Metrics for Herbie run

Date:	Thursday, September 5th, 2024
Commit:	9205cc88 on zane-concrete-values
Hostname:	nightly with Racket 8.11.1
Seed:	2024249
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

sample2.0min (42.6%)

Memory

99.2MiB live, 115 334.6MiB allocated

Samples

29.9s	41 631×	2	valid
24.8s	147 512×	0	invalid
20.4s	92 123×	1	valid
9.7s	4 781×	5	exit
9.3s	94 420×	0	valid
1.9s	2 992×	3	valid
610.0ms	4 125×	0	exit
492.0ms	2 242×	1	exit
8.0ms	5×	2	exit
7.0ms	4×	4	exit
7.0ms	3×	3	exit
2.0ms	2×	4	valid

Precisions

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

ival-tan: 13.7s (17% of total)

ival-pow: 9.9s (12.3% of total)

ival-mult: 6.3s (7.8% of total)

adjust: 5.8s (7.3% of total)

const: 5.5s (6.8% of total)

ival-cos: 4.4s (5.5% of total)

ival-sub: 4.3s (5.4% of total)

ival-div: 4.2s (5.2% of total)

ival-add: 3.5s (4.4% of total)

ival-sin: 3.5s (4.3% of total)

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

ival-expm1: 2.7s (3.3% of total)

ival-<=: 2.4s (2.9% of total)

ival-fabs: 2.3s (2.8% of total)

ival-exp: 2.1s (2.6% of total)

ival-<: 1.2s (1.5% of total)

ival-sqrt: 1.2s (1.5% of total)

ival-log1p: 1.2s (1.4% of total)

ival-and: 601.0ms (0.7% of total)

ival-fmin: 487.0ms (0.6% of total)

ival->: 443.0ms (0.6% of total)

ival-atan: 375.0ms (0.5% of total)

exact: 342.0ms (0.4% of total)

ival-cbrt: 314.0ms (0.4% of total)

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

ival-assert: 154.0ms (0.2% of total)

ival-true: 69.0ms (0.1% of total)

Bogosity

simplify36.7s (13.3%)

Memory

639.6MiB live, 31 943.8MiB allocated

Algorithm

246×	egg-herbie

Rules

2 141 648×	`lower-fma.f32`
2 141 086×	`lower-fma.f64`
754 686×	`lower-*.f32`
753 896×	`lower-*.f64`
476 568×	`lower-+.f32`

Stop Event

324×	iter limit
167×	node limit
82×	saturated

Counts

29 520 → 29 066

soundness28.3s (10.3%)

Memory

164.8MiB live, 17 277.2MiB allocated

Rules

1 164 474×	`lower-fma.f32`
1 164 188×	`lower-fma.f64`
608 344×	`lower-*.f32`
607 942×	`lower-*.f64`
332 650×	`lower-/.f32`

Stop Event

210×	iter limit
135×	node limit
22×	fuel
6×	done
2×	saturated

Compiler

Compiled 9 010 to 5 350 computations (40.6% saved)

rewrite22.6s (8.2%)

Memory

109.7MiB live, 23 440.2MiB allocated

Rules

490 150×	`lower-fma.f32`
489 594×	`lower-fma.f64`
434 262×	`lower-*.f32`
433 482×	`lower-*.f64`
400 124×	`lower-/.f32`

Stop Event

222×	iter limit
108×	node limit
3×	saturated

Counts

1 649 → 65 863

localize22.3s (8.1%)

Memory

173.5MiB live, 23 318.7MiB allocated

Samples

7.2s	5 043×	2	valid
6.7s	10 265×	1	valid
3.1s	10 599×	0	valid
810.0ms	320×	3	valid
457.0ms	1 481×	0	invalid
135.0ms	48×	5	exit
48.0ms	148×	0	exit

Compiler

Compiled 21 533 to 3 220 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.9s

ival-mult: 2.3s (15.4% of total)

ival-tan: 2.1s (14.4% of total)

adjust: 1.8s (12.4% of total)

ival-div: 1.8s (12.2% of total)

ival-add: 1.1s (7.5% of total)

ival-sin: 896.0ms (6% of total)

const: 678.0ms (4.6% of total)

ival-sub: 654.0ms (4.4% of total)

ival-cos: 592.0ms (4% of total)

ival-pow: 550.0ms (3.7% of total)

ival-log: 434.0ms (2.9% of total)

ival-sqrt: 392.0ms (2.6% of total)

ival-exp: 364.0ms (2.4% of total)

ival-log1p: 270.0ms (1.8% of total)

ival-neg: 224.0ms (1.5% of total)

ival-pow2: 165.0ms (1.1% of total)

ival-expm1: 118.0ms (0.8% of total)

ival-cosh: 106.0ms (0.7% of total)

ival-cbrt: 64.0ms (0.4% of total)

exact: 45.0ms (0.3% of total)

ival-atan: 43.0ms (0.3% of total)

ival-true: 23.0ms (0.2% of total)

ival-atan2: 18.0ms (0.1% of total)

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

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

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

eval20.3s (7.3%)

Memory: 308.5MiB live, 25 227.2MiB allocated
Compiler: Compiled 2 837 158 to 295 246 computations (89.6% saved)

prune6.7s (2.4%)

Memory: -426.2MiB live, 9 708.5MiB allocated
Counts: 111 007 → 1 900
Compiler: Compiled 60 723 to 35 553 computations (41.5% saved)

explain5.9s (2.1%)

Memory

64.5MiB live, 6 873.0MiB allocated

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`#f`	cancellation	4162	31
`log.f64`	`#f`	sensitivity	761	1
`/.f64`	`#f`	u/u	436	0
`sqrt.f64`	`#f`	oflow-rescue	400	0
`+.f64`	`#f`	cancellation	333	1
`/.f64`	`#f`	u/n	134	0
`pow.f64`	`(pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n))`	sensitivity	68	0
`sqrt.f64`	`#f`	uflow-rescue	34	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	17	0
↳	`(*.f64 b eps)`	underflow	152
↳	`(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))`	underflow	134
↳	`(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))`	underflow	152
↳	`(.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))`	underflow	230
↳	`(*.f64 a eps)`	underflow	134
`-.f64`	`#f`	nan-rescue	15	0
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	n/o	4	0
↳	`(*.f64 x x)`	overflow	67
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/o	2	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	2
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	2
↳	`(exp.f64 x)`	overflow	2
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	2
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	0
`exp.f64`	`(exp.f64 (neg.f64 x))`	sensitivity	1	0
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	1	0
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	5212	19
-	145	1792

Precision

0.9729326115363076

Recall

0.996367807302619

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5212	15	4
-	145	17	1775

Precision?

0.9699387641491928

Recall?

0.9992353278531829

Freqs

test

number	freq
0	1811
1	4550
2	652
3	104
4	51

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

1.8s	2 598×	2	valid
1.1s	5 818×	1	valid
454.0ms	5 718×	0	valid
128.0ms	202×	3	valid

Compiler

Compiled 2 154 to 763 computations (64.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.7s

ival-tan: 629.0ms (23.2% of total)

ival-exp: 282.0ms (10.4% of total)

ival-cos: 256.0ms (9.5% of total)

adjust: 240.0ms (8.9% of total)

ival-log: 220.0ms (8.1% of total)

ival-div: 183.0ms (6.8% of total)

ival-sin: 161.0ms (5.9% of total)

ival-sub: 136.0ms (5% of total)

ival-mult: 127.0ms (4.7% of total)

ival-add: 108.0ms (4% of total)

ival-pow: 90.0ms (3.3% of total)

ival-expm1: 66.0ms (2.4% of total)

ival-sqrt: 63.0ms (2.3% of total)

ival-log1p: 57.0ms (2.1% of total)

ival-cbrt: 27.0ms (1% of total)

ival-atan: 19.0ms (0.7% of total)

ival-neg: 15.0ms (0.6% of total)

ival-true: 12.0ms (0.4% of total)

exact: 8.0ms (0.3% of total)

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

preprocess4.6s (1.7%)

Memory

-178.8MiB live, 4 559.8MiB allocated

Algorithm

28×	egg-herbie

Rules

27 478×	`lower-fma.f64`
27 478×	`lower-fma.f32`
10 768×	`div-sub`
10 444×	`sub-neg`
9 190×	`lower-*.f32`

Stop Event

56×	iter limit
50×	saturated
6×	node limit

Compiler

Compiled 9 522 to 3 947 computations (58.5% saved)

series4.5s (1.6%)

Memory

-15.7MiB live, 5 774.6MiB allocated

Counts

1 649 → 29 520

Calls

504 calls:

Time	Variable		Point	Expression
76.0ms	x	@	0	((* (/ 1 (* (cbrt x) 3)) (pow (cbrt x) -1)) (/ 1 (* (cbrt x) 3)) (- (cbrt (+ x 1)) (cbrt x)) (* (cbrt x) 3) (- (cbrt (+ x 1)) (cbrt x)) (* (pow x -2/3) 1/3) (pow x -2/3) (pow (/ 1 (cbrt x)) 2) (- (cbrt (+ x 1)) (cbrt x)) (* (pow (/ 1 (cbrt x)) 2) 1/3) (cbrt x) (- (cbrt (+ x 1)) (cbrt x)) (* (pow (exp 1/3) (* (log x) -2)) 1/3) (pow (exp 1/3) (* (log x) -2)) (exp 1/3) (+ (* (cbrt (+ (* x x) -1)) (cbrt (pow (- x 1) -1))) (neg (cbrt x))) (cbrt (+ (* x x) -1)) (+ (* x x) -1) (cbrt (pow (- x 1) -1)))
60.0ms	a	@	-inf	((/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ (/ (+ b a) b) a) (/ (+ b a) b) (+ b a) (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ 1 a) (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ 1 b) (+ (* (/ (* (+ (* (* b a) b) (* (* b a) a)) -1/2) (* b b)) (/ (/ (+ b a) a) a)) (* (/ 1/2 b) (/ (pow (+ b a) 2) a))) (/ (* (+ (* (* b a) b) (* (* b a) a)) -1/2) (* b b)) (+ (* (* b a) b) (* (* b a) a)) (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (* (- (exp (* eps (+ b a))) 1) eps) (- (exp (* eps (+ b a))) 1) (* eps (+ b a)) (/ (pow (+ b a) 2) a) (* (/ 1/2 b) (/ (pow (+ b a) 2) a)) (/ (* (- (exp (* eps (+ b a))) 1) eps) (* (- (exp (* eps b)) 1) (- (exp (* eps a)) 1))) (* (- (exp (* eps b)) 1) (- (exp (* eps a)) 1)))
52.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (+ (* (* eps (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6))) x) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (* (* (+ (* (* x x) 1/6) -1) x) eps) (+ (* (* eps (+ (* (* x x) -1/120) 1/6)) (* x x)) (neg eps)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* eps (+ (* (* x x) -1/120) 1/6)) (/ x (/ -1 (+ (* (* eps eps) 1/6) -1))) (+ (* -1 (/ x (/ -1 (+ (* (* eps eps) 1/6) -1)))) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (cos x) (+ (* (* x x) 1/6) -1) (* (+ (* (* eps (+ (* (* x x) -1/120) 1/6)) (* x x)) (neg eps)) x) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)))
52.0ms	n	@	0	((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (log (+ 1 x)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)) (/ 1 n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (+ (/ x n) 1) (/ x n) (+ (* (- (/ 1/2 (* n n)) (/ 1/2 n)) x) (/ 1 n)) (+ (* (+ (* (- (/ 1/2 (* n n)) (/ 1/2 n)) x) (/ 1 n)) x) 1) (- (/ 1/2 (* n n)) (/ 1/2 n)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (+ (* (/ (pow x (/ 1 n)) x) (- (/ 1/2 (* n n)) (/ 1/2 n))) (/ (pow x (/ 1 n)) n)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (+ (* (/ (pow x (/ 1 n)) x) (- (/ 1/2 (* n n)) (/ 1/2 n))) (/ (pow x (/ 1 n)) n)) x) (log x) (pow (+ x 1) (/ 1 n)) (/ 1/2 (* n n)))
50.0ms	x	@	-inf	((* (/ 1/3 (cbrt x)) (pow (cbrt x) -1)) (- (cbrt (+ x 1)) (cbrt x)) (/ 1/3 (cbrt x)) (cbrt x) (pow x 1/3) (- (cbrt (+ x 1)) (pow x 1/3)) (cbrt (+ x 1)) (* (* -2 (log x)) 1/3) (exp (* (* -2 (log x)) 1/3)) (- (cbrt (+ x 1)) (cbrt x)) (* (exp (* (* -2 (log x)) 1/3)) 1/3) (pow (pow (cbrt x) -1) 2) (- (cbrt (+ x 1)) (cbrt x)) (* (pow (pow (cbrt x) -1) 2) 1/3) (pow (cbrt x) -1) (+ (* (cbrt (+ (pow x 3) 1)) (/ 1 (cbrt (+ (* x (- x 1)) 1)))) (neg (cbrt x))) (cbrt (+ (pow x 3) 1)) (+ (pow x 3) 1) (pow x 3) (cbrt (+ (* x (- x 1)) 1)))

regimes3.6s (1.3%)

Memory

-75.1MiB live, 4 521.1MiB allocated

Counts

3 452 → 314

Calls

43 calls:

816.0ms	x
385.0ms	eps
172.0ms	b
152.0ms	(/.f64 #s(literal 1 binary64) n)
120.0ms	a

Compiler

Compiled 2 020 to 1 880 computations (6.9% saved)

analyze1.8s (0.7%)

Memory

152.9MiB live, 2 225.6MiB 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)

bsearch1.0s (0.4%)

Memory

-24.1MiB live, 986.0MiB allocated

Algorithm

61×	binary-search
50×	left-value

Stop Event

58×	narrow-enough
3×	predicate-same

Samples

351.0ms	3 677×	0	valid
118.0ms	568×	1	valid
61.0ms	214×	2	valid
60.0ms	746×	0	invalid
1.0ms	13×	0	exit
1.0ms	5×	3	valid

Compiler

Compiled 8 773 to 9 304 computations (-6.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 434.0ms

ival-mult: 132.0ms (30.4% of total)

ival-div: 63.0ms (14.5% of total)

ival-sub: 57.0ms (13.1% of total)

ival-sqrt: 40.0ms (9.2% of total)

ival-pow: 36.0ms (8.3% of total)

ival-add: 26.0ms (6% of total)

ival-cos: 21.0ms (4.8% of total)

adjust: 18.0ms (4.2% of total)

ival-neg: 16.0ms (3.7% of total)

ival-cbrt: 6.0ms (1.4% of total)

ival-expm1: 5.0ms (1.2% of total)

ival-sin: 5.0ms (1.2% of total)

ival-true: 4.0ms (0.9% of total)

exact: 3.0ms (0.7% of total)

ival-assert: 2.0ms (0.5% of total)

start1.0ms (0%)

Memory: 1.7MiB live, 1.7MiB allocated

end0.0ms (0%)

Memory: 0.4MiB live, 0.3MiB allocated

sample2.0min (42.6%)

simplify36.7s (13.3%)

soundness28.3s (10.3%)

rewrite22.6s (8.2%)

localize22.3s (8.1%)

eval20.3s (7.3%)

prune6.7s (2.4%)

explain5.9s (2.1%)

preprocess4.6s (1.7%)

series4.5s (1.6%)

regimes3.6s (1.3%)

analyze1.8s (0.7%)

bsearch1.0s (0.4%)

start1.0ms (0%)

end0.0ms (0%)

Profiling