Metrics for Herbie run

Date:	Tuesday, August 20th, 2024
Commit:	fce740b4 on ffi-types
Hostname:	nightly with Racket 8.11.1
Seed:	2024233
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

soundness3.3min (20.7%)

Memory

219.2MiB live, 39 692.4MiB allocated

Rules

2 047 814×	`lower-fma.f32`
2 047 378×	`lower-fma.f64`
1 018 156×	`lower-*.f32`
1 016 898×	`lower-*.f64`
617 182×	`lower-+.f32`

Stop Event

340×	iter limit
222×	node limit
34×	fuel
21×	done
2×	unsound
1×	saturated

Compiler

Compiled 39 232 to 15 464 computations (60.6% saved)

prune3.1min (19.5%)

Memory: -1 002.9MiB live, 98 664.9MiB allocated
Counts: 219 359 → 3 203
Compiler: Compiled 187 339 to 73 703 computations (60.7% saved)

localize2.5min (15.8%)

Memory

-156.5MiB live, 48 111.3MiB allocated

Samples

12.9s	41 611×	0	valid
4.2s	3 912×	1	valid
2.6s	1 766×	2	valid
1.1s	2 610×	0	invalid
398.0ms	323×	1	exit
162.0ms	172×	3	valid
31.0ms	12×	2	exit
11.0ms	23×	0	exit
1.0ms	3×	5	exit

Compiler

Compiled 72 933 to 6 462 computations (91.1% saved)

Precisions

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

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

ival-add: 2.1s (13.7% of total)

ival-div: 1.8s (11.7% of total)

const: 1.3s (8.7% of total)

adjust: 863.0ms (5.6% of total)

ival-log: 700.0ms (4.5% of total)

ival-exp: 610.0ms (3.9% of total)

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

ival-hypot: 490.0ms (3.2% of total)

ival-sqrt: 428.0ms (2.8% of total)

ival-pow: 294.0ms (1.9% of total)

ival-sin: 241.0ms (1.6% of total)

ival-neg: 176.0ms (1.1% of total)

ival-cos: 166.0ms (1.1% of total)

ival-atan2: 160.0ms (1% of total)

ival-acos: 159.0ms (1% of total)

ival-asin: 139.0ms (0.9% of total)

ival-pow2: 94.0ms (0.6% of total)

ival-fabs: 86.0ms (0.6% of total)

exact: 77.0ms (0.5% of total)

ival-true: 45.0ms (0.3% of total)

ival-log1p: 40.0ms (0.3% of total)

ival-copysign: 39.0ms (0.3% of total)

ival-pi: 36.0ms (0.2% of total)

ival-cosh: 28.0ms (0.2% of total)

ival-assert: 21.0ms (0.1% of total)

ival-e: 4.0ms (0% of total)

sample2.0min (12.6%)

Memory

503.7MiB live, 136 964.8MiB allocated

Samples

56.6s	438 481×	0	valid
24.6s	3 775×	5	exit
7.6s	22 652×	1	valid
4.2s	8 638×	2	valid
1.2s	8 859×	0	exit
346.0ms	850×	3	valid
51.0ms	488×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.3min

ival-mult: 20.6s (26.5% of total)

ival-sin: 19.6s (25.3% of total)

ival-add: 5.5s (7% of total)

adjust: 4.7s (6% of total)

const: 4.1s (5.3% of total)

ival-div: 4.0s (5.1% of total)

ival-exp: 3.3s (4.2% of total)

ival-log: 2.7s (3.5% of total)

ival-sub: 2.4s (3.1% of total)

ival-hypot: 2.3s (2.9% of total)

ival-asin: 1.4s (1.8% of total)

ival-atan2: 1.3s (1.7% of total)

ival-cos: 1.3s (1.6% of total)

ival-sqrt: 840.0ms (1.1% of total)

ival->: 539.0ms (0.7% of total)

ival-pi: 527.0ms (0.7% of total)

exact: 364.0ms (0.5% of total)

ival-pow: 357.0ms (0.5% of total)

ival-acosh: 309.0ms (0.4% of total)

ival-true: 275.0ms (0.4% of total)

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

ival-fabs: 210.0ms (0.3% of total)

ival-neg: 199.0ms (0.3% of total)

ival-assert: 190.0ms (0.2% of total)

ival-<=: 177.0ms (0.2% of total)

ival-atanh: 134.0ms (0.2% of total)

ival->=: 128.0ms (0.2% of total)

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

Bogosity

simplify1.8min (11.5%)

Memory

364.0MiB live, 113 517.2MiB allocated

Algorithm

449×	egg-herbie

Rules

3 678 760×	`lower-fma.f32`
3 677 896×	`lower-fma.f64`
1 329 396×	`lower-*.f32`
1 326 996×	`lower-*.f64`
889 736×	`lower-+.f32`

Stop Event

591×	iter limit
281×	node limit
168×	saturated

Counts

57 528 → 56 723

rewrite1.2min (7.4%)

Memory

-258.4MiB live, 83 339.0MiB allocated

Rules

1 064 418×	`lower-fma.f32`
1 063 558×	`lower-fma.f64`
753 420×	`lower-*.f32`
751 202×	`lower-*.f64`
605 996×	`lower-/.f32`

Stop Event

416×	iter limit
187×	node limit
5×	saturated
4×	unsound

Counts

2 853 → 115 579

eval53.0s (5.6%)

Memory: 1 463.8MiB live, 67 631.4MiB allocated
Compiler: Compiled 11 522 559 to 509 367 computations (95.6% saved)

preprocess15.5s (1.6%)

Memory

460.9MiB live, 17 545.2MiB 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 46 879 to 11 265 computations (76% saved)

regimes14.9s (1.6%)

Memory

-6.3MiB live, 20 812.1MiB allocated

Counts

10 228 → 979

Calls

130 calls:

971.0ms	x
906.0ms	re
775.0ms	im
625.0ms	(sin.f64 re)
558.0ms	y.re

Compiler

Compiled 18 978 to 10 275 computations (45.9% saved)

explain14.7s (1.6%)

Memory

-597.0MiB live, 20 060.5MiB allocated

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`#f`	oflow-rescue	1159	0
`-.f64`	`#f`	cancellation	781	2
`/.f64`	`#f`	o/o	635	0
`/.f64`	`#f`	o/n	201	0
`sqrt.f32`	`#f`	oflow-rescue	196	0
`sin.f64`	`#f`	sensitivity	173	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	151	0
`sqrt.f64`	`#f`	uflow-rescue	141	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	120	0
`-.f64`	`#f`	nan-rescue	109	0
`/.f64`	`#f`	n/o	89	0
`/.f64`	`#f`	u/u	64	0
`*.f64`	`#f`	*nu**	59	0
`+.f64`	`#f`	nan-rescue	52	0
`/.f64`	`#f`	u/n	36	0
`*.f64`	`#f`	*no**	27	0
`/.f64`	`#f`	n/u	8	0
`log.f32`	`#f`	oflow-rescue	3	0
`*.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**	3	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	3
↳	`(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	3
↳	`(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	3
`pow.f64`	`(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)))`	sensitivity	1	0
`exp.f64`	`(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))))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	3583	38
-	184	10787

Precision

0.9511547650650385

Recall

0.9895056614194974

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3583	2	36
-	184	1	10786

Precision?

0.9509283819628647

Recall?

0.9900579950289975

Freqs

test

number	freq
0	10825
1	3225
2	540
3	2

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	37	0	0
-	0	0	20

Precision?

1.0

Recall?

1.0

Samples

3.6s	25 904×	0	valid
1.3s	2 362×	1	valid
659.0ms	860×	2	valid
21.0ms	52×	3	valid
3.0ms	6×	5	exit

Compiler

Compiled 13 675 to 2 283 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.7s

ival-mult: 960.0ms (26% of total)

ival-log: 373.0ms (10.1% of total)

ival-add: 342.0ms (9.3% of total)

ival-div: 315.0ms (8.5% of total)

ival-hypot: 218.0ms (5.9% of total)

const: 213.0ms (5.8% of total)

ival-exp: 200.0ms (5.4% of total)

ival-sub: 177.0ms (4.8% of total)

ival-copysign: 172.0ms (4.7% of total)

adjust: 159.0ms (4.3% of total)

ival-cos: 116.0ms (3.1% of total)

ival-sin: 109.0ms (3% of total)

ival-sqrt: 81.0ms (2.2% of total)

ival-asin: 74.0ms (2% of total)

ival-atan2: 43.0ms (1.2% of total)

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

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

exact: 20.0ms (0.5% of total)

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

ival-pi: 17.0ms (0.5% of total)

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

ival-neg: 11.0ms (0.3% of total)

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

series12.6s (1.3%)

Memory

49.9MiB live, 14 945.8MiB allocated

Counts

2 853 → 57 528

Calls

7080 calls:

Time	Variable		Point	Expression
784.0ms	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)))
205.0ms	alpha	@	-inf	(/ (+ 1 alpha) (+ alpha 2))
121.0ms	x	@	0	(log (+ 1 (fabs x)))
110.0ms	x	@	inf	(log (+ 1 (fabs x)))
92.0ms	u2	@	inf	(+ (* (* (/ 1 6) (pow (exp 1/2) (log (* -2 (log u1))))) (cos (* (* 2 (PI)) u2))) 1/2)

bsearch4.4s (0.5%)

Memory

32.1MiB live, 5 782.4MiB allocated

Algorithm

252×	binary-search
251×	left-value

Stop Event

239×	narrow-enough
13×	predicate-same

Samples

2.2s	16 084×	0	valid
495.0ms	1 255×	1	valid
93.0ms	324×	2	valid
38.0ms	129×	3	valid

Compiler

Compiled 71 429 to 43 160 computations (39.6% saved)

Precisions

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

ival-mult: 657.0ms (34.7% of total)

ival-hypot: 273.0ms (14.4% of total)

ival-add: 215.0ms (11.4% of total)

ival-log: 132.0ms (7% of total)

ival-sin: 104.0ms (5.5% of total)

ival-atan2: 85.0ms (4.5% of total)

ival-exp: 82.0ms (4.3% of total)

const: 68.0ms (3.6% of total)

ival-sub: 63.0ms (3.3% of total)

ival-cos: 58.0ms (3.1% of total)

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

adjust: 46.0ms (2.4% of total)

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

ival-true: 13.0ms (0.7% of total)

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

exact: 5.0ms (0.3% of total)

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

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

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

analyze2.5s (0.3%)

Memory

140.8MiB live, 3 896.2MiB 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)

start1.0ms (0%)

Memory: 2.7MiB live, 2.6MiB allocated

end0.0ms (0%)

Memory: 0.9MiB live, 0.9MiB allocated

soundness3.3min (20.7%)

prune3.1min (19.5%)

localize2.5min (15.8%)

sample2.0min (12.6%)

simplify1.8min (11.5%)

rewrite1.2min (7.4%)

eval53.0s (5.6%)

preprocess15.5s (1.6%)

regimes14.9s (1.6%)

explain14.7s (1.6%)

series12.6s (1.3%)

bsearch4.4s (0.5%)

analyze2.5s (0.3%)

start1.0ms (0%)

end0.0ms (0%)

Profiling