Metrics for Herbie run

Date:	Tuesday, November 19th, 2024
Commit:	d53963c7 on cleanup
Hostname:	nightly with Racket 8.10
Seed:	2024324
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

sample2.0min (44.3%)

Memory

304.0MiB live, 101 858.1MiB allocated

Samples

31.1s	41 678×	2	valid
26.7s	146 730×	0	invalid
18.8s	92 061×	1	valid
9.7s	4 866×	5	exit
9.6s	94 524×	0	valid
1.8s	2 904×	3	valid
479.0ms	2 244×	1	exit
393.0ms	4 212×	0	exit
48.0ms	3×	3	exit
8.0ms	4×	4	exit
2.0ms	3×	2	exit
1.0ms	1×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.4min

ival-tan: 14.8s (18% of total)

ival-pow: 10.1s (12.3% of total)

ival-mult: 6.2s (7.6% of total)

adjust: 5.6s (6.9% of total)

const: 5.4s (6.6% of total)

ival-div: 4.6s (5.6% of total)

ival-sub: 4.0s (4.8% of total)

ival-cos: 4.0s (4.8% of total)

ival-sin: 3.9s (4.7% of total)

ival-add: 3.4s (4.1% of total)

ival-exp: 3.2s (3.9% of total)

ival-log: 3.1s (3.8% of total)

ival-fabs: 2.6s (3.2% of total)

ival-expm1: 2.4s (2.9% of total)

ival-<=: 2.1s (2.6% of total)

ival-sqrt: 1.4s (1.7% of total)

ival-log1p: 969.0ms (1.2% of total)

ival-<: 892.0ms (1.1% of total)

ival-fmin: 674.0ms (0.8% of total)

ival-and: 632.0ms (0.8% of total)

ival->: 586.0ms (0.7% of total)

ival-neg: 415.0ms (0.5% of total)

exact: 354.0ms (0.4% of total)

ival-atan: 336.0ms (0.4% of total)

ival-cbrt: 294.0ms (0.4% of total)

ival-assert: 172.0ms (0.2% of total)

ival-true: 68.0ms (0.1% of total)

Bogosity

simplify36.9s (13.6%)

Memory

182.3MiB live, 26 249.3MiB allocated

Algorithm

246×	egg-herbie

Stop Event

324×	iter limit
184×	node limit
65×	saturated

Counts

8 557 → 8 471

soundness30.8s (11.3%)

Memory

129.7MiB live, 15 841.9MiB allocated

Stop Event

200×	iter limit
132×	node limit
23×	fuel
5×	done
2×	saturated

Compiler

Compiled 15 047 to 6 582 computations (56.3% saved)

rewrite23.1s (8.5%)

Memory

-0.1MiB live, 20 499.9MiB allocated

Stop Event

221×	iter limit
108×	node limit
3×	saturated

Counts

1 659 → 65 114

localize20.8s (7.6%)

Memory

-183.2MiB live, 18 594.8MiB allocated

Samples

6.9s	10 523×	1	valid
6.8s	5 509×	2	valid
2.8s	10 871×	0	valid
459.0ms	299×	3	valid
214.0ms	692×	0	invalid
11.0ms	8×	5	exit
3.0ms	2×	4	valid

Compiler

Compiled 20 858 to 3 220 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.9s

ival-mult: 2.6s (18.4% of total)

adjust: 1.6s (11.8% of total)

ival-div: 1.6s (11.7% of total)

ival-tan: 1.2s (8.7% of total)

ival-add: 1.1s (7.7% of total)

ival-sub: 935.0ms (6.7% of total)

ival-pow: 934.0ms (6.7% of total)

const: 720.0ms (5.2% of total)

ival-log: 714.0ms (5.1% of total)

ival-cos: 576.0ms (4.1% of total)

ival-sin: 362.0ms (2.6% of total)

ival-exp: 330.0ms (2.4% of total)

ival-sqrt: 319.0ms (2.3% of total)

ival-pow2: 220.0ms (1.6% of total)

ival-neg: 150.0ms (1.1% of total)

ival-log1p: 140.0ms (1% of total)

ival-expm1: 110.0ms (0.8% of total)

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

ival-atan: 70.0ms (0.5% of total)

exact: 48.0ms (0.3% of total)

ival-cosh: 37.0ms (0.3% of total)

ival-atan2: 31.0ms (0.2% of total)

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

ival-assert: 13.0ms (0.1% of total)

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

eval14.1s (5.2%)

Memory: 189.1MiB live, 15 287.2MiB allocated
Compiler: Compiled 2 651 786 to 281 301 computations (89.4% saved)

explain6.1s (2.2%)

Memory

4.7MiB live, 5 919.4MiB allocated

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`#f`	cancellation	4204	25
`log.f64`	`#f`	sensitivity	762	0
`/.f64`	`#f`	u/u	435	0
`sqrt.f64`	`#f`	oflow-rescue	426	0
`+.f64`	`#f`	cancellation	324	0
`/.f64`	`#f`	u/n	117	0
`pow.f64`	`(pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n))`	sensitivity	70	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	18	0
↳	`(*.f64 b eps)`	underflow	151
↳	`(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))`	underflow	148
↳	`(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))`	underflow	151
↳	`(.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	148
`sqrt.f64`	`#f`	uflow-rescue	16	0
`exp.f64`	`#f`	sensitivity	4	1
`-.f64`	`#f`	nan-rescue	4	0
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	n/o	3	0
↳	`(*.f64 x x)`	overflow	58
`/.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	3	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	3
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	3
↳	`(exp.f64 x)`	overflow	3
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	3
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	2	0
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	2	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	0
`/.f64`	`(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 a c))))) (.f64 #s(literal 2 binary64) a))`	o/n	1	0
↳	`(*.f64 b b)`	overflow	88
↳	`(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (*.f64 a c)))))`	overflow	1
↳	`(.f64 #s(literal 4 binary64) (.f64 a c))`	overflow	27
↳	`(*.f64 a c)`	overflow	27
↳	`(-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (*.f64 a c)))`	overflow	105

Confusion

	Predicted +	Predicted -
+	5250	12
-	144	1762

Precision

0.9733036707452726

Recall

0.9977194982896237

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5250	10	2
-	144	16	1746

Precision?

0.9704797047970479

Recall?

0.999619916381604

Freqs

test

number	freq
0	1774
1	4583
2	664
3	106
4	41

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

1.7s	2 636×	2	valid
1.2s	5 802×	1	valid
474.0ms	5 710×	0	valid
112.0ms	188×	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: 592.0ms (21.9% of total)

adjust: 334.0ms (12.3% of total)

ival-sin: 212.0ms (7.8% of total)

ival-cos: 206.0ms (7.6% of total)

ival-log: 197.0ms (7.3% of total)

ival-sub: 196.0ms (7.2% of total)

ival-div: 188.0ms (6.9% of total)

ival-exp: 168.0ms (6.2% of total)

ival-add: 155.0ms (5.7% of total)

ival-log1p: 111.0ms (4.1% of total)

ival-mult: 106.0ms (3.9% of total)

ival-pow: 83.0ms (3.1% of total)

ival-sqrt: 60.0ms (2.2% of total)

ival-expm1: 24.0ms (0.9% of total)

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

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

ival-neg: 13.0ms (0.5% of total)

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

exact: 9.0ms (0.3% of total)

ival-assert: 7.0ms (0.3% of total)

prune4.5s (1.7%)

Memory: -187.9MiB live, 6 009.4MiB allocated
Counts: 73 878 → 1 926
Compiler: Compiled 101 152 to 53 562 computations (47% saved)

preprocess4.2s (1.6%)

Memory

-83.8MiB live, 3 667.0MiB allocated

Algorithm

28×	egg-herbie

Stop Event

56×	iter limit
50×	saturated
6×	node limit

Compiler

Compiled 19 466 to 5 459 computations (72% saved)

series4.1s (1.5%)

Memory

-89.3MiB live, 3 648.5MiB allocated

Counts

1 659 → 8 557

Calls

507 calls:

Time	Variable		Point	Expression
290.0ms	n	@	-inf	((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (/ (pow x (pow n -1)) n) x) (/ (pow x (pow n -1)) n) (pow x (pow n -1)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (/ (pow x (/ 1 n)) x) n) (/ (pow x (/ 1 n)) x) (/ 1 x) (+ (/ (/ (log x) n) x) (/ 1 x)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (/ (pow x (/ 1 n)) x) n) (/ (pow x (/ 1 n)) x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (log (+ 1 x)) (- (exp (/ (log (+ 1 x)) n)) (pow x (/ 1 n))) (exp (/ (log (+ 1 x)) n)) (/ (log (+ 1 x)) n) (/ (log x) n) (/ (/ (log x) n) x) (log x) (pow x (/ 1 n)))
175.0ms	n	@	-inf	((- (* (+ 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)))
86.0ms	x	@	0	((- (cbrt (+ x 1)) (cbrt x)) (* (pow (cbrt x) -2) 1/3) (pow (cbrt x) -2) (cbrt x) (- (cbrt (+ x 1)) (cbrt (neg x))) (cbrt (+ x 1)) (cbrt (neg x)) (neg x) (- (cbrt (+ x 1)) (cbrt x)) (/ (/ 1/3 (cbrt x)) (cbrt x)) (/ 1/3 (cbrt x)) (- (cbrt (+ x 1)) (cbrt x)) (* (/ (cbrt (pow x -3/2)) (cbrt (sqrt x))) 1/3) (/ (cbrt (pow x -3/2)) (cbrt (sqrt x))) (cbrt (pow x -3/2)) (+ (* (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 (sqrt x)) (cbrt (+ (* x (- x 1)) 1)))
80.0ms	N	@	0	((- (log (+ N 1)) (log N)) (/ (- (/ (- -1/2 (/ (- (/ 1/4 N) 1/3) N)) N) -1) N) (- (/ (- -1/2 (/ (- (/ 1/4 N) 1/3) N)) N) -1) (/ (- -1/2 (/ (- (/ 1/4 N) 1/3) N)) N) (- (log (+ N 1)) (log N)) (/ (- (/ (- -1/2 (/ (- (/ 1/4 N) 1/3) N)) N) -1) N) (- (/ (- -1/2 (/ (- (/ 1/4 N) 1/3) N)) N) -1) (/ (- -1/2 (/ (- (/ 1/4 N) 1/3) N)) N) (log (/ (+ 1 N) N)) (/ (+ 1 N) N) (+ 1 N) (/ (- (pow (log (+ 1 N)) 2) (pow (exp 2) (log (log N)))) (+ (log N) (log (+ 1 N)))) (- (pow (log (+ 1 N)) 2) (pow (exp 2) (log (log N)))) (pow (log (+ 1 N)) 2) (log (+ 1 N)) (/ (- (* (pow (log (+ 1 N)) 2) (/ (+ (log N) (log (+ 1 N))) (pow (log N) 2))) (+ (log N) (log (+ 1 N)))) (* (+ (log N) (log (+ 1 N))) (/ (+ (log N) (log (+ 1 N))) (pow (log N) 2)))) (- (* (pow (log (+ 1 N)) 2) (/ (+ (log N) (log (+ 1 N))) (pow (log N) 2))) (+ (log N) (log (+ 1 N)))) (* (pow (log (+ 1 N)) 2) (/ (+ (log N) (log (+ 1 N))) (pow (log N) 2))) (+ (* -1/3 N) 1/4) (/ (+ (* -1/3 N) 1/4) (* N N)) (pow (exp 2) (log (log N))) (pow (log N) 2) (/ (+ (log N) (log (+ 1 N))) (pow (log N) 2)))
76.0ms	eps	@	0	((/ (* -1 (- 1 (* eps eps))) (* (+ 1 eps) (- -1 eps))) (* -1 (- 1 (* eps eps))) (log (/ (* -1 (- 1 (* eps eps))) (* (+ 1 eps) (- -1 eps)))) (- 1 (* eps eps)) (/ (- (- -1 eps) (* (- -1 eps) eps)) (* (- -1 eps) (+ 1 eps))) (- (- -1 eps) (* (- -1 eps) eps)) (log (/ (- (- -1 eps) (* (- -1 eps) eps)) (* (- -1 eps) (+ 1 eps)))) (- -1 eps) (+ (log (+ 1 (neg (pow eps 6)))) (log (/ -1 (* (+ 1 eps) (* (- -1 eps) (+ (+ (* eps eps) (pow eps 4)) 1)))))) (log (+ 1 (neg (pow eps 6)))) (neg (pow eps 6)) (pow eps 6) (- (log (+ 1 (neg eps))) (log (+ 1 eps))) (log (+ 1 (neg eps))) (neg eps) (log (+ 1 eps)) (* (+ 1 eps) (- -1 eps)) (* (- -1 eps) eps) (* (- -1 eps) (+ 1 eps)) (log (/ -1 (* (+ 1 eps) (* (- -1 eps) (+ (+ (* eps eps) (pow eps 4)) 1))))) (* (+ 1 eps) (* (- -1 eps) (+ (+ (* eps eps) (pow eps 4)) 1))) (/ -1 (* (+ 1 eps) (* (- -1 eps) (+ (+ (* eps eps) (pow eps 4)) 1)))) (* (- -1 eps) (+ (+ (* eps eps) (pow eps 4)) 1)))

regimes4.0s (1.5%)

Memory

97.3MiB live, 4 190.5MiB allocated

Counts

3 719 → 333

Calls

43 calls:

1.0s	x
291.0ms	c
231.0ms	eps
209.0ms	(/.f64 #s(literal 1 binary64) n)
178.0ms	(exp.f64 (*.f64 a x))

Compiler

Compiled 2 390 to 2 195 computations (8.2% saved)

analyze2.0s (0.7%)

Memory

-24.0MiB live, 1 804.6MiB 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)

bsearch1.1s (0.4%)

Memory

-11.4MiB live, 1 131.0MiB allocated

Algorithm

60×	binary-search
47×	left-value

Stop Event

57×	narrow-enough
3×	predicate-same

Samples

508.0ms	3 429×	0	valid
126.0ms	294×	2	valid
104.0ms	593×	1	valid
48.0ms	648×	0	invalid
2.0ms	28×	0	exit
1.0ms	4×	3	valid

Compiler

Compiled 20 132 to 15 204 computations (24.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 433.0ms

ival-mult: 102.0ms (23.5% of total)

ival-pow: 92.0ms (21.2% of total)

ival-div: 57.0ms (13.2% of total)

ival-sub: 55.0ms (12.7% of total)

adjust: 27.0ms (6.2% of total)

ival-sqrt: 25.0ms (5.8% of total)

ival-add: 17.0ms (3.9% of total)

ival-neg: 17.0ms (3.9% of total)

ival-cos: 12.0ms (2.8% of total)

ival-exp: 8.0ms (1.8% of total)

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

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

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

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

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

exact: 2.0ms (0.5% of total)

start1.0ms (0%)

Memory: 1.5MiB live, 1.4MiB allocated

end0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated

sample2.0min (44.3%)

simplify36.9s (13.6%)

soundness30.8s (11.3%)

rewrite23.1s (8.5%)

localize20.8s (7.6%)

eval14.1s (5.2%)

explain6.1s (2.2%)

prune4.5s (1.7%)

preprocess4.2s (1.6%)

series4.1s (1.5%)

regimes4.0s (1.5%)

analyze2.0s (0.7%)

bsearch1.1s (0.4%)

start1.0ms (0%)

end0.0ms (0%)

Profiling