Metrics for Herbie run

Date:	Thursday, May 23rd, 2024
Commit:	6b737c7e on explanations-trifurcate
Hostname:	nightly with Racket 8.11.1
Seed:	2024144
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

sample1.6min (21.7%)

Results

40.0s	221328×	0	valid
12.9s	28900×	1	valid
10.4s	64939×	0	invalid
5.9s	13978×	1	invalid
3.3s	6769×	2	valid
3.3s	6294×	3	valid
636.0ms	897×	4	valid
424.0ms	969×	2	invalid
37.0ms	248×	0	unsamplable
4.0ms	5×	5	exit
3.0ms	4×	5	valid

Precisions

Click to see histograms. Total time spent on operations: 57.4s

ival-mult: 14.5s (25.3% of total)

ival-div: 8.5s (14.8% of total)

ival-pow: 6.7s (11.6% of total)

ival-tan: 4.5s (7.8% of total)

ival-sub: 4.2s (7.3% of total)

ival-sqrt: 3.3s (5.7% of total)

ival-add: 3.0s (5.2% of total)

ival-sin: 2.9s (5% of total)

ival-exp: 2.4s (4.2% of total)

backward-pass: 2.0s (3.5% of total)

ival-cos: 960.0ms (1.7% of total)

...c/correct-round.rkt:121:19: 769.0ms (1.3% of total)

const: 681.0ms (1.2% of total)

ival-neg: 636.0ms (1.1% of total)

ival-pi: 628.0ms (1.1% of total)

ival-acos: 562.0ms (1% of total)

ival-log: 347.0ms (0.6% of total)

ival-asin: 281.0ms (0.5% of total)

ival-hypot: 280.0ms (0.5% of total)

ival-<: 133.0ms (0.2% of total)

ival-fabs: 114.0ms (0.2% of total)

ival-atan: 91.0ms (0.2% of total)

ival-and: 11.0ms (0% of total)

Bogosity

simplify1.4min (18.3%)

Algorithm

286×	egg-herbie

Rules

111922×	`fma-define`
66317×	`fma-neg`
62595×	`times-frac`
58666×	`associate-r`
55267×	`distribute-lft-in`

Stop Event

76×	saturated
210×	node limit

Counts

94154 → 78213

soundness1.0min (13.7%)

Rules

51780×	`fma-define`
44454×	`log1p-expm1-u`
37401×	`times-frac`
34920×	`associate-r`
33627×	`expm1-log1p-u`

Stop Event

8×	saturated
170×	node limit
29×	fuel
1×	unsound
3×	done

Compiler

Compiled 40327 to 12592 computations (68.8% saved)

localize36.8s (8.3%)

Results

10.3s	21392×	0	valid
5.0s	4398×	1	valid
3.2s	782×	5	exit
2.9s	4205×	0	invalid
2.3s	608×	3	valid
1.5s	860×	2	valid
1.2s	115×	4	valid
52.0ms	152×	0	unsamplable

Compiler

Compiled 36649 to 4245 computations (88.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.9s

ival-mult: 3.6s (22.7% of total)

ival-div: 2.2s (14.1% of total)

ival-pow: 1.9s (12.2% of total)

ival-tan: 1.0s (6.4% of total)

backward-pass: 1.0s (6.3% of total)

ival-sqrt: 960.0ms (6.1% of total)

ival-add: 693.0ms (4.4% of total)

ival-sin: 678.0ms (4.3% of total)

ival-fma: 573.0ms (3.6% of total)

ival-sub: 567.0ms (3.6% of total)

ival-cos: 492.0ms (3.1% of total)

ival-exp: 442.0ms (2.8% of total)

ival-log: 282.0ms (1.8% of total)

ival-expm1: 227.0ms (1.4% of total)

ival-hypot: 206.0ms (1.3% of total)

ival-cbrt: 162.0ms (1% of total)

...c/correct-round.rkt:121:19: 157.0ms (1% of total)

ival-acos: 155.0ms (1% of total)

const: 121.0ms (0.8% of total)

ival-asin: 109.0ms (0.7% of total)

ival-log1p: 86.0ms (0.5% of total)

ival-neg: 76.0ms (0.5% of total)

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

ival-atan: 34.0ms (0.2% of total)

ival-fabs: 19.0ms (0.1% of total)

rewrite33.8s (7.6%)

Algorithm

127×	batch-egg-rewrite

Rules

71162×	`log1p-expm1-u`
54581×	`expm1-log1p-u`
32999×	`pow1`
32568×	`add-exp-log`
32138×	`add-log-exp`

Stop Event

126×	node limit
1×	unsound

Counts

1891 → 49649

prune29.1s (6.6%)

Counts: 112073 → 3166
Compiler: Compiled 144830 to 81044 computations (44% saved)

eval23.6s (5.3%)

Compiler: Compiled 3440046 to 462743 computations (86.5% saved)

series16.7s (3.8%)

Counts

1891 → 44505

Calls

12171 calls:

Time	Variable		Point	Expression
392.0ms	U	@	-inf	(log U)
309.0ms	x	@	0	(* (+ 1 x) (/ -1 B))
188.0ms	v	@	0	(log (acos (/ (+ 1 (* (pow v 2) -5)) (+ (* v v) -1))))
170.0ms	K	@	inf	(log (+ 1 (cos (* K 1/2))))
157.0ms	D	@	0	(+ (* (/ c0 (* w h)) (/ (* d d) (* D D))) (sqrt (- (* (* (/ c0 (* w h)) (/ (* d d) (* D D))) (* (/ c0 (* w h)) (/ (* d d) (* D D)))) (* M M))))

regimes16.4s (3.7%)

Counts

9636 → 668

Calls

156 calls:

1.5s	l
858.0ms	t
734.0ms	k
474.0ms	F
459.0ms	(.f64 (.f64 (.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (.f64 #s(literal 2 binary64) (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U))))

Compiler

Compiled 8130 to 6032 computations (25.8% saved)

bsearch13.9s (3.1%)

Algorithm

281×	binary-search
66×	left-value

Stop Event

8×	predicate-same
273×	narrow-enough

Results

7.5s	30936×	0	valid
1.6s	7902×	0	invalid
360.0ms	677×	2	valid
297.0ms	1144×	1	valid
93.0ms	167×	3	valid
84.0ms	83×	2	invalid
79.0ms	52×	4	valid
38.0ms	173×	1	invalid

Compiler

Compiled 77960 to 56535 computations (27.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.6s

ival-mult: 2.4s (31.1% of total)

ival-div: 1.4s (18.3% of total)

ival-pow: 1.4s (18.2% of total)

ival-add: 479.0ms (6.3% of total)

ival-tan: 430.0ms (5.7% of total)

ival-sub: 351.0ms (4.6% of total)

ival-sin: 314.0ms (4.1% of total)

ival-neg: 254.0ms (3.3% of total)

ival-exp: 221.0ms (2.9% of total)

ival-sqrt: 123.0ms (1.6% of total)

backward-pass: 85.0ms (1.1% of total)

ival-cos: 83.0ms (1.1% of total)

const: 72.0ms (0.9% of total)

...c/correct-round.rkt:121:19: 19.0ms (0.3% of total)

ival-hypot: 13.0ms (0.2% of total)

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

ival-pi: 5.0ms (0.1% of total)

ival-asin: 4.0ms (0.1% of total)

ival-fabs: 1.0ms (0% of total)

analyze13.3s (3%)

Algorithm

32×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	98.2%	1.8%	0%	0%	0%	0
22.2%	21.8%	76.4%	1.8%	0%	0%	0%	1
22.6%	21.8%	74.8%	1.8%	0%	1.6%	0%	2
28.6%	26.5%	66.3%	1.8%	0%	5.5%	0%	3
32.6%	29.6%	61.2%	1.8%	0%	7%	0.4%	4
35.8%	32.3%	58%	1.8%	0%	7.4%	0.6%	5
40.1%	36.1%	54%	1.8%	0%	7.4%	0.7%	6
45.5%	40.6%	48.7%	1.8%	0%	8.1%	0.8%	7
47.9%	42.1%	45.8%	1.8%	0%	9.5%	0.8%	8
51%	44.7%	42.9%	1.8%	0%	9.8%	0.9%	9
52.1%	45.5%	41.8%	1.8%	0%	10%	0.9%	10
53.9%	46.8%	39.9%	1.8%	0%	10.6%	1%	11
55.7%	47.9%	38.2%	1.8%	0%	11.1%	1%	12

Compiler

Compiled 861 to 546 computations (36.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.5s

ival-mult: 2.5s (33.7% of total)

ival-pow: 1.4s (19.1% of total)

ival-div: 956.0ms (12.8% of total)

ival-add: 877.0ms (11.8% of total)

ival-sub: 341.0ms (4.6% of total)

ival-sqrt: 274.0ms (3.7% of total)

ival-sin: 254.0ms (3.4% of total)

...c/correct-round.rkt:121:19: 205.0ms (2.7% of total)

ival-tan: 191.0ms (2.6% of total)

ival-neg: 85.0ms (1.1% of total)

const: 81.0ms (1.1% of total)

ival-acos: 52.0ms (0.7% of total)

ival-exp: 50.0ms (0.7% of total)

ival-<: 30.0ms (0.4% of total)

ival-asin: 26.0ms (0.3% of total)

ival-pi: 25.0ms (0.3% of total)

ival-fabs: 19.0ms (0.3% of total)

ival-cos: 17.0ms (0.2% of total)

backward-pass: 17.0ms (0.2% of total)

ival-log: 13.0ms (0.2% of total)

ival-and: 4.0ms (0.1% of total)

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

ival-hypot: 0.0ms (0% of total)

explain12.0s (2.7%)

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`#f`	oflow-rescue	490	0
`-.f64`	`#f`	cancellation	440	0
`cos.f64`	`#f`	sensitivity	406	0
`+.f64`	`#f`	nan-rescue	264	0
`acos.f64`	`(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))`	sensitivity	254	2
`*.f64`	`#f`	*no**	247	0
`sqrt.f64`	`#f`	uflow-rescue	166	0
`pow.f64`	`#f`	oflow-rescue	147	0
`asin.f64`	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))`	sensitivity	129	0
`*.f64`	`#f`	*uo**	121	0
`tan.f64`	`(tan.f64 (*.f64 (PI.f64) l))`	sensitivity	121	0
`-.f64`	`#f`	nan-rescue	119	0
`*.f64`	`#f`	*nu**	76	0
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	75	27
`/.f64`	`#f`	o/o	71	0
`*.f64`	`#f`	*ou**	70	0
`/.f64`	`#f`	o/n	66	0
`+.f64`	`#f`	cancellation	66	0
`cos.f64`	`(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))`	oflow-rescue	54	0
↳	`(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))`	overflow	54
↳	`(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)`	overflow	54
↳	`(*.f64 K (+.f64 m n))`	overflow	54
`pow.f64`	`#f`	uflow-rescue	48	0
`/.f64`	`#f`	n/u	43	0
`/.f64`	`#f`	u/u	42	0
`/.f64`	`#f`	n/o	40	0
`/.f64`	`#f`	u/n	18	0
`log.f64`	`(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))`	sensitivity	6	0
`exp.f64`	`(exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	1970	42
-	1146	5034

Precision

0.6322207958921694

Recall

0.9791252485089463

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1970	2	40
-	1146	27	5007

Precision?

0.6270270270270271

Recall?

0.9801192842942346

Freqs

test

number	freq
0	5076
1	2721
2	333
3	54
4	8

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	26	0	0
-	1	0	5

Precision?

0.9629629629629629

Recall?

1.0

Results

3.5s	13132×	0	valid
1.4s	2260×	1	valid
434.0ms	494×	2	valid
316.0ms	418×	3	valid
74.0ms	62×	4	valid
19.0ms	18×	5	exit

Compiler

Compiled 8566 to 2100 computations (75.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.2s

ival-mult: 644.0ms (20.2% of total)

ival-div: 538.0ms (16.9% of total)

ival-tan: 390.0ms (12.2% of total)

ival-pow: 327.0ms (10.2% of total)

ival-sub: 270.0ms (8.5% of total)

ival-pi: 186.0ms (5.8% of total)

backward-pass: 158.0ms (5% of total)

ival-add: 135.0ms (4.2% of total)

ival-sqrt: 107.0ms (3.4% of total)

ival-sin: 107.0ms (3.4% of total)

ival-exp: 91.0ms (2.9% of total)

ival-cos: 61.0ms (1.9% of total)

const: 40.0ms (1.3% of total)

ival-neg: 39.0ms (1.2% of total)

ival-acos: 31.0ms (1% of total)

ival-hypot: 18.0ms (0.6% of total)

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

...c/correct-round.rkt:121:19: 12.0ms (0.4% of total)

ival-asin: 9.0ms (0.3% of total)

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

ival-fabs: 5.0ms (0.2% of total)

preprocess9.7s (2.2%)

Algorithm

32×	egg-herbie

Rules

20025×	`fma-define`
13409×	`fma-neg`
8518×	`times-frac`
7943×	`unsub-neg`
7239×	`distribute-lft-in`

Stop Event

9×	saturated
23×	node limit

Compiler

Compiled 46594 to 20104 computations (56.9% saved)

Herbie run

sample1.6min (21.7%)

simplify1.4min (18.3%)

soundness1.0min (13.7%)

localize36.8s (8.3%)

rewrite33.8s (7.6%)

prune29.1s (6.6%)

eval23.6s (5.3%)

series16.7s (3.8%)

regimes16.4s (3.7%)

bsearch13.9s (3.1%)

analyze13.3s (3%)

explain12.0s (2.7%)

preprocess9.7s (2.2%)

end0.0ms (0%)

Profiling