Metrics for Herbie run

Date:	Friday, April 5th, 2024
Commit:	9a443234 on explanations-eval-top3
Hostname:	nightly with Racket 8.11.1
Seed:	2024096
Parameters:	256 points for 4 iterations
Flags:	`reduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionssetup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:proofs` default

sample1.9min (25.2%)

Results

55.4s	270350×	256	valid
7.6s	31085×	256	infinite
11.0s	19574×	1024	valid
19.1s	13624×	2048	valid
3.3s	10982×	512	valid
588.0ms	4138×	256	invalid
196.0ms	953×	256	unsamplable
889.0ms	780×	4096	valid
1.9s	202×	8192	exit
85.0ms	197×	512	infinite
113.0ms	144×	1024	infinite
18.0ms	16×	2048	infinite

Precisions

Click to see histograms. Total time spent on operations: 1.0min

Operation ival-mult, time spent: 11.9s, 19.0% of total-time

Operation ival-pow, time spent: 7.7s, 13.0% of total-time

Operation ival-tan, time spent: 7.0s, 11.0% of total-time

Operation ival-add, time spent: 6.1s, 10.0% of total-time

Operation ival-div, time spent: 6.0s, 10.0% of total-time

Operation ival-<=, time spent: 4.7s, 8.0% of total-time

Operation ival-sub, time spent: 4.2s, 7.0% of total-time

Operation ival-sin, time spent: 3.6s, 6.0% of total-time

Operation ival-cos, time spent: 2.2s, 4.0% of total-time

Operation ival-log, time spent: 1.7s, 3.0% of total-time

Operation const, time spent: 1.5s, 2.0% of total-time

Operation ival-sqrt, time spent: 917.0ms, 2.0% of total-time

Operation ival-exp, time spent: 812.0ms, 1.0% of total-time

Operation ival-neg, time spent: 764.0ms, 1.0% of total-time

Operation ival-and, time spent: 733.0ms, 1.0% of total-time

Operation composed, time spent: 432.0ms, 1.0% of total-time

Operation ival-==, time spent: 330.0ms, 1.0% of total-time

Operation ival-atan, time spent: 272.0ms, 0.0% of total-time

Operation ival-<, time spent: 120.0ms, 0.0% of total-time

Operation ival-pi, time spent: 50.0ms, 0.0% of total-time

Operation ival-fabs, time spent: 48.0ms, 0.0% of total-time

Operation ival-if, time spent: 8.0ms, 0.0% of total-time

Bogosity

localize1.4min (19.3%)

Compiler: Compiled 28902 to 17166 computations (40.6% saved)
Precisions: Click to see histograms. Total time spent on operations: 56.3s
Operation ival-mult, time spent: 17.4s, 31.0% of total-time
Operation ival-pow, time spent: 8.6s, 15.0% of total-time
Operation ival-div, time spent: 7.8s, 14.0% of total-time
Operation ival-add, time spent: 7.7s, 14.0% of total-time
Operation composed, time spent: 5.0s, 9.0% of total-time
Operation ival-sub, time spent: 4.6s, 8.0% of total-time
Operation const, time spent: 1.5s, 3.0% of total-time
Operation ival-exp, time spent: 1.3s, 2.0% of total-time
Operation ival-sqrt, time spent: 504.0ms, 1.0% of total-time
Operation ival-log, time spent: 472.0ms, 1.0% of total-time
Operation ival-cbrt, time spent: 349.0ms, 1.0% of total-time
Operation ival-tan, time spent: 323.0ms, 1.0% of total-time
Operation ival-atan, time spent: 223.0ms, 0.0% of total-time
Operation ival-cos, time spent: 205.0ms, 0.0% of total-time
Operation ival-sin, time spent: 150.0ms, 0.0% of total-time
Operation ival-neg, time spent: 130.0ms, 0.0% of total-time
Operation ival-pi, time spent: 9.0ms, 0.0% of total-time
Operation ival-e, time spent: 6.0ms, 0.0% of total-time

eval55.9s (12.6%)

Compiler: Compiled 2471409 to 1639611 computations (33.7% saved)

simplify35.7s (8.1%)

Algorithm

164×	egg-herbie

Rules

85266×	`fma-define`
75722×	`distribute-lft-in`
70046×	`fma-neg`
68328×	`distribute-rgt-in`
65062×	`*-commutative`

Stop Event

41×	saturated
123×	node limit
23×	fuel
18×	done

Counts

55113 → 51541

Compiler

Compiled 8093 to 5419 computations (33% saved)

preprocess34.7s (7.9%)

Algorithm

42×	egg-herbie

Rules

37136×	`fma-define`
36960×	`fma-neg`
19878×	`unsub-neg`
18560×	`sub-neg`
15262×	`distribute-rgt-in`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`#f`	cancellation	1426	2
`+.f64`	`#f`	cancellation	389	87
`-.f64`	(-.f64 (*.f64 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 t) 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)	oflow-left	217	0
`sqrt.f64`	`#f`	oflow-rescue	198	0
`log.f64`	`(log.f64 (+.f64 1 x))`	sensitivity	170	0
`/.f64`	`#f`	n/o	159	0
`/.f64`	`#f`	o/o	157	0
`pow.f64`	`(pow.f64 (+.f64 1 (/.f64 i n)) n)`	sensitivity	119	0
`-.f64`	`#f`	nan-rescue	75	0
`/.f64`	`#f`	u/n	69	0
`/.f64`	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`	u/u	44	0
↳	`(*.f64 (-.f64 x y) (+.f64 x y))`	underflow	44
↳	`(*.f64 y y)`	underflow	80
↳	`(*.f64 x x)`	underflow	114
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	44
`+.f64`	(+.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) 6))) (+.f64 (.f64 x1 x1) 1)) (.f64 (.f64 (.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)))) (.f64 (*.f64 x1 x1) x1))	nan-rescue	38	0
↳	`(*.f64 x1 x1)`	overflow	402
↳	`(-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (*.f64 2 x2)) x1)`	overflow	268
↳	`(.f64 (.f64 (.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))`	overflow	67
↳	`(+.f64 (.f64 (.f64 3 x1) x1) (*.f64 2 x2))`	overflow	268
↳	`(+.f64 (.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) 6)))`	overflow	90
↳	(+.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) 6))) (+.f64 (.f64 x1 x1) 1)) (.f64 (.f64 (.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))))	overflow	121
↳	`(.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3))`	overflow	23
↳	`(.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))`	overflow	67
↳	`(.f64 (+.f64 (.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) 6))) (+.f64 (.f64 x1 x1) 1))`	overflow	121
↳	`(.f64 (.f64 3 x1) x1)`	overflow	335
↳	`(+.f64 (*.f64 x1 x1) 1)`	overflow	335
↳	`(*.f64 x1 x1)`	overflow	67
↳	`(.f64 (.f64 x1 x1) x1)`	overflow	85
`/.f64`	`#f`	o/n	38	0
`*.f64`	`#f`	*nu**	35	0
`/.f64`	`(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))`	n/u	32	0
↳	`(/.f64 i n)`	underflow	32
`*.f64`	`#f`	*no**	16	0

Confusion

	Predicted +	Predicted -
+	3363	520
-	376	6237

Precision

0.8994383525006686

Recall

0.8660829255730106

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3363	170	350
-	376	175	6062

Precision?

0.8650832517140059

Recall?

0.9098635075972187

Stop Event

20×	saturated
22×	node limit

Compiler

Compiled 31381 to 19911 computations (36.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.1s

Operation ival-mult, time spent: 4.0s, 33.0% of total-time

Operation ival-add, time spent: 2.1s, 17.0% of total-time

Operation ival-div, time spent: 1.9s, 16.0% of total-time

Operation ival-pow, time spent: 1.9s, 15.0% of total-time

Operation ival-sub, time spent: 976.0ms, 8.0% of total-time

Operation const, time spent: 341.0ms, 3.0% of total-time

Operation ival-tan, time spent: 275.0ms, 2.0% of total-time

Operation ival-exp, time spent: 129.0ms, 1.0% of total-time

Operation ival-sin, time spent: 126.0ms, 1.0% of total-time

Operation ival-log, time spent: 117.0ms, 1.0% of total-time

Operation ival-cos, time spent: 108.0ms, 1.0% of total-time

Operation ival-neg, time spent: 80.0ms, 1.0% of total-time

Operation ival-sqrt, time spent: 68.0ms, 1.0% of total-time

Operation ival-atan, time spent: 26.0ms, 0.0% of total-time

Operation composed, time spent: 24.0ms, 0.0% of total-time

Operation ival-pi, time spent: 2.0ms, 0.0% of total-time

soundness28.6s (6.5%)

Rules

66860×	`fma-define`
53002×	`distribute-lft-in`
52786×	`fma-neg`
48450×	`distribute-rgt-in`
44242×	`associate-r`

Stop Event

6×	saturated
124×	node limit

Compiler

Compiled 22182 to 13684 computations (38.3% saved)

rewrite24.5s (5.5%)

Algorithm

123×	batch-egg-rewrite

Rules

69949×	`log1p-expm1-u`
56299×	`expm1-log1p-u`
41146×	`prod-diff`
38550×	`log-prod`
35146×	`unpow-prod-down`

Stop Event

123×	node limit

Counts

960 → 35107

prune21.4s (4.8%)

Counts: 74626 → 1873
Compiler: Compiled 77215 to 52718 computations (31.7% saved)

regimes15.3s (3.5%)

Counts

3855 → 548

Calls

92 calls:

1.9s	x
1.8s	x1
1.5s	b
1.2s	d
1.1s	c

Compiler

Compiled 3775 to 2676 computations (29.1% saved)

bsearch13.2s (3%)

Algorithm

274×	binary-search
19×	left-value

Stop Event

31×	predicate-same
243×	narrow-enough

Results

6.1s	22157×	256	valid
3.2s	7226×	256	infinite
176.0ms	1625×	256	invalid
831.0ms	1319×	1024	valid
394.0ms	1108×	512	valid
136.0ms	164×	2048	valid
50.0ms	61×	1024	infinite
6.0ms	32×	256	unsamplable
16.0ms	29×	512	infinite

Compiler

Compiled 71393 to 51798 computations (27.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.6s

Operation ival-mult, time spent: 2.5s, 37.0% of total-time

Operation ival-div, time spent: 1.3s, 20.0% of total-time

Operation ival-add, time spent: 985.0ms, 15.0% of total-time

Operation ival-sub, time spent: 823.0ms, 12.0% of total-time

Operation ival-pow, time spent: 568.0ms, 9.0% of total-time

Operation const, time spent: 194.0ms, 3.0% of total-time

Operation ival-exp, time spent: 134.0ms, 2.0% of total-time

Operation ival-neg, time spent: 110.0ms, 2.0% of total-time

Operation ival-sqrt, time spent: 33.0ms, 0.0% of total-time

Operation ival-pi, time spent: 0.0ms, 0.0% of total-time

analyze11.5s (2.6%)

Algorithm

43×	search
2×	random

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	54.5%	45.5%	0%	0%	0%	0
23.5%	12.8%	41.7%	45.5%	0%	0%	0%	1
39.5%	21.5%	33%	45.5%	0%	0%	0%	2
50.8%	26.8%	25.9%	45.5%	0%	1.7%	0%	3
58.9%	31%	21.7%	45.5%	0%	1.8%	0%	4
71.8%	37.8%	14.8%	45.6%	0%	1.8%	0%	5
73.2%	38.5%	14.1%	45.6%	0%	1.8%	0%	6
78%	40.8%	11.5%	45.6%	0%	2.1%	0%	7
81.6%	42.6%	9.6%	45.7%	0%	2.1%	0%	8
84.2%	43.8%	8.2%	45.7%	0%	2.2%	0%	9
86.2%	44.6%	7.1%	45.7%	0%	2.5%	0%	10
88.2%	45.6%	6.1%	45.7%	0%	2.5%	0.1%	11
89.1%	45.9%	5.6%	45.7%	0%	2.6%	0.1%	12

Compiler

Compiled 1441 to 1017 computations (29.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.1s

Operation ival-mult, time spent: 1.4s, 18.0% of total-time

Operation ival-add, time spent: 1.4s, 18.0% of total-time

Operation ival-sub, time spent: 1.2s, 15.0% of total-time

Operation ival-pow, time spent: 1.1s, 13.0% of total-time

Operation ival-div, time spent: 905.0ms, 11.0% of total-time

Operation ival-sqrt, time spent: 894.0ms, 11.0% of total-time

Operation ival-fabs, time spent: 390.0ms, 5.0% of total-time

Operation const, time spent: 203.0ms, 3.0% of total-time

Operation ival-<, time spent: 156.0ms, 2.0% of total-time

Operation ival-<=, time spent: 109.0ms, 1.0% of total-time

Operation ival-exp, time spent: 108.0ms, 1.0% of total-time

Operation ival-if, time spent: 62.0ms, 1.0% of total-time

Operation ival-==, time spent: 54.0ms, 1.0% of total-time

Operation ival-neg, time spent: 29.0ms, 0.0% of total-time

Operation ival-and, time spent: 19.0ms, 0.0% of total-time

Operation ival-pi, time spent: 4.0ms, 0.0% of total-time

Operation composed, time spent: 0.0ms, 0.0% of total-time

Operation ival-atan, time spent: 0.0ms, 0.0% of total-time

Operation ival-tan, time spent: 0.0ms, 0.0% of total-time

Operation ival-cos, time spent: 0.0ms, 0.0% of total-time

Operation ival-sin, time spent: 0.0ms, 0.0% of total-time

Operation ival-log, time spent: 0.0ms, 0.0% of total-time

series4.7s (1.1%)

Counts

960 → 20006

Calls

5046 calls:

Time	Variable		Point	Expression
97.0ms	x2	@	0	(* 3 (/ (- (- (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))
79.0ms	c	@	-inf	(+ (* (/ c (sqrt (+ (* c c) (* d d)))) (/ b (sqrt (+ (* c c) (* d d))))) (neg (* a (/ (/ d (sqrt (+ (* d d) (* c c)))) (sqrt (+ (* d d) (* c c)))))))
74.0ms	eps	@	-inf	(* (pow eps 4) (+ eps (* 5 x)))
71.0ms	u	@	-inf	(/ (/ v (+ t1 u)) (neg (+ t1 u)))
70.0ms	b	@	inf	(* (+ a b) (+ a b))

Herbie run

sample1.9min (25.2%)

localize1.4min (19.3%)

eval55.9s (12.6%)

simplify35.7s (8.1%)

preprocess34.7s (7.9%)

soundness28.6s (6.5%)

rewrite24.5s (5.5%)

prune21.4s (4.8%)

regimes15.3s (3.5%)

bsearch13.2s (3%)

analyze11.5s (2.6%)

series4.7s (1.1%)

end39.0ms (0%)

Profiling