Metrics for Herbie run

Date:	Monday, December 2nd, 2024
Commit:	a3fa83c3 on main
Hostname:	nightly with Racket 8.10
Seed:	2024337
Parameters:	256 points for 4 iterations
Flags:	`localize:costslocalize:errorsreduce:regimesreduce:binary-searchreduce:branch-expressionssetup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:proofs` default
Memory:	238 917.6 MB

sample2.0min (45.4%)

Memory

812.4MiB live, 112 904.3MiB allocated

Samples

29.1s	41 467×	2	valid
23.8s	149 567×	0	invalid
20.1s	92 127×	1	valid
10.2s	4 952×	5	exit
10.0s	94 538×	0	valid
1.9s	3 029×	3	valid
431.0ms	2 298×	1	exit
430.0ms	4 240×	0	exit
19.0ms	9×	4	exit
8.0ms	7×	4	valid
2.0ms	3×	3	exit
1.0ms	1×	2	exit

Precisions

Click to see histograms. Total time spent on operations: 1.3min

ival-tan: 12.8s (16.2% of total)

ival-pow: 10.5s (13.2% of total)

ival-mult: 6.5s (8.2% of total)

const: 6.0s (7.6% of total)

adjust: 5.3s (6.7% of total)

ival-cos: 4.3s (5.5% of total)

ival-div: 4.0s (5.1% of total)

ival-sub: 4.0s (5% of total)

ival-log: 3.9s (5% of total)

ival-add: 3.3s (4.1% of total)

ival-sin: 3.2s (4% of total)

ival-<=: 2.5s (3.2% of total)

ival-fabs: 2.5s (3.1% of total)

ival-exp: 2.2s (2.8% of total)

ival-expm1: 1.9s (2.4% of total)

ival-sqrt: 1.4s (1.8% of total)

ival-log1p: 1.3s (1.6% of total)

ival-<: 781.0ms (1% of total)

ival-and: 635.0ms (0.8% of total)

ival-fmin: 447.0ms (0.6% of total)

ival-cbrt: 404.0ms (0.5% of total)

exact: 362.0ms (0.5% of total)

ival-atan: 359.0ms (0.5% of total)

ival->: 306.0ms (0.4% of total)

ival-neg: 286.0ms (0.4% of total)

ival-assert: 153.0ms (0.2% of total)

ival-true: 73.0ms (0.1% of total)

Bogosity

simplify35.2s (13.5%)

Memory

432.7MiB live, 30 087.2MiB allocated

Algorithm

244×	egg-herbie

Stop Event

325×	iter limit
215×	node limit
29×	saturated

Counts

8 497 → 8 400

soundness26.4s (10.1%)

Memory

148.6MiB live, 14 476.9MiB allocated

Stop Event

191×	iter limit
129×	node limit
23×	fuel
5×	done

Compiler

Compiled 13 071 to 5 760 computations (55.9% saved)

rewrite22.7s (8.7%)

Memory

195.7MiB live, 19 959.6MiB allocated

Stop Event

219×	iter limit
108×	node limit

Counts

1 675 → 45 781

localize22.0s (8.4%)

Memory

582.7MiB live, 23 022.7MiB allocated

Samples

7.9s	6 434×	2	valid
6.6s	10 445×	1	valid
2.6s	10 078×	0	valid
787.0ms	387×	3	valid
178.0ms	56×	5	exit
97.0ms	117×	0	exit
44.0ms	128×	0	invalid
2.0ms	2×	3	exit
2.0ms	1×	4	valid

Compiler

Compiled 25 025 to 3 481 computations (86.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.3s

ival-mult: 2.5s (17.5% of total)

adjust: 1.9s (13.6% of total)

ival-tan: 1.9s (13.5% of total)

ival-div: 1.6s (11.5% of total)

ival-add: 1.3s (9.3% of total)

ival-sub: 873.0ms (6.1% of total)

const: 530.0ms (3.7% of total)

ival-pow: 516.0ms (3.6% of total)

ival-cos: 502.0ms (3.5% of total)

ival-log: 490.0ms (3.4% of total)

ival-sin: 458.0ms (3.2% of total)

ival-exp: 374.0ms (2.6% of total)

ival-sqrt: 283.0ms (2% of total)

ival-pow2: 222.0ms (1.6% of total)

ival-log1p: 177.0ms (1.2% of total)

ival-neg: 114.0ms (0.8% of total)

ival-expm1: 75.0ms (0.5% of total)

exact: 66.0ms (0.5% of total)

ival-cbrt: 61.0ms (0.4% of total)

ival-atan2: 59.0ms (0.4% of total)

ival-cosh: 58.0ms (0.4% of total)

ival-hypot: 55.0ms (0.4% of total)

ival-true: 24.0ms (0.2% of total)

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

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

ival-pi: 5.0ms (0% of total)

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

eval10.8s (4.1%)

Memory: 129.2MiB live, 12 271.5MiB allocated
Compiler: Compiled 2 295 111 to 241 241 computations (89.5% saved)

explain6.1s (2.3%)

Memory

-85.5MiB live, 5 786.0MiB allocated

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`#f`	cancellation	4171	24
`log.f64`	`#f`	sensitivity	763	1
`sqrt.f64`	`#f`	oflow-rescue	436	0
`/.f64`	`#f`	u/u	435	0
`+.f64`	`#f`	cancellation	339	0
`/.f64`	`#f`	u/n	134	0
`pow.f64`	`#f`	sensitivity	70	0
`-.f64`	`#f`	nan-rescue	28	0
`/.f64`	`(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))`	n/u	25	0
↳	`(*.f64 b eps)`	underflow	147
↳	`(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))`	underflow	137
↳	`(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))`	underflow	147
↳	`(.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))`	underflow	229
↳	`(*.f64 a eps)`	underflow	137
`sqrt.f64`	`#f`	uflow-rescue	24	0
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	n/o	4	0
↳	`(*.f64 x x)`	overflow	60
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	3	1

Confusion

	Predicted +	Predicted -
+	5258	15
-	141	1754

Precision

0.9738840526023338

Recall

0.997155319552437

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5258	13	2
-	141	12	1742

Precision?

0.9717920353982301

Recall?

0.9996207092736583

Freqs

test

number	freq
0	1769
1	4580
2	655
3	114
4	50

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	28	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

1.7s	2 620×	2	valid
1.4s	5 776×	1	valid
561.0ms	5 766×	0	valid
166.0ms	174×	3	valid

Compiler

Compiled 2 154 to 763 computations (64.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0s

ival-tan: 877.0ms (29% of total)

ival-log: 306.0ms (10.1% of total)

adjust: 305.0ms (10.1% of total)

ival-div: 222.0ms (7.4% of total)

ival-cos: 183.0ms (6.1% of total)

ival-sub: 182.0ms (6% of total)

ival-exp: 162.0ms (5.4% of total)

ival-mult: 158.0ms (5.2% of total)

ival-sin: 152.0ms (5% of total)

ival-add: 143.0ms (4.7% of total)

ival-pow: 86.0ms (2.8% of total)

ival-sqrt: 64.0ms (2.1% of total)

ival-log1p: 57.0ms (1.9% of total)

ival-expm1: 44.0ms (1.5% of total)

ival-atan: 20.0ms (0.7% of total)

ival-neg: 17.0ms (0.6% of total)

ival-cbrt: 16.0ms (0.5% of total)

ival-true: 13.0ms (0.4% of total)

exact: 9.0ms (0.3% of total)

ival-assert: 6.0ms (0.2% of total)

preprocess5.5s (2.1%)

Memory

265.2MiB live, 4 628.0MiB allocated

Algorithm

28×	egg-herbie

Stop Event

56×	iter limit
33×	saturated
23×	node limit

Compiler

Compiled 18 408 to 5 213 computations (71.7% saved)

prune3.8s (1.4%)

Memory: -756.2MiB live, 5 024.6MiB allocated
Counts: 56 698 → 1 726
Compiler: Compiled 110 192 to 53 678 computations (51.3% saved)

series3.5s (1.3%)

Memory

-88.6MiB live, 3 613.0MiB allocated

Counts

1 675 → 8 497

Calls

504 calls:

Time	Variable		Point	Expression
88.0ms	x	@	inf	((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (- (* (* (* x x) eps) 1/6) eps) x) (- (* (* (* x x) eps) 1/6) eps) (+ (* (+ (* (* (* (- (* 1/24 (* eps eps)) 1/2) eps) x) -1/2) (- (* (* eps eps) 1/6) 1)) x) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (+ (* (* (* (- (* 1/24 (* eps eps)) 1/2) eps) x) -1/2) (- (* (* eps eps) 1/6) 1)) (- (* 1/24 (* eps eps)) 1/2) (- (* (* eps eps) 1/6) 1) (+ (* (+ (* (* (* (- (* 1/24 (* eps eps)) 1/2) eps) x) -1/2) (* (* eps eps) 1/6)) x) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (+ (* (* (* (- (* 1/24 (* eps eps)) 1/2) eps) x) -1/2) (* (* eps eps) 1/6)) (- (cos (+ x eps)) (cos x)) (* (* (* x x) eps) 1/6) (* (* x x) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* 1/24 (* eps eps)) (* (* eps eps) 1/6) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps))
87.0ms	x	@	-inf	((- (/ (pow (+ (* (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (log (+ 1 x))) 2) (+ (* (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (+ (log (+ 1 x)) (log x)))) (/ (pow (log x) 2) (+ (* (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (+ (log (+ 1 x)) (log x))))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (/ (pow (+ (* (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (log (+ 1 x))) 2) (+ (* (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (+ (log (+ 1 x)) (log x)))) (/ (pow (log x) 2) (+ (* (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (+ (log (+ 1 x)) (log x))))) n) (/ (pow (+ (* (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (log (+ 1 x))) 2) (+ (* (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (+ (log (+ 1 x)) (log x)))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (+ (* (/ (/ (+ -1/2 (/ 1/2 n)) n) x) (exp (/ (log x) n))) (/ (exp (/ (log x) n)) n)) x) (+ (* (/ (/ (+ -1/2 (/ 1/2 n)) n) x) (exp (/ (log x) n))) (/ (exp (/ (log x) n)) n)) (/ (- 1 (/ 1/2 x)) n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (+ (* 1/2 (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n)) (log (+ 1 x))) (log x)) n) (- (+ (* 1/2 (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n)) (log (+ 1 x))) (log x)) (+ (* 1/2 (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n)) (log (+ 1 x))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (+ (* 1/2 (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n)) (log (+ 1 x))) (log x)) n) (- (+ (* 1/2 (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n)) (log (+ 1 x))) (log x)) (+ (* 1/2 (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n)) (log (+ 1 x))) (/ (- (* (+ (* (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (log (+ 1 x))) n) (* n (log x))) (* n n)) (- (* (+ (* (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (log (+ 1 x))) n) (* n (log x))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (* (+ (* (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (log (+ 1 x))) n) (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) (pow (log x) 2))
83.0ms	x	@	0	((- (cbrt (+ x 1)) (cbrt x)) (* (/ (cbrt (/ -1 x)) (cbrt (neg x))) 1/3) (/ (cbrt (/ -1 x)) (cbrt (neg x))) (cbrt (/ -1 x)) (pow x 1/3) (- (cbrt (+ x 1)) (pow x 1/3)) (cbrt (+ x 1)) (- (cbrt (+ x 1)) (cbrt x)) (/ 1/3 (pow (cbrt x) 2)) (pow (cbrt x) 2) (cbrt x) (* (cbrt (exp (* (log (* x x)) -1))) 1/3) (exp (* (log (* x x)) -1)) (* (log (* x x)) -1) (- (cbrt (+ x 1)) (cbrt x)) (- (+ 1 x) x) (/ (- (+ 1 x) x) (+ (* (cbrt x) (+ (cbrt (+ 1 x)) (cbrt x))) (exp (* (log (+ 1 x)) 2/3)))) (+ 1 x) (+ (* (cbrt x) (+ (cbrt (+ 1 x)) (cbrt x))) (exp (* (log (+ 1 x)) 2/3))) (cbrt (neg x)) (log (* x x)) (cbrt (exp (* (log (* x x)) -1))) (exp (* (log (+ 1 x)) 2/3)) (cbrt (+ 1 x)))
56.0ms	x	@	-inf	((/ (neg (pow (sin x) 2)) (* (+ (cos x) 1) (* (neg x) x))) (/ (* (/ (tan (* 1/2 x)) x) (sin x)) x) (* (/ (tan (* 1/2 x)) x) (sin x)) (/ (tan (* 1/2 x)) x) (/ (- 1 (cos x)) (* x x)) (- 1 (cos x)) (cos x) (* x x) (* (* (neg x) x) x) (/ (- (* -1 x) (* (* (neg x) x) (/ (cos x) x))) (* (* (neg x) x) x)) (- (* -1 x) (* (* (neg x) x) (/ (cos x) x))) (* (+ -1 (cos x)) x) (/ (* x (- x (* (cos x) x))) (* (* x x) (* x x))) (* (* x x) (* x x)) (* x (- x (* (cos x) x))) (- x (* (cos x) x)) (+ (* (/ (cos x) x) (* x x)) (neg x)) (/ (+ (* (/ (cos x) x) (* x x)) (neg x)) (* (* (neg x) x) x)) (/ (cos x) x) (+ -1 (cos x)) (* (cos x) x))
53.0ms	n	@	0	((- (* (+ n 1) (log (+ n 1))) (* n (log n))) (log (+ n 1)) (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (* (+ n 1) (log (+ n 1))) (* n (log n)))

regimes3.3s (1.3%)

Memory

20.0MiB live, 3 909.1MiB allocated

Counts

3 334 → 280

Calls

43 calls:

1.0s	x
344.0ms	eps
161.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
106.0ms	(-.f64 (cbrt.f64 (+.f64 x #s(literal 1 binary64))) (cbrt.f64 x))
106.0ms	b_2

Compiler

Compiled 2 073 to 1 932 computations (6.8% saved)

analyze2.2s (0.8%)

Memory

59.8MiB live, 2 009.3MiB allocated

Algorithm

28×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	61.1%	38.9%	0%	0%	0%	0
7.4%	4.5%	56.6%	38.9%	0%	0%	0%	1
22.3%	13.6%	47.5%	38.9%	0%	0%	0%	2
40.2%	23.5%	34.9%	38.9%	0%	2.7%	0%	3
53.4%	31.1%	27.2%	38.9%	0%	2.8%	0%	4
63%	36.3%	21.3%	38.9%	0%	3.6%	0%	5
65.9%	37.5%	19.4%	38.9%	0%	4.2%	0%	6
70.4%	38.8%	16.3%	38.9%	0%	6%	0%	7
73.6%	40.2%	14.4%	38.9%	0%	6.5%	0%	8
76.3%	40.9%	12.7%	38.9%	0%	7.5%	0%	9
78.4%	41.4%	11.4%	38.9%	0%	8.3%	0%	10
81.1%	42.4%	9.9%	38.9%	0%	8.8%	0%	11
82.3%	42.7%	9.2%	38.9%	0%	9.3%	0%	12

Compiler

Compiled 483 to 337 computations (30.2% saved)

bsearch1.1s (0.4%)

Memory

38.0MiB live, 1 223.3MiB allocated

Algorithm

68×	binary-search
12×	left-value

Stop Event

61×	narrow-enough
7×	predicate-same

Samples

327.0ms	3 582×	0	valid
146.0ms	515×	2	valid
145.0ms	879×	0	invalid
121.0ms	762×	1	valid
5.0ms	21×	3	valid
1.0ms	14×	0	exit

Compiler

Compiled 27 507 to 19 793 computations (28% saved)

Precisions

Click to see histograms. Total time spent on operations: 543.0ms

ival-mult: 139.0ms (25.6% of total)

ival-div: 95.0ms (17.5% of total)

ival-pow: 68.0ms (12.5% of total)

ival-sub: 65.0ms (12% of total)

ival-neg: 42.0ms (7.7% of total)

ival-sqrt: 38.0ms (7% of total)

adjust: 35.0ms (6.4% of total)

ival-add: 28.0ms (5.2% of total)

ival-cbrt: 11.0ms (2% of total)

ival-cos: 7.0ms (1.3% of total)

ival-expm1: 5.0ms (0.9% of total)

ival-true: 4.0ms (0.7% of total)

exact: 3.0ms (0.6% of total)

ival-exp: 2.0ms (0.4% of total)

ival-assert: 2.0ms (0.4% of total)

start1.0ms (0%)

Memory: 1.8MiB live, 1.8MiB allocated

end0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated

sample2.0min (45.4%)

simplify35.2s (13.5%)

soundness26.4s (10.1%)

rewrite22.7s (8.7%)

localize22.0s (8.4%)

eval10.8s (4.1%)

explain6.1s (2.3%)

preprocess5.5s (2.1%)

prune3.8s (1.4%)

series3.5s (1.3%)

regimes3.3s (1.3%)

analyze2.2s (0.8%)

bsearch1.1s (0.4%)

start1.0ms (0%)

end0.0ms (0%)

Profiling