Metrics for Herbie run

Date:	Saturday, May 25th, 2024
Commit:	445b0ec4 on explanations-trifurcate
Hostname:	nightly with Racket 8.11.1
Seed:	2024146
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

sample2.4min (28.1%)

Results

59.6s	434434×	0	valid
42.3s	7757×	5	exit
13.4s	28919×	1	valid
3.9s	6886×	2	valid
1.1s	5228×	0	unsamplable
133.0ms	398×	3	valid
128.0ms	511×	0	invalid

Precisions

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

ival-sin: 33.9s (35.3% of total)

ival-mult: 18.2s (18.9% of total)

ival-add: 8.0s (8.3% of total)

...c/correct-round.rkt:121:19: 5.6s (5.8% of total)

ival-div: 5.4s (5.7% of total)

ival-exp: 3.6s (3.7% of total)

backward-pass: 3.6s (3.7% of total)

ival-sub: 3.0s (3.2% of total)

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

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

ival-cos: 1.5s (1.6% of total)

ival-pow: 1.4s (1.5% of total)

ival-neg: 1.3s (1.4% of total)

ival-asin: 1.3s (1.3% of total)

ival-pi: 776.0ms (0.8% of total)

ival-atan2: 736.0ms (0.8% of total)

const: 695.0ms (0.7% of total)

ival->: 658.0ms (0.7% of total)

ival-asinh: 561.0ms (0.6% of total)

ival-atanh: 448.0ms (0.5% of total)

ival-<=: 331.0ms (0.3% of total)

ival-fabs: 306.0ms (0.3% of total)

ival-acosh: 288.0ms (0.3% of total)

ival->=: 142.0ms (0.1% of total)

ival-and: 83.0ms (0.1% of total)

Bogosity

simplify1.6min (18.3%)

Algorithm

440×	egg-herbie

Rules

157389×	`fma-define`
107955×	`fma-neg`
99828×	`associate-r`
91985×	`distribute-lft-in`
78857×	`*-commutative`

Stop Event

142×	saturated
288×	node limit
10×	unsound

Counts

97391 → 89017

soundness52.9s (10.3%)

Rules

54123×	`fma-define`
49785×	`log1p-expm1-u`
46578×	`fma-neg`
41976×	`associate-r`
33872×	`expm1-log1p-u`

Stop Event

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

Compiler

Compiled 41391 to 11491 computations (72.2% saved)

rewrite47.9s (9.4%)

Algorithm

190×	batch-egg-rewrite

Rules

126833×	`log1p-expm1-u`
88574×	`expm1-log1p-u`
39928×	`pow1`
38394×	`add-exp-log`
36886×	`add-log-exp`

Stop Event

180×	node limit
10×	unsound

Counts

2133 → 61127

localize39.1s (7.6%)

Results

13.3s	38616×	0	valid
5.5s	3835×	1	valid
2.7s	1359×	2	valid
2.7s	629×	5	exit
2.5s	4360×	0	invalid
666.0ms	221×	1	invalid
262.0ms	260×	0	unsamplable
142.0ms	128×	3	valid

Compiler

Compiled 43641 to 5072 computations (88.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.2s

ival-mult: 3.5s (21.6% of total)

ival-pow: 2.0s (12.5% of total)

ival-div: 1.7s (10.6% of total)

backward-pass: 1.5s (9.5% of total)

ival-add: 1.5s (9.1% of total)

...c/correct-round.rkt:121:19: 1.2s (7.7% of total)

ival-log: 878.0ms (5.4% of total)

ival-sub: 530.0ms (3.3% of total)

ival-fma: 523.0ms (3.2% of total)

ival-sqrt: 386.0ms (2.4% of total)

ival-hypot: 346.0ms (2.1% of total)

ival-exp: 334.0ms (2.1% of total)

ival-sin: 230.0ms (1.4% of total)

ival-asin: 199.0ms (1.2% of total)

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

ival-cos: 161.0ms (1% of total)

ival-atan2: 140.0ms (0.9% of total)

const: 138.0ms (0.9% of total)

ival-neg: 136.0ms (0.8% of total)

ival-expm1: 132.0ms (0.8% of total)

ival-log1p: 125.0ms (0.8% of total)

ival-acos: 107.0ms (0.7% of total)

ival-cbrt: 75.0ms (0.5% of total)

ival-fabs: 56.0ms (0.3% of total)

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

ival-e: 9.0ms (0.1% of total)

prune30.7s (6%)

Counts: 131964 → 3073
Compiler: Compiled 126388 to 68710 computations (45.6% saved)

eval29.4s (5.7%)

Compiler: Compiled 3875848 to 513026 computations (86.8% saved)

series19.4s (3.8%)

Counts

2133 → 36264

Calls

9486 calls:

Time	Variable		Point	Expression
363.0ms	alpha	@	inf	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
255.0ms	re	@	-inf	(/ 1 (* (/ 1 (atan2 im re)) (log base)))
254.0ms	u1	@	inf	(* (/ 1 6) (pow (* -2 (log u1)) 1/2))
234.0ms	im	@	-inf	(log (+ 1 (atan2 im re)))
230.0ms	re	@	0	(pow (* 2 (+ re (sqrt (+ (* re re) (* im im))))) 1/4)

explain17.5s (3.4%)

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`#f`	oflow-rescue	1165	0
`-.f64`	`#f`	cancellation	780	0
`/.f64`	`#f`	o/o	676	0
`/.f64`	`#f`	o/n	192	0
`sin.f64`	`#f`	sensitivity	182	0
`sqrt.f32`	`#f`	oflow-rescue	181	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	178	0
`+.f64`	`#f`	cancellation	158	0
`sqrt.f64`	`#f`	uflow-rescue	139	0
`log.f32`	`(log.f32 (+.f32 (fabs.f32 x) (sqrt.f32 (+.f32 (*.f32 x x) #s(literal 1 binary32)))))`	sensitivity	136	0
`log.f64`	`(log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`	sensitivity	135	0
`/.f64`	`#f`	n/o	97	0
`-.f64`	`#f`	nan-rescue	80	0
`*.f64`	`#f`	*nu**	66	0
`/.f64`	`#f`	u/u	62	0
`+.f64`	`#f`	nan-rescue	49	0
`/.f64`	`#f`	u/n	39	0
`*.f64`	`#f`	*no**	31	0
`/.f64`	`#f`	n/u	15	0
`exp.f64`	`#f`	sensitivity	6	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**	4	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	4
↳	`(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	4
↳	`(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	4
`log.f32`	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`	oflow-rescue	1	0
↳	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`	overflow	1
↳	`(*.f32 x x)`	overflow	123
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	123

Confusion

	Predicted +	Predicted -
+	3626	22
-	177	10767

Precision

0.953457796476466

Recall

0.9939692982456141

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3626	0	22
-	177	0	10767

Precision?

0.953457796476466

Recall?

0.9939692982456141

Freqs

test

number	freq
0	10789
1	3234
2	569

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	36	0	0
-	2	0	19

Precision?

0.9473684210526315

Recall?

1.0

Results

4.5s	25588×	0	valid
1.7s	2946×	1	valid
488.0ms	618×	2	valid
13.0ms	28×	3	valid
5.0ms	4×	5	exit

Compiler

Compiled 15172 to 2854 computations (81.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.5s

ival-mult: 1.3s (36.4% of total)

ival-add: 494.0ms (14.1% of total)

ival-div: 261.0ms (7.5% of total)

...c/correct-round.rkt:121:19: 223.0ms (6.4% of total)

ival-sqrt: 217.0ms (6.2% of total)

ival-log: 177.0ms (5.1% of total)

backward-pass: 168.0ms (4.8% of total)

ival-exp: 142.0ms (4.1% of total)

ival-sub: 122.0ms (3.5% of total)

ival-sin: 67.0ms (1.9% of total)

ival-asin: 65.0ms (1.9% of total)

ival-cos: 58.0ms (1.7% of total)

const: 53.0ms (1.5% of total)

ival-atan2: 48.0ms (1.4% of total)

ival-pow: 39.0ms (1.1% of total)

ival-fabs: 38.0ms (1.1% of total)

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

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

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

ival-log1p: 9.0ms (0.3% of total)

preprocess12.6s (2.5%)

Algorithm

57×	egg-herbie

Rules

20546×	`fma-neg`
20224×	`fma-define`
10466×	`unsub-neg`
9196×	`sub-neg`
8861×	`distribute-lft-in`

Stop Event

32×	saturated
25×	node limit

Compiler

Compiled 28386 to 11064 computations (61% saved)

regimes10.9s (2.1%)

Counts

7926 → 742

Calls

132 calls:

1.2s	y.re
970.0ms	im
842.0ms	y.im
837.0ms	x.im
768.0ms	re

Compiler

Compiled 5809 to 3652 computations (37.1% saved)

bsearch10.6s (2.1%)

Algorithm

316×	binary-search
34×	left-value

Stop Event

11×	predicate-same
305×	narrow-enough

Results

5.8s	33515×	0	valid
2.0s	2663×	1	valid
82.0ms	206×	2	valid
11.0ms	32×	3	valid

Compiler

Compiled 71183 to 47905 computations (32.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.6s

ival-mult: 2.3s (40.7% of total)

ival-add: 549.0ms (9.8% of total)

ival-log: 377.0ms (6.7% of total)

ival-sub: 370.0ms (6.6% of total)

ival-sin: 354.0ms (6.3% of total)

ival-cos: 300.0ms (5.4% of total)

ival-div: 284.0ms (5.1% of total)

backward-pass: 281.0ms (5% of total)

ival-sqrt: 212.0ms (3.8% of total)

ival-exp: 206.0ms (3.7% of total)

...c/correct-round.rkt:121:19: 171.0ms (3.1% of total)

ival-atan2: 112.0ms (2% of total)

const: 47.0ms (0.8% of total)

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

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

ival-copysign: 12.0ms (0.2% of total)

ival-fabs: 12.0ms (0.2% of total)

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

analyze3.5s (0.7%)

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 1558 to 790 computations (49.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.2s

ival-mult: 638.0ms (29.2% of total)

ival-add: 272.0ms (12.5% of total)

...c/correct-round.rkt:121:19: 271.0ms (12.4% of total)

ival-div: 224.0ms (10.3% of total)

ival-log: 211.0ms (9.7% of total)

ival-sqrt: 117.0ms (5.4% of total)

ival-sub: 109.0ms (5% of total)

ival-pow: 80.0ms (3.7% of total)

ival-atan2: 69.0ms (3.2% of total)

ival-exp: 65.0ms (3% of total)

ival-cos: 35.0ms (1.6% of total)

ival-sin: 24.0ms (1.1% of total)

const: 21.0ms (1% of total)

ival->: 12.0ms (0.5% of total)

ival-<=: 10.0ms (0.5% of total)

ival-pi: 8.0ms (0.4% of total)

ival-neg: 8.0ms (0.4% of total)

backward-pass: 5.0ms (0.2% of total)

ival-and: 2.0ms (0.1% of total)

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

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

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

ival->=: 0.0ms (0% of total)

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

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

Herbie run

sample2.4min (28.1%)

simplify1.6min (18.3%)

soundness52.9s (10.3%)

rewrite47.9s (9.4%)

localize39.1s (7.6%)

prune30.7s (6%)

eval29.4s (5.7%)

series19.4s (3.8%)

explain17.5s (3.4%)

preprocess12.6s (2.5%)

regimes10.9s (2.1%)

bsearch10.6s (2.1%)

analyze3.5s (0.7%)

end0.0ms (0%)

Profiling