Metrics for Herbie run

Date:	Friday, May 24th, 2024
Commit:	7841f259 on main
Hostname:	nightly with Racket 8.11.1
Seed:	2024145
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

simplify2.6min (26%)

Algorithm

268×	egg-herbie

Rules

211904×	`fma-define`
120428×	`distribute-lft-in`
116402×	`*-commutative`
115944×	`times-frac`
109948×	`fma-neg`

Stop Event

63×	saturated
205×	node limit

Counts

106406 → 74700

sample1.6min (15.4%)

Results

1.2min	247619×	0	valid
1.2s	8335×	0	invalid
1.0s	2049×	0	precondition
11.0ms	61×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 58.9s

ival-mult: 12.7s (21.6% of total)

ival-<=: 10.7s (18.2% of total)

...c/correct-round.rkt:121:19: 8.5s (14.4% of total)

ival-div: 4.9s (8.3% of total)

ival-fabs: 2.6s (4.5% of total)

ival-sub: 2.3s (3.9% of total)

ival-add: 2.1s (3.6% of total)

ival-sin: 2.0s (3.3% of total)

ival-log: 1.9s (3.3% of total)

ival-and: 1.6s (2.7% of total)

ival-sqrt: 1.5s (2.6% of total)

ival-pi: 928.0ms (1.6% of total)

ival-floor: 914.0ms (1.6% of total)

ival-cos: 895.0ms (1.5% of total)

ival-exp: 883.0ms (1.5% of total)

ival-neg: 742.0ms (1.3% of total)

ival-if: 537.0ms (0.9% of total)

const: 510.0ms (0.9% of total)

ival-tan: 397.0ms (0.7% of total)

ival-fmax: 368.0ms (0.6% of total)

ival->: 344.0ms (0.6% of total)

ival-<: 339.0ms (0.6% of total)

ival-sinh: 278.0ms (0.5% of total)

ival-log2: 241.0ms (0.4% of total)

ival-asin: 178.0ms (0.3% of total)

ival->=: 171.0ms (0.3% of total)

ival-==: 170.0ms (0.3% of total)

ival-atan: 126.0ms (0.2% of total)

backward-pass: 74.0ms (0.1% of total)

Bogosity

soundness1.5min (15.3%)

Rules

98304×	`fma-define`
67054×	`*-commutative`
65614×	`times-frac`
61184×	`associate-r`
56408×	`distribute-lft-in`

Stop Event

8×	saturated
167×	node limit
29×	fuel
1×	done

Compiler

Compiled 63515 to 12661 computations (80.1% saved)

prune44.6s (7.4%)

Counts: 145593 → 4294
Compiler: Compiled 394856 to 142644 computations (63.9% saved)

localize41.2s (6.8%)

Results

18.8s	26645×	0	valid
4.6s	706×	5	exit
1.6s	586×	1	valid
1.5s	1940×	0	invalid
240.0ms	587×	0	unsamplable

Compiler

Compiled 106809 to 5587 computations (94.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.1s

ival-mult: 4.6s (28.3% of total)

ival-div: 2.2s (13.5% of total)

ival-pow: 1.6s (10.1% of total)

ival-add: 758.0ms (4.7% of total)

ival-sqrt: 661.0ms (4.1% of total)

ival-hypot: 564.0ms (3.5% of total)

...c/correct-round.rkt:121:19: 538.0ms (3.3% of total)

ival-exp: 537.0ms (3.3% of total)

backward-pass: 516.0ms (3.2% of total)

ival-sin: 471.0ms (2.9% of total)

ival-sub: 450.0ms (2.8% of total)

ival-fma: 410.0ms (2.5% of total)

ival-log1p: 387.0ms (2.4% of total)

ival-tan: 382.0ms (2.4% of total)

ival-log: 339.0ms (2.1% of total)

ival-neg: 274.0ms (1.7% of total)

ival-cos: 196.0ms (1.2% of total)

ival-fmax: 167.0ms (1% of total)

ival-if: 139.0ms (0.9% of total)

ival-expm1: 122.0ms (0.8% of total)

ival-log2: 114.0ms (0.7% of total)

ival-floor: 108.0ms (0.7% of total)

ival->=: 104.0ms (0.6% of total)

const: 98.0ms (0.6% of total)

ival-atan: 97.0ms (0.6% of total)

ival-cbrt: 96.0ms (0.6% of total)

ival-pi: 82.0ms (0.5% of total)

ival-asin: 49.0ms (0.3% of total)

ival->: 37.0ms (0.2% of total)

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

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

ival-<: 11.0ms (0.1% of total)

ival-e: 4.0ms (0% of total)

series36.7s (6.1%)

Counts

2057 → 60576

Calls

14868 calls:

Time	Variable		Point	Expression
719.0ms	d	@	0	(pow (cbrt (sqrt (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)) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2)))) 3)
305.0ms	w	@	-inf	(log (+ 1 (sqrt (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)))))
303.0ms	u1	@	-inf	(* (pow u2 2) (+ (* -9740909103402808085817682884085781839780052161/18750000000000000000000000000000000000000000 (/ (* u1 (pow u2 2)) (- 1 u1))) (* 98696044010906577398881/2500000000000000000000 (/ u1 (- 1 u1)))))
298.0ms	dY.u	@	-inf	(if (< (if (> (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (/ (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))) (floor maxAniso)) (/ (fabs (* (* (neg dX.v) (* (floor h) dY.u)) (floor w))) (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))))) 1) (fmax 1 (* (if (> (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (floor maxAniso) (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))))) (if (> (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (/ (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))) (floor maxAniso)) (/ (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))) (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))))))) (if (> (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (floor maxAniso) (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))))))
201.0ms	dX.v	@	inf	(log (fmax (pow (sqrt (+ (* (* dX.v (floor h)) (* dX.v (floor h))) (* (* dX.u (floor w)) (* dX.u (floor w))))) 2) (pow (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) 2)))

analyze32.8s (5.4%)

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: 21.5s

ival-mult: 4.8s (22.1% of total)

ival-<=: 4.4s (20.4% of total)

...c/correct-round.rkt:121:19: 2.3s (10.7% of total)

ival-fabs: 1.4s (6.3% of total)

ival-div: 1.2s (5.4% of total)

ival-add: 974.0ms (4.5% of total)

ival-floor: 917.0ms (4.3% of total)

ival-and: 711.0ms (3.3% of total)

ival-sub: 672.0ms (3.1% of total)

ival-sqrt: 561.0ms (2.6% of total)

ival-if: 467.0ms (2.2% of total)

ival-log: 436.0ms (2% of total)

ival-fmax: 403.0ms (1.9% of total)

ival-sin: 395.0ms (1.8% of total)

ival-cos: 364.0ms (1.7% of total)

ival->=: 314.0ms (1.5% of total)

ival-==: 275.0ms (1.3% of total)

ival-log2: 201.0ms (0.9% of total)

ival->: 172.0ms (0.8% of total)

const: 142.0ms (0.7% of total)

ival-tan: 104.0ms (0.5% of total)

ival-pi: 101.0ms (0.5% of total)

ival-exp: 78.0ms (0.4% of total)

ival-neg: 78.0ms (0.4% of total)

ival-<: 62.0ms (0.3% of total)

ival-sinh: 42.0ms (0.2% of total)

ival-atan: 38.0ms (0.2% of total)

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

ival-asin: 18.0ms (0.1% of total)

rewrite32.0s (5.3%)

Algorithm

119×	batch-egg-rewrite

Rules

62619×	`log1p-expm1-u`
51140×	`expm1-log1p-u`
37978×	`pow1`
36666×	`log-prod`
36517×	`add-exp-log`

Stop Event

119×	node limit

Counts

2057 → 45830

eval29.4s (4.9%)

Compiler: Compiled 14089995 to 624935 computations (95.6% saved)

regimes29.1s (4.8%)

Counts

10173 → 399

Calls

145 calls:

803.0ms	s
770.0ms	ux
733.0ms	uy
687.0ms	u2
683.0ms	maxCos

Compiler

Compiled 14154 to 9859 computations (30.3% saved)

preprocess8.8s (1.4%)

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 52656 to 15352 computations (70.8% saved)

explain7.5s (1.2%)

Results

4.1s	15284×	0	valid
40.0ms	76×	1	valid

Compiler

Compiled 16652 to 1662 computations (90% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0s

ival-mult: 612.0ms (31.1% of total)

ival-add: 222.0ms (11.3% of total)

ival-div: 201.0ms (10.2% of total)

ival-sqrt: 175.0ms (8.9% of total)

ival-sub: 149.0ms (7.6% of total)

ival-log: 85.0ms (4.3% of total)

ival-sin: 83.0ms (4.2% of total)

ival-exp: 79.0ms (4% of total)

ival-floor: 79.0ms (4% of total)

ival-cos: 45.0ms (2.3% of total)

ival-neg: 32.0ms (1.6% of total)

ival-pi: 29.0ms (1.5% of total)

const: 28.0ms (1.4% of total)

...c/correct-round.rkt:121:19: 25.0ms (1.3% of total)

ival-fmax: 21.0ms (1.1% of total)

ival-tan: 20.0ms (1% of total)

ival-if: 15.0ms (0.8% of total)

ival-log2: 14.0ms (0.7% of total)

ival-asin: 10.0ms (0.5% of total)

ival-fabs: 10.0ms (0.5% of total)

backward-pass: 8.0ms (0.4% of total)

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

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

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

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

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

bsearch43.0ms (0%)

Algorithm

51×	binary-search
23×	left-value

Stop Event

51×	narrow-enough

Compiler

Compiled 4787 to 1924 computations (59.8% saved)

Herbie run

simplify2.6min (26%)

sample1.6min (15.4%)

soundness1.5min (15.3%)

prune44.6s (7.4%)

localize41.2s (6.8%)

series36.7s (6.1%)

analyze32.8s (5.4%)

rewrite32.0s (5.3%)

eval29.4s (4.9%)

regimes29.1s (4.8%)

preprocess8.8s (1.4%)

explain7.5s (1.2%)

bsearch43.0ms (0%)

end0.0ms (0%)

Profiling