Metrics for Herbie run

Date:	Monday, May 20th, 2024
Commit:	c2f4097e on main
Hostname:	nightly with Racket 8.11.1
Seed:	2024141
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

simplify2.3min (23.9%)

Algorithm

270×	egg-herbie

Rules

223474×	`fma-define`
130526×	`fma-neg`
124168×	`times-frac`
122110×	`distribute-lft-in`
113702×	`associate-r`

Stop Event

67×	saturated
203×	node limit

Counts

100382 → 71066

sample1.6min (16.4%)

Results

1.3min	247628×	0	valid
1.3s	8470×	0	invalid
809.0ms	2076×	0	precondition
10.0ms	52×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.0min

ival-mult: 13.5s (21.5% of total)

ival-<=: 10.1s (16.2% of total)

...c/correct-round.rkt:121:19: 9.4s (15% of total)

ival-div: 5.4s (8.7% of total)

ival-log: 2.6s (4.2% of total)

ival-add: 2.4s (3.8% of total)

ival-sin: 2.2s (3.5% of total)

ival-sub: 2.0s (3.2% of total)

ival-exp: 1.8s (2.9% of total)

ival-sqrt: 1.8s (2.9% of total)

ival-and: 1.6s (2.5% of total)

ival-fabs: 1.6s (2.5% of total)

ival-neg: 1.3s (2% of total)

ival-cos: 1.1s (1.7% of total)

ival-pi: 883.0ms (1.4% of total)

ival-floor: 769.0ms (1.2% of total)

ival->: 595.0ms (0.9% of total)

ival-log2: 519.0ms (0.8% of total)

ival-fmax: 489.0ms (0.8% of total)

const: 470.0ms (0.7% of total)

ival-<: 447.0ms (0.7% of total)

ival-sinh: 393.0ms (0.6% of total)

ival-tan: 359.0ms (0.6% of total)

ival-if: 310.0ms (0.5% of total)

ival-==: 192.0ms (0.3% of total)

ival-atan: 186.0ms (0.3% of total)

ival-asin: 140.0ms (0.2% of total)

ival->=: 85.0ms (0.1% of total)

backward-pass: 75.0ms (0.1% of total)

Bogosity

soundness1.5min (15.6%)

Rules

110144×	`fma-define`
73096×	`associate-r`
68898×	`times-frac`
67516×	`*-commutative`
61004×	`distribute-lft-in`

Stop Event

8×	saturated
171×	node limit
30×	fuel

Compiler

Compiled 65404 to 12964 computations (80.2% saved)

prune43.2s (7.4%)

Counts: 143455 → 3938
Compiler: Compiled 333571 to 127056 computations (61.9% saved)

localize42.9s (7.4%)

Results

18.8s	27172×	0	valid
5.0s	594×	5	exit
3.0s	896×	1	valid
1.7s	1870×	0	invalid
81.0ms	188×	0	unsamplable

Compiler

Compiled 103222 to 5489 computations (94.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.8s

ival-mult: 4.7s (26.2% of total)

ival-div: 2.2s (12.3% of total)

ival-pow: 1.8s (10.2% of total)

ival-sin: 1.0s (5.6% of total)

ival-hypot: 978.0ms (5.5% of total)

ival-fma: 730.0ms (4.1% of total)

ival-tan: 706.0ms (4% of total)

ival-add: 681.0ms (3.8% of total)

backward-pass: 603.0ms (3.4% of total)

ival-sqrt: 584.0ms (3.3% of total)

ival-exp: 467.0ms (2.6% of total)

ival-atan: 402.0ms (2.3% of total)

ival-log1p: 368.0ms (2.1% of total)

ival-sub: 341.0ms (1.9% of total)

ival-log: 330.0ms (1.9% of total)

ival-if: 285.0ms (1.6% of total)

...c/correct-round.rkt:121:19: 260.0ms (1.5% of total)

ival-fmax: 257.0ms (1.4% of total)

ival-neg: 198.0ms (1.1% of total)

ival-cos: 175.0ms (1% of total)

ival-log2: 127.0ms (0.7% of total)

ival-floor: 120.0ms (0.7% of total)

const: 111.0ms (0.6% of total)

ival-pi: 65.0ms (0.4% of total)

ival-cbrt: 53.0ms (0.3% of total)

ival-expm1: 51.0ms (0.3% of total)

ival->=: 46.0ms (0.3% of total)

ival-asin: 44.0ms (0.2% of total)

ival->: 41.0ms (0.2% of total)

ival-fabs: 35.0ms (0.2% of total)

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

ival-sinh: 12.0ms (0.1% of total)

ival-e: 10.0ms (0.1% of total)

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

series33.8s (5.8%)

Counts

1969 → 56239

Calls

13716 calls:

Time	Variable		Point	Expression
854.0ms	dY.u	@	inf	(* (log (fmax (+ (pow (* (floor d) dX.w) 2) (/ (- (pow (* (floor w) dX.u) 4) (pow (* (floor h) dX.v) 4)) (- (pow (* (floor w) dX.u) 2) (pow (* (floor h) dX.v) 2)))) (pow (sqrt (+ (* (* (floor d) dY.w) (* (floor d) dY.w)) (* (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))))) 2))) 1/2)
751.0ms	h	@	-inf	(* (log (fmax (pow (sqrt (+ (* (* (floor d) dX.w) (* (floor d) dX.w)) (* (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v)))) (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))))))) 2) (pow (sqrt (+ (* (* (floor d) dY.w) (* (floor d) dY.w)) (* (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))))) 2))) 1/2)
427.0ms	cosTheta_O	@	inf	(log (+ 1 (exp (+ 6931/10000 (+ (* cosTheta_O (/ cosTheta_i v)) (log (/ 1/2 v)))))))
321.0ms	dX.v	@	inf	(/ (fmax (pow (sqrt (+ (* (* (floor h) dX.v) (* (floor h) dX.v)) (* (* dX.u (floor w)) (* dX.u (floor w))))) 2) (pow (sqrt (+ (* (* dY.v (floor h)) (* dY.v (floor h))) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2)) (* (* (floor h) (floor w)) (- (* dX.u dY.v) (* dX.v dY.u))))
316.0ms	c	@	inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))

analyze32.7s (5.6%)

Algorithm

30×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	2.6%	97.4%	0%	0%	0%	0
0%	0%	2.6%	97.4%	0%	0%	0%	1
7.8%	0.2%	2.4%	97.4%	0%	0%	0%	2
8.5%	0.2%	2.4%	97.4%	0%	0%	0%	3
12.8%	0.3%	2.3%	97.4%	0%	0%	0%	4
47%	1.2%	1.4%	97.4%	0%	0%	0%	5
51.8%	1.3%	1.2%	97.4%	0%	0%	0%	6
69.5%	1.8%	0.8%	97.4%	0%	0%	0%	7
71.6%	1.8%	0.7%	97.4%	0%	0.1%	0%	8
81.1%	2.1%	0.5%	97.4%	0%	0.1%	0%	9
82.6%	2.1%	0.4%	97.4%	0%	0.1%	0%	10
88.3%	2.2%	0.3%	97.4%	0%	0.1%	0%	11
89.1%	2.2%	0.3%	97.4%	0%	0.1%	0%	12

Compiler

Compiled 2668 to 1046 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.2s

ival-mult: 4.6s (21.9% of total)

ival-<=: 3.4s (16.1% of total)

...c/correct-round.rkt:121:19: 2.4s (11.3% of total)

ival-fabs: 2.0s (9.6% of total)

ival-div: 1.4s (6.5% of total)

ival-sub: 946.0ms (4.5% of total)

ival-add: 852.0ms (4% of total)

ival-sqrt: 802.0ms (3.8% of total)

ival-floor: 709.0ms (3.3% of total)

ival-and: 682.0ms (3.2% of total)

ival-if: 577.0ms (2.7% of total)

ival-fmax: 365.0ms (1.7% of total)

ival-sin: 335.0ms (1.6% of total)

ival-cos: 290.0ms (1.4% of total)

ival->: 283.0ms (1.3% of total)

ival-==: 271.0ms (1.3% of total)

ival-log: 190.0ms (0.9% of total)

ival-log2: 184.0ms (0.9% of total)

ival-exp: 157.0ms (0.7% of total)

const: 135.0ms (0.6% of total)

ival-pi: 115.0ms (0.5% of total)

ival-tan: 107.0ms (0.5% of total)

ival->=: 84.0ms (0.4% of total)

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

ival-<: 67.0ms (0.3% of total)

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

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

backward-pass: 24.0ms (0.1% of total)

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

rewrite32.4s (5.6%)

Algorithm

120×	batch-egg-rewrite

Rules

61931×	`log1p-expm1-u`
50563×	`expm1-log1p-u`
37759×	`pow1`
35837×	`add-exp-log`
35278×	`log-prod`

Stop Event

120×	node limit

Counts

1969 → 44143

eval28.8s (5%)

Compiler: Compiled 14224425 to 591502 computations (95.8% saved)

regimes27.6s (4.7%)

Counts

9169 → 394

Calls

145 calls:

1.1s	s
990.0ms	uy
779.0ms	maxCos
762.0ms	dY.u
631.0ms	cosTheta_i

Compiler

Compiled 14370 to 9895 computations (31.1% saved)

preprocess8.7s (1.5%)

Algorithm

30×	egg-herbie

Rules

30630×	`fma-define`
21782×	`fma-neg`
15892×	`unsub-neg`
14706×	`distribute-lft-neg-in`
11858×	`distribute-rgt-neg-in`

Stop Event

11×	saturated
19×	node limit

Compiler

Compiled 47660 to 14426 computations (69.7% saved)

explain6.2s (1.1%)

Results

3.4s	15306×	0	valid
35.0ms	54×	1	valid

Compiler

Compiled 16652 to 1662 computations (90% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.8s

ival-mult: 680.0ms (37.8% of total)

ival-div: 237.0ms (13.2% of total)

ival-log: 131.0ms (7.3% of total)

ival-add: 102.0ms (5.7% of total)

ival-sub: 91.0ms (5.1% of total)

ival-sin: 90.0ms (5% of total)

ival-sqrt: 89.0ms (4.9% of total)

ival-cos: 53.0ms (2.9% of total)

ival-floor: 46.0ms (2.6% of total)

ival-exp: 40.0ms (2.2% of total)

ival-neg: 33.0ms (1.8% of total)

const: 28.0ms (1.6% of total)

ival-pi: 26.0ms (1.4% of total)

...c/correct-round.rkt:121:19: 25.0ms (1.4% of total)

ival-fmax: 22.0ms (1.2% of total)

ival-if: 20.0ms (1.1% of total)

ival-tan: 19.0ms (1.1% of total)

ival-log2: 16.0ms (0.9% of total)

ival-fabs: 10.0ms (0.6% of total)

backward-pass: 7.0ms (0.4% of total)

ival-atan: 7.0ms (0.4% of total)

ival-sinh: 7.0ms (0.4% of total)

ival->: 6.0ms (0.3% of total)

ival->=: 6.0ms (0.3% of total)

ival-asin: 5.0ms (0.3% of total)

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

bsearch38.0ms (0%)

Algorithm

54×	binary-search
28×	left-value

Stop Event

54×	narrow-enough

Compiler

Compiled 3857 to 1858 computations (51.8% saved)

Herbie run

simplify2.3min (23.9%)

sample1.6min (16.4%)

soundness1.5min (15.6%)

prune43.2s (7.4%)

localize42.9s (7.4%)

series33.8s (5.8%)

analyze32.7s (5.6%)

rewrite32.4s (5.6%)

eval28.8s (5%)

regimes27.6s (4.7%)

preprocess8.7s (1.5%)

explain6.2s (1.1%)

bsearch38.0ms (0%)

end0.0ms (0%)

Profiling