* x (+ (* 2/3 (* x x)) 2)) (* (pow x 7) 1/21)))) (/ (* (* (pow x 7) 1/21) 1) (sqrt (PI))) (* (* (* (neg x) x) x) (* (* (neg x) x) x)) (* (/ 1 (sqrt (PI))) (+ (+ (+ (* 2 (fabs x)) (* (* x x) (* x 2/3))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (neg x) x) x) (* (* (neg x) x) x)) (fabs x))))) (+ (+ (+ (* 2 (fabs x)) (* (* x x) (* x 2/3))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (neg x) x) x) (* (* (neg x) x) x)) (fabs x)))) (* (* (fabs x) (fabs x)) (fabs x)) (PI) (+ (* (* x x) 2/3) 2) (* (pow x 7) 1/21) (* x 2/3) (* (* x x) (* x 2/3)))
124.0ms	base	@	0	((/ (log base) (pow (log base) 2)) (* (log (sqrt (+ (* im im) (* re re)))) (/ (log base) (pow (log base) 2))) (log (sqrt (+ (* im im) (* re re)))) (sqrt (+ (* im im) (* re re))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (* (log (+ (* im im) (* re re))) 1/2) (log base)) (* (log (* im im)) (/ 1/2 (log base))) (log (* im im)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (log (pow (+ (* re re) (* im im)) (/ 1/2 (log base)))) (pow (+ (* re re) (* im im)) (/ 1/2 (log base))) (+ (* re re) (* im im)) (* (log (sqrt (+ (* im im) (* re re)))) (pow (sqrt (log base)) -2)) (pow (sqrt (log base)) -2) (* (log (sqrt (+ (* im im) (* re re)))) (exp (neg (log (log base))))) (exp (neg (log (log base)))) (pow (log base) 2) (log base) (/ 1/2 (log base)) (sqrt (log base)) (log (log base)))
104.0ms	x	@	-inf	((log (* (log x) x)) (* (log x) x) (log x) (log (/ x (log x))) (/ x (log x)))
94.0ms	u1	@	-inf	((/ 1 6) (+ (* (* (/ 1 6) (pow (* -2 (log u1)) 1/2)) (cos (* (* 2 (PI)) u2))) 1/2) (pow (* -2 (log u1)) 1/2) (* (* (/ 1 6) (pow (* -2 (log u1)) 1/2)) (cos (* (* 2 (PI)) u2))) (* (/ 1 6) (pow (* -2 (log u1)) 1/2)) (* (* 2 (PI)) u2))

prune7.8s (2.1%)

Memory: -247.1MiB live, 10 730.0MiB allocated
Counts: 106 562 → 2 616
Compiler: Compiled 249 729 to 104 999 computations (58% saved)

bsearch4.1s (1.1%)

Memory

-77.6MiB live, 3 623.8MiB allocated

Algorithm

213×	left-value
183×	binary-search

Stop Event

175×	narrow-enough
8×	predicate-same

Samples

1.6s	12 450×	0	valid
812.0ms	1 301×	1	valid
18.0ms	78×	2	valid
7.0ms	27×	3	valid

Compiler

Compiled 127 672 to 68 649 computations (46.2% saved)

Precisions

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

ival-mult: 707.0ms (37.6% of total)

ival-hypot: 258.0ms (13.7% of total)

ival-add: 180.0ms (9.6% of total)

ival-log: 117.0ms (6.2% of total)

const: 101.0ms (5.4% of total)

adjust: 100.0ms (5.3% of total)

ival-sin: 100.0ms (5.3% of total)

ival-div: 68.0ms (3.6% of total)

ival-exp: 57.0ms (3% of total)

ival-sub: 55.0ms (2.9% of total)

ival-atan2: 53.0ms (2.8% of total)

ival-cos: 52.0ms (2.8% of total)

ival-sqrt: 14.0ms (0.7% of total)

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

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

exact: 3.0ms (0.2% of total)

analyze3.0s (0.8%)

Memory

-4.4MiB live, 3 172.9MiB 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)

start4.0ms (0%)

Memory: 5.2MiB live, 5.0MiB allocated

end0.0ms (0%)

Memory: 0.8MiB live, 0.7MiB allocated

sample1.8min (29%)

simplify1.0min (16.1%)

soundness57.5s (15.1%)

rewrite37.8s (9.9%)

localize28.3s (7.5%)

eval22.7s (6%)

explain13.9s (3.7%)

regimes12.4s (3.3%)

preprocess11.7s (3.1%)

series9.4s (2.5%)

prune7.8s (2.1%)

bsearch4.1s (1.1%)

analyze3.0s (0.8%)

start4.0ms (0%)

end0.0ms (0%)

Profiling