Metrics for Herbie run

Date:	Wednesday, June 5th, 2024
Commit:	8a54fd57 on main
Hostname:	nightly with Racket 8.11.1
Seed:	2024157
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

sample2.6min (27.4%)

Results

1.2min	434646×	0	valid
44.0s	7898×	5	exit
13.4s	28886×	1	valid
3.5s	6776×	2	valid
1.9s	6735×	0	invalid
147.0ms	364×	3	valid

Precisions

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

ival-sin: 33.5s (32.5% of total)

ival-mult: 25.6s (24.8% of total)

ival-add: 7.0s (6.8% of total)

...c/correct-round.rkt:168:19: 6.0s (5.8% of total)

ival-div: 5.3s (5.2% of total)

adjust: 5.2s (5% of total)

ival-exp: 3.0s (2.9% of total)

ival-sub: 2.8s (2.7% of total)

ival-log: 2.3s (2.2% of total)

ival-sqrt: 2.2s (2.1% of total)

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

ival-pow: 1.3s (1.2% of total)

ival-cos: 1.0s (1% of total)

ival-atan2: 932.0ms (0.9% of total)

ival-pi: 650.0ms (0.6% of total)

ival->: 610.0ms (0.6% of total)

const: 567.0ms (0.5% of total)

ival-true: 557.0ms (0.5% of total)

ival-neg: 551.0ms (0.5% of total)

ival-acosh: 551.0ms (0.5% of total)

ival-assert: 531.0ms (0.5% of total)

ival-<=: 357.0ms (0.3% of total)

ival-asinh: 313.0ms (0.3% of total)

ival-fabs: 264.0ms (0.3% of total)

ival-atanh: 181.0ms (0.2% of total)

ival->=: 148.0ms (0.1% of total)

ival-and: 84.0ms (0.1% of total)

Bogosity

simplify1.6min (16.2%)

Algorithm

432×	egg-herbie

Rules

156062×	`fma-define`
108105×	`fmm-def`
96027×	`distribute-lft-in`
89985×	`associate-r`
83287×	`distribute-rgt-in`

Stop Event

144×	saturated
276×	node limit
12×	unsound

Counts

98235 → 93587

soundness1.2min (12.1%)

Rules

61479×	`fma-define`
50269×	`log1p-expm1-u`
47003×	`fmm-def`
46498×	`associate-r`
37541×	`distribute-lft-in`

Stop Event

19×	saturated
197×	node limit
35×	fuel
12×	unsound
22×	done

Compiler

Compiled 47880 to 13369 computations (72.1% saved)

localize59.0s (10.2%)

Results

21.3s	35885×	0	valid
10.9s	5521×	1	valid
5.5s	867×	5	exit
4.8s	4834×	0	invalid
3.3s	1287×	2	valid
480.0ms	229×	1	invalid
71.0ms	17×	3	valid

Compiler

Compiled 50032 to 5492 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.3s

ival-mult: 4.0s (20.7% of total)

ival-pow: 2.2s (11.2% of total)

adjust: 2.1s (11.1% of total)

ival-add: 1.8s (9.2% of total)

...c/correct-round.rkt:168:19: 1.8s (9.1% of total)

ival-div: 1.4s (7.4% of total)

ival-log: 1.2s (6.1% of total)

ival-fma: 863.0ms (4.5% of total)

ival-sub: 752.0ms (3.9% of total)

ival-exp: 457.0ms (2.4% of total)

ival-sqrt: 400.0ms (2.1% of total)

ival-hypot: 353.0ms (1.8% of total)

ival-neg: 262.0ms (1.4% of total)

ival-asin: 244.0ms (1.3% of total)

ival-sin: 216.0ms (1.1% of total)

ival-cos: 210.0ms (1.1% of total)

ival-atan2: 200.0ms (1% of total)

const: 135.0ms (0.7% of total)

ival-fabs: 130.0ms (0.7% of total)

ival-log1p: 121.0ms (0.6% of total)

ival-cbrt: 105.0ms (0.5% of total)

ival-acos: 103.0ms (0.5% of total)

ival-copysign: 89.0ms (0.5% of total)

ival-true: 86.0ms (0.4% of total)

ival-assert: 60.0ms (0.3% of total)

ival-pi: 47.0ms (0.2% of total)

ival-expm1: 39.0ms (0.2% of total)

ival-e: 2.0ms (0% of total)

rewrite47.9s (8.3%)

Algorithm

185×	batch-egg-rewrite

Rules

120454×	`log1p-expm1-u`
83175×	`expm1-log1p-u`
38632×	`pow1`
38227×	`add-exp-log`
37522×	`add-log-exp`

Stop Event

177×	node limit
8×	unsound

Counts

2218 → 61122

prune35.9s (6.2%)

Counts: 134995 → 3097
Compiler: Compiled 136496 to 72404 computations (47% saved)

eval29.3s (5.1%)

Compiler: Compiled 4206164 to 538334 computations (87.2% saved)

explain19.1s (3.3%)

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`#f`	oflow-rescue	1162	0
`-.f64`	`#f`	cancellation	766	2
`/.f64`	`#f`	o/o	645	0
`sin.f64`	`#f`	sensitivity	191	1
`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	188	0
`/.f64`	`#f`	o/n	183	0
`sqrt.f32`	`#f`	oflow-rescue	178	0
`sqrt.f64`	`#f`	uflow-rescue	155	0
`+.f64`	`#f`	cancellation	146	0
`log.f64`	`(log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`	sensitivity	139	0
`log.f32`	`(log.f32 (+.f32 (fabs.f32 x) (sqrt.f32 (+.f32 (*.f32 x x) #s(literal 1 binary32)))))`	sensitivity	123	2
`/.f64`	`#f`	n/o	96	0
`-.f64`	`#f`	nan-rescue	93	0
`+.f64`	`#f`	nan-rescue	69	0
`*.f64`	`#f`	*nu**	62	0
`/.f64`	`#f`	u/u	60	0
`/.f64`	`#f`	u/n	42	0
`*.f64`	`#f`	*no**	31	0
`/.f64`	`#f`	n/u	12	0
`exp.f64`	`#f`	sensitivity	10	0
`log.f32`	`#f`	oflow-rescue	4	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
`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	57
↳	`(+.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	63
`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	57
↳	`(+.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	63
`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

Confusion

	Predicted +	Predicted -
+	3611	43
-	212	10726

Precision

0.9445461679309443

Recall

0.988232074438971

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3611	4	39
-	212	2	10724

Precision?

0.9441107338730739

Recall?

0.9893267651888341

Freqs

test

number	freq
0	10769
1	3286
2	534
3	3

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	36	0	0
-	3	1	17

Precision?

0.9

Recall?

1.0

Results

6.2s	25578×	0	valid
2.7s	3012×	1	valid
419.0ms	568×	2	valid
15.0ms	24×	3	valid
2.0ms	2×	5	exit

Compiler

Compiled 15052 to 2968 computations (80.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.3s

ival-mult: 964.0ms (29.6% of total)

ival-add: 352.0ms (10.8% of total)

ival-div: 283.0ms (8.7% of total)

...c/correct-round.rkt:168:19: 225.0ms (6.9% of total)

adjust: 214.0ms (6.6% of total)

ival-sqrt: 179.0ms (5.5% of total)

ival-log: 176.0ms (5.4% of total)

ival-exp: 174.0ms (5.3% of total)

ival-sub: 129.0ms (4% of total)

ival-sin: 83.0ms (2.5% of total)

ival-asin: 74.0ms (2.3% of total)

ival-atan2: 62.0ms (1.9% of total)

ival-cos: 58.0ms (1.8% of total)

ival-log1p: 58.0ms (1.8% of total)

ival-true: 49.0ms (1.5% of total)

ival-pow: 38.0ms (1.2% of total)

ival-assert: 35.0ms (1.1% of total)

const: 32.0ms (1% of total)

ival-fabs: 23.0ms (0.7% of total)

ival-pi: 20.0ms (0.6% of total)

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

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

bsearch18.1s (3.1%)

Algorithm

322×	binary-search
52×	left-value

Stop Event

14×	predicate-same
308×	narrow-enough

Results

12.1s	33925×	0	valid
2.0s	2638×	1	valid
355.0ms	733×	2	valid

Compiler

Compiled 68254 to 47014 computations (31.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.5s

ival-mult: 1.9s (35.4% of total)

ival-exp: 617.0ms (11.3% of total)

ival-log: 499.0ms (9.1% of total)

ival-add: 465.0ms (8.5% of total)

ival-cos: 295.0ms (5.4% of total)

...c/correct-round.rkt:168:19: 294.0ms (5.4% of total)

ival-sin: 285.0ms (5.2% of total)

ival-sub: 200.0ms (3.7% of total)

ival-atan2: 188.0ms (3.4% of total)

ival-div: 173.0ms (3.2% of total)

ival-sqrt: 166.0ms (3% of total)

adjust: 113.0ms (2.1% of total)

ival-asin: 62.0ms (1.1% of total)

ival-true: 55.0ms (1% of total)

ival-assert: 40.0ms (0.7% of total)

const: 23.0ms (0.4% of total)

ival-fabs: 21.0ms (0.4% of total)

ival-neg: 16.0ms (0.3% of total)

ival-copysign: 14.0ms (0.3% of total)

ival-pi: 6.0ms (0.1% of total)

series17.7s (3.1%)

Counts

2218 → 37113

Calls

9684 calls:

Time	Variable		Point	Expression
395.0ms	y.im	@	-inf	(log (cos (+ (* y.re (atan2 x.im x.re)) (* y.im (log (sqrt (+ (* x.im x.im) (* x.re x.re))))))))
352.0ms	x	@	-inf	(log (+ 1 (fabs x)))
299.0ms	base	@	inf	(log (+ 1 (log base)))
217.0ms	x.re	@	-inf	(+ (* (+ x.im x.re) (* x.im (+ x.re -3))) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
194.0ms	alpha	@	0	(/ (+ alpha (* beta (+ 1 (+ alpha (/ 1 beta))))) (* (+ beta (+ alpha 3)) (* (+ alpha (+ beta 2)) (+ alpha (+ beta 2)))))

preprocess13.1s (2.3%)

Algorithm

57×	egg-herbie

Rules

20513×	`fmm-def`
20193×	`fma-define`
9595×	`unsub-neg`
9128×	`sub-neg`
8864×	`distribute-lft-in`

Stop Event

32×	saturated
25×	node limit

Compiler

Compiled 31322 to 12176 computations (61.1% saved)

regimes12.1s (2.1%)

Counts

8236 → 784

Calls

132 calls:

1.2s	y.re
917.0ms	x.im
786.0ms	x
739.0ms	im
544.0ms	re

Compiler

Compiled 6280 to 3901 computations (37.9% saved)

analyze3.3s (0.6%)

Algorithm

58×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	86.3%	13.7%	0%	0%	0%	0
53.4%	46.1%	40.2%	13.7%	0%	0%	0%	1
62.8%	53.1%	31.4%	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 1498 to 848 computations (43.4% saved)

Herbie run

sample2.6min (27.4%)

simplify1.6min (16.2%)

soundness1.2min (12.1%)

localize59.0s (10.2%)

rewrite47.9s (8.3%)

prune35.9s (6.2%)

eval29.3s (5.1%)

explain19.1s (3.3%)

bsearch18.1s (3.1%)

series17.7s (3.1%)

preprocess13.1s (2.3%)

regimes12.1s (2.1%)

analyze3.3s (0.6%)

end0.0ms (0%)

Profiling