Metrics for Herbie run

Date:	Saturday, February 17th, 2024
Commit:	77dd996a on explanations-table
Hostname:	nightly with Racket 8.11.1
Seed:	2024048
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

sample2.9min (43.6%)

Results

31.7s	141557×	256	precondition
16.6s	94806×	256	valid
30.3s	58718×	1024	valid
45.6s	36055×	2048	valid
11.0s	34917×	512	valid
17.8s	7399×	8192	exit
927.0ms	4372×	256	infinite
520.0ms	4212×	256	invalid
706.0ms	3978×	256	unsamplable
1.5s	1962×	4096	valid
125.0ms	186×	512	infinite
178.0ms	152×	1024	infinite

Precisions

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

Operation ival-pow, time spent: 16.3s, 15.0% of total-time

Operation ival-tan, time spent: 14.6s, 13.0% of total-time

Operation ival-exp, time spent: 13.4s, 12.0% of total-time

Operation ival-mult, time spent: 9.3s, 8.0% of total-time

Operation ival-sub, time spent: 8.0s, 7.0% of total-time

Operation ival-log, time spent: 7.9s, 7.0% of total-time

Operation ival-div, time spent: 7.0s, 6.0% of total-time

Operation ival-sin, time spent: 6.5s, 6.0% of total-time

Operation ival-cos, time spent: 5.5s, 5.0% of total-time

Operation ival-add, time spent: 5.4s, 5.0% of total-time

Operation ival-<=, time spent: 5.0s, 4.0% of total-time

Operation ival-fabs, time spent: 2.5s, 2.0% of total-time

Operation ival-sqrt, time spent: 2.4s, 2.0% of total-time

Operation ival-<, time spent: 2.2s, 2.0% of total-time

Operation const, time spent: 1.6s, 1.0% of total-time

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

Operation ival->, time spent: 938.0ms, 1.0% of total-time

Operation ival-neg, time spent: 746.0ms, 1.0% of total-time

Operation ival-fmin, time spent: 553.0ms, 0.0% of total-time

Operation ival-atan, time spent: 437.0ms, 0.0% of total-time

Operation ival-cbrt, time spent: 315.0ms, 0.0% of total-time

Operation ...c/syntax/syntax.rkt:185:8, time spent: 68.0ms, 0.0% of total-time

Bogosity

localize55.4s (14.1%)

Compiler: Compiled 14468 to 8821 computations (39% saved)
Precisions: Click to see histograms. Total time spent on operations: 40.1s
Operation ival-pow, time spent: 9.2s, 23.0% of total-time
Operation ival-mult, time spent: 5.4s, 13.0% of total-time
Operation composed, time spent: 4.6s, 11.0% of total-time
Operation ival-div, time spent: 4.3s, 11.0% of total-time
Operation ival-log, time spent: 3.9s, 10.0% of total-time
Operation ival-add, time spent: 3.7s, 9.0% of total-time
Operation ival-exp, time spent: 1.9s, 5.0% of total-time
Operation ival-sqrt, time spent: 1.5s, 4.0% of total-time
Operation ival-sub, time spent: 1.5s, 4.0% of total-time
Operation ival-sin, time spent: 1.4s, 3.0% of total-time
Operation const, time spent: 907.0ms, 2.0% of total-time
Operation ival-cbrt, time spent: 645.0ms, 2.0% of total-time
Operation ival-cos, time spent: 547.0ms, 1.0% of total-time
Operation ival-tan, time spent: 455.0ms, 1.0% of total-time
Operation ival-neg, time spent: 110.0ms, 0.0% of total-time
Operation ival-cosh, time spent: 79.0ms, 0.0% of total-time
Operation ival-atan2, time spent: 53.0ms, 0.0% of total-time
Operation ival-atan, time spent: 21.0ms, 0.0% of total-time

soundness37.7s (9.6%)

Rules

92390×	`fma-define`
83224×	`fma-neg`
51035×	`log1p-expm1-u`
50272×	`log-prod`
47350×	`associate-r`

Stop Event

3×	saturated
157×	node limit
1×	unsound

Compiler

Compiled 15473 to 10216 computations (34% saved)

eval36.0s (9.2%)

Compiler: Compiled 1462217 to 1001820 computations (31.5% saved)

simplify22.6s (5.8%)

Algorithm

119×	egg-herbie

Rules

65074×	`fma-define`
47254×	`fma-neg`
38888×	`times-frac`
37214×	`associate-r`
35400×	`*-commutative`

Stop Event

28×	saturated
89×	node limit
18×	fuel
2×	unsound
10×	done

Counts

34903 → 35156

Compiler

Compiled 2608 to 1872 computations (28.2% saved)

rewrite18.8s (4.8%)

Algorithm

91×	batch-egg-rewrite

Rules

57481×	`log1p-expm1-u`
48004×	`expm1-log1p-u`
30690×	`prod-diff`
28618×	`log-prod`
26832×	`unpow-prod-down`

Stop Event

91×	node limit

Counts

684 → 24985

preprocess18.1s (4.6%)

Algorithm

28×	egg-herbie

Rules

23796×	`fma-neg`
15718×	`fma-define`
9020×	`distribute-lft-in`
8670×	`sub-neg`
8024×	`div-sub`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1
`sqrt.f64`	`#f`	uflow-rescue	46
`pow.f64`	`(pow.f64 (+.f64 x 1) (/.f64 1 n))`	sensitivity	40
`/.f64`	`(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))`	n/o	2
↳	`(*.f64 x x)`	overflow	69
`sqrt.f64`	`#f`	oflow-rescue	374
`/.f64`	`(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))`	n/u	30
↳	`(-.f64 (exp.f64 (*.f64 b eps)) 1)`	underflow	147
↳	`(*.f64 b eps)`	underflow	146
↳	`(-.f64 (exp.f64 (*.f64 a eps)) 1)`	underflow	149
↳	`(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))`	underflow	240
↳	`(*.f64 a eps)`	underflow	148
`log.f64`	`#f`	sensitivity	762
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))`	o/o	5
↳	`(-.f64 (exp.f64 (*.f64 2 x)) 1)`	overflow	5
↳	`(exp.f64 (*.f64 2 x))`	overflow	5
↳	`(exp.f64 x)`	overflow	5
↳	`(-.f64 (exp.f64 x) 1)`	overflow	5
`/.f64`	`#f`	u/u	431
`-.f64`	`#f`	nan-rescue	29
`-.f64`	`#f`	cancellation	4213
`+.f64`	`#f`	cancellation	360
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	1
`/.f64`	`#f`	u/n	125

Confusion

	Predicted +	Predicted -
+	5272	11
-	117	1768

Precision

0.9782891074410837

Recall

0.9979178497066061

Stop Event

15×	saturated
13×	node limit

Compiler

Compiled 10492 to 6632 computations (36.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0s

Operation ival-log, time spent: 906.0ms, 15.0% of total-time

Operation ival-exp, time spent: 840.0ms, 14.0% of total-time

Operation ival-tan, time spent: 840.0ms, 14.0% of total-time

Operation ival-div, time spent: 570.0ms, 10.0% of total-time

Operation ival-sub, time spent: 543.0ms, 9.0% of total-time

Operation ival-pow, time spent: 450.0ms, 8.0% of total-time

Operation ival-add, time spent: 428.0ms, 7.0% of total-time

Operation ival-mult, time spent: 381.0ms, 6.0% of total-time

Operation ival-cos, time spent: 319.0ms, 5.0% of total-time

Operation ival-sin, time spent: 244.0ms, 4.0% of total-time

Operation ival-sqrt, time spent: 227.0ms, 4.0% of total-time

Operation const, time spent: 127.0ms, 2.0% of total-time

Operation ival-atan, time spent: 41.0ms, 1.0% of total-time

Operation ival-cbrt, time spent: 30.0ms, 1.0% of total-time

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

prune11.5s (2.9%)

Counts: 53305 → 1772
Compiler: Compiled 60033 to 43935 computations (26.8% saved)

regimes9.0s (2.3%)

Counts

2751 → 232

Calls

43 calls:

1.8s	x
1.6s	c
1.4s	a
1.2s	b_2
476.0ms	b

Compiler

Compiled 1344 to 941 computations (30% saved)

series6.5s (1.6%)

Counts

684 → 9918

Calls

3087 calls:

Time	Variable		Point	Expression
396.0ms	x	@	inf	(log.f64 (/.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (+.f64 x 1)))) (exp.f64 (cbrt.f64 x))))
180.0ms	b	@	0	(pow.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (pow.f64 b 2)) 1/4) 2)
178.0ms	x	@	0	(.f64 (.f64 (-.f64 x (log.f64 x)) (pow.f64 n -1/2)) (pow.f64 n -1/2))
89.0ms	x	@	0	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
88.0ms	eps	@	0	(.f64 (/.f64 eps (expm1.f64 (.f64 eps b))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))

bsearch3.5s (0.9%)

Algorithm

17×	left-value
60×	binary-search

Stop Event

3×	predicate-same
57×	narrow-enough

Results

1.4s	6500×	256	valid
310.0ms	2437×	256	invalid
315.0ms	740×	1024	valid
155.0ms	554×	256	infinite
364.0ms	425×	512	valid
284.0ms	220×	2048	valid
40.0ms	211×	256	unsamplable
27.0ms	30×	512	infinite
8.0ms	9×	1024	infinite
2.0ms	2×	4096	valid

Compiler

Compiled 12526 to 9375 computations (25.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.6s

Operation ival-pow, time spent: 430.0ms, 27.0% of total-time

Operation ival-mult, time spent: 415.0ms, 26.0% of total-time

Operation ival-sub, time spent: 229.0ms, 15.0% of total-time

Operation ival-div, time spent: 146.0ms, 9.0% of total-time

Operation ival-sqrt, time spent: 121.0ms, 8.0% of total-time

Operation ival-exp, time spent: 75.0ms, 5.0% of total-time

Operation ival-add, time spent: 53.0ms, 3.0% of total-time

Operation ival-neg, time spent: 51.0ms, 3.0% of total-time

Operation const, time spent: 26.0ms, 2.0% of total-time

Operation ival-cos, time spent: 21.0ms, 1.0% of total-time

Operation ival-cbrt, time spent: 7.0ms, 0.0% of total-time

analyze2.9s (0.7%)

Algorithm

28×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	61.1%	38.9%	0%	0%	0%	0
18.1%	11.1%	50%	38.9%	0%	0%	0%	1
25.4%	15.5%	45.6%	38.9%	0%	0%	0%	2
40.7%	23.8%	34.6%	41.6%	0%	0%	0%	3
49.4%	28.8%	29.5%	41.7%	0%	0%	0%	4
56.4%	32.5%	25.1%	42.4%	0%	0%	0%	5
58.7%	33.4%	23.5%	43.1%	0%	0%	0%	6
62.4%	34.4%	20.7%	44%	0%	0.8%	0.1%	7
65.4%	35.7%	18.9%	44.5%	0%	0.8%	0.1%	8
67.8%	36.4%	17.3%	44.9%	0%	1.2%	0.3%	9
69.8%	36.8%	15.9%	45.2%	0%	1.7%	0.3%	10
72.3%	37.8%	14.5%	45.4%	0%	1.9%	0.4%	11
73.5%	38.1%	13.7%	45.6%	0%	2.2%	0.4%	12

Compiler

Compiled 505 to 355 computations (29.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.6s

Operation ival-sub, time spent: 237.0ms, 15.0% of total-time

Operation ival-mult, time spent: 227.0ms, 14.0% of total-time

Operation ival-log, time spent: 193.0ms, 12.0% of total-time

Operation ival-pow, time spent: 168.0ms, 10.0% of total-time

Operation ival-div, time spent: 122.0ms, 8.0% of total-time

Operation ival-<=, time spent: 101.0ms, 6.0% of total-time

Operation ival-sqrt, time spent: 90.0ms, 6.0% of total-time

Operation ival-add, time spent: 84.0ms, 5.0% of total-time

Operation ival-sin, time spent: 68.0ms, 4.0% of total-time

Operation ival-exp, time spent: 63.0ms, 4.0% of total-time

Operation ival-tan, time spent: 51.0ms, 3.0% of total-time

Operation ival-neg, time spent: 44.0ms, 3.0% of total-time

Operation const, time spent: 43.0ms, 3.0% of total-time

Operation ival-fabs, time spent: 32.0ms, 2.0% of total-time

Operation ival-cos, time spent: 26.0ms, 2.0% of total-time

Operation ival-and, time spent: 16.0ms, 1.0% of total-time

Operation ival->, time spent: 15.0ms, 1.0% of total-time

Operation ival-<, time spent: 10.0ms, 1.0% of total-time

Operation ...c/syntax/syntax.rkt:185:8, time spent: 8.0ms, 0.0% of total-time

Operation ival-fmin, time spent: 3.0ms, 0.0% of total-time

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

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

Herbie run

sample2.9min (43.6%)

localize55.4s (14.1%)

soundness37.7s (9.6%)

eval36.0s (9.2%)

simplify22.6s (5.8%)

rewrite18.8s (4.8%)

preprocess18.1s (4.6%)

prune11.5s (2.9%)

regimes9.0s (2.3%)

series6.5s (1.6%)

bsearch3.5s (0.9%)

analyze2.9s (0.7%)

end3.0ms (0%)

Profiling