Metrics for Herbie run

Date:	Wednesday, March 20th, 2024
Commit:	23dc2d0f on exact-hallucinations
Hostname:	nightly with Racket 8.11.1
Seed:	2024080
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

localize7.7min (28.5%)

Results

Compiler

Compiled 85426 to 46522 computations (45.5% saved)

Precisions

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

Operation ival-sin, time spent: 3.0min, 46.0% of total-time

Operation ival-mult, time spent: 51.9s, 13.0% of total-time

Operation ival-pow, time spent: 40.9s, 10.0% of total-time

Operation ival-cos, time spent: 34.6s, 9.0% of total-time

Operation ival-div, time spent: 26.1s, 7.0% of total-time

Operation composed, time spent: 17.4s, 4.0% of total-time

Operation ival-log, time spent: 8.0s, 2.0% of total-time

Operation ival-add, time spent: 7.3s, 2.0% of total-time

Operation ival-exp, time spent: 5.2s, 1.0% of total-time

Operation ival-sub, time spent: 4.9s, 1.0% of total-time

Operation ival-sqrt, time spent: 4.8s, 1.0% of total-time

Operation const, time spent: 4.2s, 1.0% of total-time

Operation ival-cbrt, time spent: 2.6s, 1.0% of total-time

Operation ival-atan2, time spent: 1.8s, 0.0% of total-time

Operation ival-atan, time spent: 841.0ms, 0.0% of total-time

Operation ival-tan, time spent: 722.0ms, 0.0% of total-time

Operation ival-neg, time spent: 632.0ms, 0.0% of total-time

Operation ival-acos, time spent: 251.0ms, 0.0% of total-time

Operation ival-pi, time spent: 195.0ms, 0.0% of total-time

Operation ival-fabs, time spent: 137.0ms, 0.0% of total-time

Operation ival-asin, time spent: 126.0ms, 0.0% of total-time

sample7.7min (28.4%)

Results

1.3min	298853×	256	valid
38.7s	45851×	512	valid
5.6s	28114×	256	invalid
6.9s	26874×	256	infinite
7.6s	26831×	256	unsamplable
21.0s	25572×	1024	valid
2.7min	16875×	8192	exit
29.4s	11192×	2048	valid
51.2s	7408×	4096	valid
5.6s	5987×	512	infinite
1.3s	1689×	1024	invalid
620.0ms	1155×	512	invalid
1.1s	1137×	2048	invalid
19.8s	1103×	8192	valid
115.0ms	949×	256	precondition
2.7s	654×	2048	infinite
1.9s	548×	1024	infinite
3.0s	387×	4096	infinite
7.0ms	8×	512	unsamplable
3.0ms	1×	1024	unsamplable
35.0ms	1×	8192	unsamplable

Precisions

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

Operation ival-pow, time spent: 2.5min, 42.0% of total-time

Operation ival-sin, time spent: 44.5s, 12.0% of total-time

Operation ival-mult, time spent: 40.3s, 11.0% of total-time

Operation ival-cos, time spent: 33.6s, 9.0% of total-time

Operation ival-div, time spent: 30.1s, 8.0% of total-time

Operation ival-exp, time spent: 10.9s, 3.0% of total-time

Operation ival-log, time spent: 10.0s, 3.0% of total-time

Operation ival-add, time spent: 10.0s, 3.0% of total-time

Operation ival-sub, time spent: 8.1s, 2.0% of total-time

Operation ival-sqrt, time spent: 4.6s, 1.0% of total-time

Operation const, time spent: 3.7s, 1.0% of total-time

Operation ival-<, time spent: 3.0s, 1.0% of total-time

Operation ival-neg, time spent: 2.6s, 1.0% of total-time

Operation ival-atan2, time spent: 1.4s, 0.0% of total-time

Operation ival-pi, time spent: 1.0s, 0.0% of total-time

Operation ival-atan, time spent: 1.0s, 0.0% of total-time

Operation ival-tan, time spent: 758.0ms, 0.0% of total-time

Operation ival-acos, time spent: 703.0ms, 0.0% of total-time

Operation ival-and, time spent: 505.0ms, 0.0% of total-time

Operation ival-asin, time spent: 351.0ms, 0.0% of total-time

Operation ival-<=, time spent: 259.0ms, 0.0% of total-time

Operation ival-cbrt, time spent: 224.0ms, 0.0% of total-time

Operation ival-fabs, time spent: 163.0ms, 0.0% of total-time

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

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

Bogosity

eval3.0min (11.1%)

Compiler: Compiled 7185399 to 4339946 computations (39.6% saved)

preprocess2.2min (8.2%)

Algorithm

51×	egg-herbie

Rules

63000×	`fma-define`
37664×	`fma-neg`
25928×	`div-sub`
22916×	`unsub-neg`
22266×	`sub-neg`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`#f`	n/o	106	0
`sqrt.f64`	`#f`	oflow-rescue	1396	0
`acos.f64`	`(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))`	sensitivity	27	3
`/.f64`	`#f`	n/u	36	0
`/.f64`	`#f`	o/o	366	0
`asin.f64`	`(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))`	sensitivity	1	2
`sin.f64`	`#f`	sensitivity	1692	3
`/.f64`	`#f`	u/u	276	0
`cbrt.f64`	`#f`	oflow-rescue	91	0
`/.f64`	`#f`	u/n	173	0
`*.f64`	`#f`	*uo**	38	0
`cos.f64`	`#f`	sensitivity	1955	5
`*.f64`	`#f`	*no**	201	0
`sqrt.f64`	`#f`	uflow-rescue	160	0
`exp.f64`	`(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))`	sensitivity	150	27
`/.f64`	`#f`	o/n	497	0
`log.f64`	`#f`	sensitivity	596	0
`log.f64`	`#f`	oflow-rescue	6	0
`-.f64`	`#f`	nan-rescue	662	0
`-.f64`	`#f`	cancellation	979	14
`cbrt.f64`	`#f`	uflow-rescue	39	0
`*.f64`	`#f`	*nu**	118	0
`+.f64`	`#f`	cancellation	1807	34
`*.f64`	`#f`	*ou**	41	0

Confusion

	Predicted +	Predicted -
+	5765	57
-	1396	5838

Precision

0.8050551598938696

Recall

0.9902095499828237

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5765	36	21
-	1396	34	5804

Precision?

0.8022403540312544

Recall?

0.9963929920989351

Stop Event

21×	saturated
30×	node limit

Compiler

Compiled 77260 to 47230 computations (38.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.4min

Operation ival-sin, time spent: 24.1s, 28.0% of total-time

Operation ival-cos, time spent: 16.7s, 19.0% of total-time

Operation ival-mult, time spent: 14.8s, 17.0% of total-time

Operation ival-div, time spent: 11.7s, 14.0% of total-time

Operation ival-pow, time spent: 9.9s, 11.0% of total-time

Operation ival-add, time spent: 2.2s, 3.0% of total-time

Operation ival-sub, time spent: 1.7s, 2.0% of total-time

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

Operation ival-sqrt, time spent: 924.0ms, 1.0% of total-time

Operation ival-exp, time spent: 701.0ms, 1.0% of total-time

Operation ival-log, time spent: 678.0ms, 1.0% of total-time

Operation ival-tan, time spent: 471.0ms, 1.0% of total-time

Operation ival-neg, time spent: 276.0ms, 0.0% of total-time

Operation ival-atan, time spent: 189.0ms, 0.0% of total-time

Operation ival-pi, time spent: 160.0ms, 0.0% of total-time

Operation ival-atan2, time spent: 153.0ms, 0.0% of total-time

Operation ival-cbrt, time spent: 72.0ms, 0.0% of total-time

Operation ival-acos, time spent: 57.0ms, 0.0% of total-time

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

Operation ival-fabs, time spent: 14.0ms, 0.0% of total-time

regimes1.5min (5.5%)

Counts

17053 → 807

Calls

138 calls:

6.9s	phi1
5.5s	lambda2
5.3s	phi2
5.2s	b
5.2s	lambda1

Results

Compiler

Compiled 10994 to 8139 computations (26% saved)

simplify1.2min (4.3%)

Algorithm

226×	egg-herbie

Rules

158630×	`fma-define`
108858×	`*-commutative`
102364×	`distribute-lft-in`
100096×	`associate-r`
97128×	`fma-neg`

Stop Event

50×	saturated
38×	fuel
175×	node limit
1×	unsound
10×	done

Counts

84124 → 73491

Compiler

Compiled 13039 to 8835 computations (32.2% saved)

soundness1.0min (3.7%)

Rules

151106×	`fma-define`
88954×	`associate-r`
82616×	`fma-neg`
79740×	`distribute-lft-in`
77174×	`*-commutative`

Stop Event

14×	saturated
202×	node limit
4×	unsound

Compiler

Compiled 46047 to 26824 computations (41.7% saved)

prune55.0s (3.4%)

Counts: 161837 → 6547
Compiler: Compiled 431784 to 299436 computations (30.7% saved)

analyze38.1s (2.3%)

Algorithm

53×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	79.4%	20.6%	0%	0%	0%	0
14.8%	11.8%	67.6%	20.6%	0%	0%	0%	1
22.6%	17.7%	60.4%	21%	0%	0.9%	0%	2
32.7%	24.7%	50.8%	21.2%	0%	3.3%	0%	3
39.8%	29.8%	45%	21.2%	0%	4%	0%	4
45.4%	33.8%	40.6%	21.2%	0%	4.5%	0%	5
48.4%	35.7%	38%	21.2%	0%	5.1%	0%	6
51.8%	37.8%	35.2%	21.2%	0%	5.7%	0.1%	7
53.5%	38.9%	33.8%	21.3%	0%	6%	0.1%	8
56.4%	40.6%	31.4%	21.3%	0%	6.6%	0.2%	9
57.7%	41.4%	30.3%	21.3%	0%	6.8%	0.2%	10
59.8%	42.7%	28.7%	21.3%	0%	7.1%	0.3%	11
61.3%	43.5%	27.5%	21.3%	0%	7.5%	0.3%	12

Compiler

Compiled 1919 to 1343 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0s

Operation ival-mult, time spent: 8.5s, 31.0% of total-time

Operation ival-sin, time spent: 3.8s, 14.0% of total-time

Operation ival-pow, time spent: 3.5s, 13.0% of total-time

Operation ival-div, time spent: 3.5s, 13.0% of total-time

Operation ival-cos, time spent: 2.7s, 10.0% of total-time

Operation ival-add, time spent: 1.4s, 5.0% of total-time

Operation ival-sub, time spent: 1.2s, 5.0% of total-time

Operation const, time spent: 512.0ms, 2.0% of total-time

Operation ival-sqrt, time spent: 451.0ms, 2.0% of total-time

Operation ival-atan2, time spent: 272.0ms, 1.0% of total-time

Operation ival-neg, time spent: 251.0ms, 1.0% of total-time

Operation ival-<, time spent: 187.0ms, 1.0% of total-time

Operation ival-pi, time spent: 114.0ms, 0.0% of total-time

Operation ival-exp, time spent: 90.0ms, 0.0% of total-time

Operation ival-tan, time spent: 90.0ms, 0.0% of total-time

Operation ival-atan, time spent: 70.0ms, 0.0% of total-time

Operation ival-fabs, time spent: 63.0ms, 0.0% of total-time

Operation ival-log, time spent: 60.0ms, 0.0% of total-time

Operation ival-and, time spent: 43.0ms, 0.0% of total-time

Operation ival-acos, time spent: 41.0ms, 0.0% of total-time

Operation ival-asin, time spent: 38.0ms, 0.0% of total-time

Operation ival-cbrt, time spent: 21.0ms, 0.0% of total-time

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

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

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

rewrite36.3s (2.2%)

Algorithm

178×	batch-egg-rewrite

Rules

110906×	`log1p-expm1-u`
87015×	`expm1-log1p-u`
59344×	`log-prod`
48806×	`prod-diff`
45236×	`unpow-prod-down`

Stop Event

175×	node limit
3×	unsound

Counts

1623 → 45740

bsearch21.1s (1.3%)

Algorithm

299×	binary-search
73×	left-value

Stop Event

9×	predicate-same
290×	narrow-enough

Results

8.0s	26434×	256	valid
4.7s	4840×	512	valid
1.8s	1725×	4096	valid
1.4s	1600×	2048	valid
237.0ms	1494×	256	invalid
854.0ms	1001×	256	infinite
909.0ms	969×	1024	valid
642.0ms	391×	512	infinite
1.0ms	18×	256	unsamplable

Compiler

Compiled 79863 to 60334 computations (24.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.6s

Operation ival-mult, time spent: 2.7s, 21.0% of total-time

Operation ival-cos, time spent: 1.8s, 15.0% of total-time

Operation ival-sin, time spent: 1.8s, 14.0% of total-time

Operation ival-div, time spent: 1.2s, 9.0% of total-time

Operation ival-pow, time spent: 1.1s, 9.0% of total-time

Operation ival-sub, time spent: 1.1s, 9.0% of total-time

Operation ival-add, time spent: 562.0ms, 4.0% of total-time

Operation ival-atan, time spent: 533.0ms, 4.0% of total-time

Operation ival-sqrt, time spent: 433.0ms, 3.0% of total-time

Operation ival-acos, time spent: 274.0ms, 2.0% of total-time

Operation ival-atan2, time spent: 227.0ms, 2.0% of total-time

Operation ival-neg, time spent: 200.0ms, 2.0% of total-time

Operation const, time spent: 181.0ms, 1.0% of total-time

Operation ival-pi, time spent: 127.0ms, 1.0% of total-time

Operation ival-log, time spent: 93.0ms, 1.0% of total-time

Operation ival-exp, time spent: 72.0ms, 1.0% of total-time

Operation ival-asin, time spent: 66.0ms, 1.0% of total-time

Operation ival-cbrt, time spent: 15.0ms, 0.0% of total-time

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

Operation ival-fabs, time spent: 1.0ms, 0.0% of total-time

series16.5s (1%)

Counts

1623 → 38384

Calls

9306 calls:

Time	Variable		Point	Expression
292.0ms	b	@	0	(- (* (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (+ 1 (* -1/64800 (* (pow angle 2) (pow (PI) 2))))) x-scale) y-scale) (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale)) (* (* 4 (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b 1) 2)) x-scale) x-scale)) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)))
254.0ms	a	@	inf	(/ (/ (- (pow b 2) (* (+ b (sqrt (* a (* c 3)))) (- b (sqrt (* a (* c 3)))))) (- (neg b) (sqrt (* (+ b (sqrt (* a (* c 3)))) (- b (sqrt (* a (* c 3)))))))) (* 3 a))
248.0ms	theta	@	0	(cbrt (* (sin delta) (sin theta)))
129.0ms	F	@	0	(pow (* (* F (+ (* B B) (* (* A C) -4))) (* 2 (+ A (+ C (sqrt (+ (* (- A C) (- A C)) (* B B))))))) 1/4)
128.0ms	A	@	inf	(/ (* (sqrt (+ (* B B) (* (sqrt (* (* -4 A) C)) (sqrt (* (* -4 A) C))))) (sqrt (* (* F 2) (+ A (+ C (sqrt (+ (* B B) (* (- A C) (- A C))))))))) (neg (+ (* B B) (* A (* C -4)))))

Herbie run

localize7.7min (28.5%)

sample7.7min (28.4%)

eval3.0min (11.1%)

preprocess2.2min (8.2%)

regimes1.5min (5.5%)

simplify1.2min (4.3%)

soundness1.0min (3.7%)

prune55.0s (3.4%)

analyze38.1s (2.3%)

rewrite36.3s (2.2%)

bsearch21.1s (1.3%)

series16.5s (1%)

end33.0ms (0%)

Profiling