Metrics for Herbie run

Date:	Wednesday, May 22nd, 2024
Commit:	a80fb046 on main
Hostname:	nightly with Racket 8.11.1
Seed:	2024143
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

sample9.4min (26%)

Results

2.1min	22602×	5	exit
2.1min	129524×	1	valid
1.5min	269388×	0	valid
47.1s	8017×	3	valid
36.4s	19367×	2	valid
24.3s	41469×	0	unsamplable
14.4s	1380×	4	valid
6.6s	18947×	0	invalid
5.9s	10967×	1	invalid
2.2s	1774×	2	invalid
183.0ms	920×	0	precondition
104.0ms	3×	5	valid
65.0ms	46×	1	unsamplable
28.0ms	20×	3	invalid

Precisions

Click to see histograms. Total time spent on operations: 6.9min

ival-pow: 2.1min (30.6% of total)

ival-mult: 58.5s (14.2% of total)

ival-div: 36.5s (8.8% of total)

ival-sin: 32.5s (7.9% of total)

ival-cos: 32.2s (7.8% of total)

backward-pass: 29.7s (7.2% of total)

ival-add: 20.4s (4.9% of total)

ival-sub: 17.4s (4.2% of total)

ival-sqrt: 13.9s (3.4% of total)

ival-exp: 10.0s (2.4% of total)

ival-log: 8.7s (2.1% of total)

ival-neg: 7.3s (1.8% of total)

ival-<: 5.3s (1.3% of total)

...c/correct-round.rkt:121:19: 2.8s (0.7% of total)

ival-atan2: 2.4s (0.6% of total)

const: 1.8s (0.4% of total)

ival-pi: 1.4s (0.3% of total)

ival-tan: 1.2s (0.3% of total)

ival-and: 1.2s (0.3% of total)

ival-acos: 861.0ms (0.2% of total)

ival-atan: 802.0ms (0.2% of total)

ival-cbrt: 671.0ms (0.2% of total)

ival-<=: 627.0ms (0.2% of total)

ival-fabs: 398.0ms (0.1% of total)

ival-asin: 371.0ms (0.1% of total)

ival-==: 6.0ms (0% of total)

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

Bogosity

simplify7.2min (19.8%)

Algorithm

442×	egg-herbie

Rules

181385×	`fma-define`
113875×	`fma-neg`
100208×	`distribute-lft-in`
92948×	`*-commutative`
89157×	`times-frac`

Stop Event

117×	saturated
324×	node limit
1×	unsound

Counts

139463 → 114781

soundness3.5min (9.8%)

Rules

84051×	`fma-define`
62718×	`log1p-expm1-u`
49415×	`fma-neg`
48247×	`expm1-log1p-u`
48042×	`distribute-lft-in`

Stop Event

15×	saturated
42×	fuel
246×	node limit
3×	unsound
7×	done

Compiler

Compiled 68505 to 19795 computations (71.1% saved)

localize3.5min (9.7%)

Results

57.3s	11835×	1	valid
38.0s	29401×	0	valid
24.9s	1729×	5	exit
18.5s	2404×	2	valid
9.0s	4083×	0	invalid
7.4s	545×	3	valid
2.0s	372×	1	invalid
965.0ms	46×	4	valid
161.0ms	17×	2	invalid

Compiler

Compiled 89910 to 7232 computations (92% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.5min

ival-mult: 19.4s (20.9% of total)

ival-pow: 12.0s (12.9% of total)

backward-pass: 10.7s (11.6% of total)

ival-sin: 9.9s (10.6% of total)

ival-div: 9.2s (9.9% of total)

ival-cos: 7.7s (8.3% of total)

ival-add: 6.2s (6.7% of total)

...c/correct-round.rkt:121:19: 3.1s (3.3% of total)

ival-sub: 2.8s (3% of total)

ival-sqrt: 2.0s (2.2% of total)

ival-fma: 1.8s (1.9% of total)

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

ival-hypot: 1.2s (1.3% of total)

ival-exp: 956.0ms (1% of total)

ival-atan2: 731.0ms (0.8% of total)

ival-atan: 641.0ms (0.7% of total)

ival-log1p: 630.0ms (0.7% of total)

ival-cbrt: 532.0ms (0.6% of total)

ival-neg: 508.0ms (0.5% of total)

const: 357.0ms (0.4% of total)

ival-acos: 319.0ms (0.3% of total)

ival-expm1: 260.0ms (0.3% of total)

ival-tan: 206.0ms (0.2% of total)

ival-fabs: 189.0ms (0.2% of total)

ival-pi: 171.0ms (0.2% of total)

ival-asin: 87.0ms (0.1% of total)

prune2.3min (6.3%)

Counts: 185141 → 7841
Compiler: Compiled 544531 to 268511 computations (50.7% saved)

rewrite2.0min (5.6%)

Algorithm

195×	batch-egg-rewrite

Rules

119194×	`log1p-expm1-u`
89049×	`expm1-log1p-u`
48779×	`pow1`
45777×	`add-exp-log`
44939×	`add-log-exp`

Stop Event

192×	node limit
3×	unsound

Counts

2873 → 75715

eval1.8min (5%)

Compiler: Compiled 8312009 to 818977 computations (90.1% saved)

regimes1.6min (4.4%)

Counts

25157 → 938

Calls

142 calls:

6.0s	phi1
5.5s	phi2
5.2s	lambda1
4.1s	lambda2
3.6s	a

Compiler

Compiled 13152 to 8601 computations (34.6% saved)

series1.5min (4.1%)

Counts

2873 → 64490

Calls

16620 calls:

Time	Variable		Point	Expression
1.3s	b	@	inf	(/ (- (- (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) (pow y-scale 2)) (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* (cos (* (/ angle 180) (PI))) b) 2)) (pow x-scale 2))) (sqrt (+ (* (- (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* (cos (* (/ angle 180) (PI))) b) 2)) (pow x-scale 2)) (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) (pow y-scale 2))) (- (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* (cos (* (/ angle 180) (PI))) b) 2)) (pow x-scale 2)) (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) (pow y-scale 2)))) (* (* (cos (* (/ angle 180) (PI))) (/ (* 2 (* (sin (* (/ angle 180) (PI))) (- (pow b 2) (pow a 2)))) (* y-scale x-scale))) (* (cos (* (/ angle 180) (PI))) (/ (* 2 (* (sin (* (/ angle 180) (PI))) (- (pow b 2) (pow a 2)))) (* y-scale x-scale))))))) (* (cos (* (/ angle 180) (PI))) (/ (* 2 (* (sin (* (/ angle 180) (PI))) (- (pow b 2) (pow a 2)))) (* y-scale x-scale))))
1.0s	x-scale	@	-inf	(pow (cbrt (* -4 (exp (+ (* (log (* x-scale y-scale)) -2) (* (log (* a b)) 2))))) 3)
944.0ms	a	@	-inf	(log (+ 1 (pow (sqrt (+ (* (* a (sin (* angle (* 1/180 (PI))))) (* a (sin (* angle (* 1/180 (PI)))))) (* (* b (cos (* angle (* 1/180 (PI))))) (* b (cos (* angle (* 1/180 (PI)))))))) 6)))
913.0ms	b	@	-inf	(- (- (/ (/ (+ (+ (* (pow angle 2) (+ (* -1/32400 (* (pow a 2) (pow (PI) 2))) (* (pow a 2) (* (pow angle 2) (+ (* 1/12597120000 (pow (PI) 4)) (* 1/4199040000 (pow (PI) 4))))))) (pow a 2)) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale) (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))
672.0ms	lambda2	@	-inf	(- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))))

bsearch1.0min (2.8%)

Algorithm

380×	binary-search
45×	left-value

Stop Event

3×	predicate-same
377×	narrow-enough

Results

26.4s	16904×	1	valid
15.0s	27767×	0	valid
3.6s	1074×	3	valid
2.7s	1903×	2	valid
589.0ms	1466×	0	invalid

Compiler

Compiled 126685 to 86964 computations (31.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.3s

ival-mult: 8.1s (21.1% of total)

ival-cos: 6.9s (18% of total)

ival-sin: 6.3s (16.6% of total)

ival-div: 3.4s (9% of total)

ival-pow: 3.3s (8.6% of total)

ival-sub: 2.6s (6.9% of total)

backward-pass: 2.2s (5.8% of total)

ival-add: 1.9s (5.1% of total)

ival-sqrt: 1.1s (2.7% of total)

ival-atan2: 537.0ms (1.4% of total)

ival-acos: 406.0ms (1.1% of total)

ival-atan: 370.0ms (1% of total)

ival-exp: 202.0ms (0.5% of total)

ival-neg: 195.0ms (0.5% of total)

ival-tan: 163.0ms (0.4% of total)

const: 161.0ms (0.4% of total)

ival-log: 140.0ms (0.4% of total)

ival-pi: 130.0ms (0.3% of total)

ival-asin: 44.0ms (0.1% of total)

ival-fabs: 41.0ms (0.1% of total)

analyze1.0min (2.8%)

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 947 computations (50.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.2s

ival-mult: 11.2s (30.1% of total)

ival-pow: 6.5s (17.5% of total)

ival-cos: 3.0s (8.1% of total)

ival-div: 3.0s (8.1% of total)

ival-add: 2.8s (7.4% of total)

ival-sin: 2.4s (6.5% of total)

ival-<: 2.1s (5.6% of total)

ival-sub: 1.7s (4.7% of total)

ival-sqrt: 1.5s (4% of total)

ival-neg: 767.0ms (2.1% of total)

...c/correct-round.rkt:121:19: 569.0ms (1.5% of total)

ival-atan2: 292.0ms (0.8% of total)

const: 198.0ms (0.5% of total)

ival-exp: 173.0ms (0.5% of total)

ival-and: 159.0ms (0.4% of total)

ival-pi: 145.0ms (0.4% of total)

ival-tan: 132.0ms (0.4% of total)

ival-log: 126.0ms (0.3% of total)

ival-atan: 117.0ms (0.3% of total)

ival-asin: 88.0ms (0.2% of total)

ival-fabs: 85.0ms (0.2% of total)

ival-acos: 83.0ms (0.2% of total)

ival-cbrt: 57.0ms (0.2% of total)

backward-pass: 37.0ms (0.1% of total)

ival-<=: 26.0ms (0.1% of total)

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

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

explain43.2s (2%)

Results

13.6s	8374×	1	valid
8.9s	15236×	0	valid
4.7s	1860×	2	valid
3.1s	564×	3	valid
930.0ms	78×	4	valid

Compiler

Compiled 19842 to 2382 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.6s

ival-mult: 4.5s (24% of total)

ival-sin: 2.8s (15% of total)

ival-div: 2.0s (10.8% of total)

ival-cos: 1.8s (9.9% of total)

ival-pow: 1.6s (8.7% of total)

backward-pass: 1.5s (8.3% of total)

ival-exp: 1.2s (6.2% of total)

ival-sub: 817.0ms (4.4% of total)

ival-add: 674.0ms (3.6% of total)

ival-sqrt: 513.0ms (2.8% of total)

ival-log: 383.0ms (2.1% of total)

ival-neg: 205.0ms (1.1% of total)

const: 96.0ms (0.5% of total)

ival-atan2: 88.0ms (0.5% of total)

ival-tan: 87.0ms (0.5% of total)

ival-atan: 81.0ms (0.4% of total)

ival-pi: 75.0ms (0.4% of total)

ival-cbrt: 47.0ms (0.3% of total)

ival-acos: 43.0ms (0.2% of total)

ival-fabs: 29.0ms (0.2% of total)

ival-asin: 17.0ms (0.1% of total)

preprocess34.4s (1.6%)

Algorithm

51×	egg-herbie

Rules

31500×	`fma-define`
18832×	`fma-neg`
12964×	`div-sub`
11458×	`unsub-neg`
11133×	`sub-neg`

Stop Event

21×	saturated
30×	node limit

Compiler

Compiled 50752 to 19858 computations (60.9% saved)

end0.0ms (0%)

Precisions: Click to see histograms. Total time spent on operations: 5.9s
ival-add: 5.9s (100% of total)

sample9.4min (26%)

simplify7.2min (19.8%)

soundness3.5min (9.8%)

localize3.5min (9.7%)

prune2.3min (6.3%)

rewrite2.0min (5.6%)

eval1.8min (5%)

regimes1.6min (4.4%)

series1.5min (4.1%)

bsearch1.0min (2.8%)

analyze1.0min (2.8%)

explain43.2s (2%)

preprocess34.4s (1.6%)

end0.0ms (0%)

Profiling