Metrics for Herbie run

Date:	Monday, October 21st, 2024
Commit:	15c1caf3 on main
Hostname:	nightly with Racket 8.10
Seed:	2024295
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

sample1.9min (43%)

Memory

130.7MiB live, 101 976.5MiB allocated

Samples

27.7s	41 318×	2	valid
25.7s	147 772×	0	invalid
19.1s	92 125×	1	valid
9.4s	4 911×	5	exit
8.6s	94 757×	0	valid
1.8s	2 962×	3	valid
550.0ms	2 374×	1	exit
329.0ms	4 164×	0	exit
15.0ms	6×	4	exit
7.0ms	6×	4	valid
5.0ms	3×	3	exit
3.0ms	3×	2	exit

Precisions

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

ival-tan: 12.9s (16.8% of total)

ival-pow: 9.3s (12.2% of total)

ival-mult: 5.7s (7.4% of total)

const: 5.6s (7.3% of total)

adjust: 5.5s (7.1% of total)

ival-cos: 4.3s (5.7% of total)

ival-div: 4.0s (5.2% of total)

ival-add: 3.7s (4.9% of total)

ival-sub: 3.7s (4.8% of total)

ival-sin: 3.3s (4.4% of total)

ival-log: 3.0s (3.9% of total)

ival-exp: 2.5s (3.3% of total)

ival-fabs: 2.4s (3.2% of total)

ival-expm1: 2.3s (3% of total)

ival-<=: 2.1s (2.8% of total)

ival-sqrt: 1.3s (1.8% of total)

ival-log1p: 1.0s (1.3% of total)

ival-<: 966.0ms (1.3% of total)

ival-fmin: 642.0ms (0.8% of total)

ival-and: 628.0ms (0.8% of total)

exact: 351.0ms (0.5% of total)

ival-atan: 320.0ms (0.4% of total)

ival-neg: 297.0ms (0.4% of total)

ival-cbrt: 249.0ms (0.3% of total)

ival->: 248.0ms (0.3% of total)

ival-assert: 157.0ms (0.2% of total)

ival-true: 70.0ms (0.1% of total)

Bogosity

simplify37.9s (14.1%)

Memory

598.6MiB live, 28 482.6MiB allocated

Algorithm

246×	egg-herbie

Stop Event

324×	iter limit
171×	node limit
78×	saturated

Counts

8 953 → 8 858

soundness30.3s (11.3%)

Memory

127.1MiB live, 15 673.9MiB allocated

Stop Event

212×	iter limit
140×	node limit
25×	fuel
3×	done
2×	saturated

Compiler

Compiled 15 665 to 7 016 computations (55.2% saved)

rewrite23.4s (8.7%)

Memory

-179.1MiB live, 20 913.6MiB allocated

Stop Event

220×	iter limit
108×	node limit
3×	saturated

Counts

1 694 → 66 991

localize22.2s (8.3%)

Memory

236.5MiB live, 20 934.4MiB allocated

Samples

7.4s	10 582×	1	valid
6.7s	5 059×	2	valid
3.5s	11 104×	0	valid
513.0ms	861×	0	invalid
446.0ms	285×	3	valid
56.0ms	13×	5	exit

Compiler

Compiled 53 900 to 7 226 computations (86.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0s

ival-mult: 2.5s (16.8% of total)

adjust: 1.8s (11.9% of total)

ival-div: 1.7s (11.1% of total)

ival-add: 1.4s (9.4% of total)

ival-tan: 1.2s (7.9% of total)

const: 1.1s (7.5% of total)

ival-sub: 1.1s (7.1% of total)

ival-pow: 730.0ms (4.9% of total)

ival-log: 661.0ms (4.4% of total)

ival-cos: 596.0ms (4% of total)

ival-exp: 388.0ms (2.6% of total)

ival-sqrt: 355.0ms (2.4% of total)

ival-sin: 292.0ms (2% of total)

ival-pow2: 258.0ms (1.7% of total)

ival-neg: 246.0ms (1.6% of total)

ival-cosh: 206.0ms (1.4% of total)

ival-log1p: 199.0ms (1.3% of total)

ival-expm1: 104.0ms (0.7% of total)

exact: 47.0ms (0.3% of total)

ival-cbrt: 45.0ms (0.3% of total)

ival-atan: 26.0ms (0.2% of total)

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

ival-assert: 22.0ms (0.1% of total)

ival-atan2: 17.0ms (0.1% of total)

ival-fabs: 3.0ms (0% of total)

eval13.4s (5%)

Memory: 83.9MiB live, 15 816.5MiB allocated
Compiler: Compiled 2 735 976 to 293 382 computations (89.3% saved)

explain6.2s (2.3%)

Memory

56.4MiB live, 5 916.5MiB allocated

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`#f`	cancellation	4041	38
`log.f64`	`#f`	sensitivity	759	0
`/.f64`	`#f`	u/u	467	0
`sqrt.f64`	`#f`	oflow-rescue	384	0
`+.f64`	`#f`	cancellation	344	0
`/.f64`	`#f`	u/n	106	0
`pow.f64`	`(pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n))`	sensitivity	67	0
`-.f64`	`#f`	nan-rescue	24	0
`sqrt.f64`	`#f`	uflow-rescue	20	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	15	0
↳	`(*.f64 b eps)`	underflow	153
↳	`(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))`	underflow	153
↳	`(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))`	underflow	153
↳	`(.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))`	underflow	233
↳	`(*.f64 a eps)`	underflow	153
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	n/o	3	0
↳	`(*.f64 x x)`	overflow	67
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	0
`exp.f64`	`(exp.f64 (neg.f64 x))`	sensitivity	1	1
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	1	1
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	1	1

Confusion

	Predicted +	Predicted -
+	5145	21
-	129	1873

Precision

0.9755403868031854

Recall

0.9959349593495935

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5145	16	5
-	129	23	1850

Precision?

0.971390927912667

Recall?

0.9990321331784746

Freqs

test

number	freq
0	1894
1	4507
2	615
3	110
4	42

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

1.7s	2 610×	2	valid
1.1s	5 682×	1	valid
763.0ms	5 848×	0	valid
152.0ms	196×	3	valid

Compiler

Compiled 3 034 to 980 computations (67.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.1s

ival-tan: 752.0ms (24.6% of total)

ival-cos: 345.0ms (11.3% of total)

adjust: 243.0ms (8% of total)

ival-log: 241.0ms (7.9% of total)

ival-expm1: 216.0ms (7.1% of total)

ival-mult: 188.0ms (6.2% of total)

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

ival-sin: 154.0ms (5% of total)

ival-exp: 149.0ms (4.9% of total)

ival-sub: 144.0ms (4.7% of total)

ival-log1p: 111.0ms (3.6% of total)

ival-add: 95.0ms (3.1% of total)

ival-pow: 91.0ms (3% of total)

ival-sqrt: 87.0ms (2.9% of total)

ival-atan: 21.0ms (0.7% of total)

ival-cbrt: 15.0ms (0.5% of total)

ival-neg: 14.0ms (0.5% of total)

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

exact: 8.0ms (0.3% of total)

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

preprocess4.6s (1.7%)

Memory

5.3MiB live, 3 764.9MiB allocated

Algorithm

28×	egg-herbie

Stop Event

56×	iter limit
50×	saturated
6×	node limit

Compiler

Compiled 19 356 to 5 413 computations (72% saved)

prune4.2s (1.6%)

Memory: -328.6MiB live, 6 443.7MiB allocated
Counts: 74 634 → 2 017
Compiler: Compiled 111 474 to 56 493 computations (49.3% saved)

regimes3.9s (1.4%)

Memory

31.4MiB live, 4 695.4MiB allocated

Counts

3 945 → 331

Calls

43 calls:

1.0s	x
369.0ms	b
269.0ms	eps
148.0ms	(-.f64 (cbrt.f64 (+.f64 x #s(literal 1 binary64))) (cbrt.f64 x))
148.0ms	(/.f64 #s(literal 1 binary64) n)

Compiler

Compiled 2 234 to 2 053 computations (8.1% saved)

series3.8s (1.4%)

Memory

-62.0MiB live, 3 847.4MiB allocated

Counts

1 694 → 8 953

Calls

507 calls:

Time	Variable		Point	Expression
96.0ms	n	@	0	((+ (* (/ (- (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 (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (- (log (+ 1 x)) (log x))) n) (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) (- (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 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)) (+ (* (* x x) (- (/ 1/2 (* n n)) (/ 1/2 n))) (- (/ x n) (- (exp (/ (log x) n)) 1))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (* x x) (- (/ 1/2 (* n n)) (/ 1/2 n)) (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) (pow (log x) 2) (log x) (/ (log x) n) (/ 1/2 (* n n)))
95.0ms	x	@	0	((+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))) (/ (- (/ 2 (* x x)) -2) (pow x 3)) (- (/ 2 (* x x)) -2) (* x x) (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))) (/ -2 x) (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))) (- (/ 1 (+ x 1)) (/ 2 x)) (/ (- (/ -1 x) 1) x) (- (/ -1 x) 1) (/ (/ (- x (* 2 (+ x 1))) (+ x 1)) x) (- x (* 2 (+ x 1))) (* 2 (+ x 1)) (+ (/ (/ (- x (* 2 (+ x 1))) (+ x 1)) x) (/ 1 (- x 1))) (+ (* 1 (* (+ x 1) x)) (* (- x 1) (- x (* 2 (+ x 1))))) (* (+ x 1) x) (* (- x 1) (- x (* 2 (+ x 1)))) (/ 2 (* x x)) (pow x 3) (/ (- x (* 2 (+ x 1))) (+ x 1)) (/ (+ (* 1 (* (+ x 1) x)) (* (- x 1) (- x (* 2 (+ x 1))))) (* (- x 1) (* (+ x 1) x))) (* (- x 1) (* (+ x 1) x)))
91.0ms	x	@	0	((+ (* (/ (- (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 (log (+ 1 x)) 2) (pow (log x) 2)) n) 1/2) (- (log (+ 1 x)) (log x))) n) (/ (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) n) (- (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 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)) (+ (* (* x x) (- (/ 1/2 (* n n)) (/ 1/2 n))) (- (/ x n) (- (exp (/ (log x) n)) 1))) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (* x x) (- (/ 1/2 (* n n)) (/ 1/2 n)) (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) (pow (log x) 2) (log x) (/ (log x) n) (/ 1/2 (* n n)))
82.0ms	x	@	0	((* (cbrt (/ (/ 1 x) x)) 1/3) (- (cbrt (+ x 1)) (cbrt x)) (/ (/ 1 x) x) (/ 1 x) (- (cbrt (+ x 1)) (cbrt x)) (cbrt (+ x 1)) (cbrt x) (pow (pow x 1/6) 2) (- (cbrt (+ x 1)) (pow (pow x 1/6) 2)) (cbrt (+ x 1)) (+ x 1) (- (pow (exp 1/3) (log (+ 1 x))) (cbrt x)) (pow (exp 1/3) (log (+ 1 x))) (exp 1/3) (log (+ 1 x)) (+ (* (pow (cbrt x) 2) (cbrt x)) 1) (- (cbrt (+ (* (pow (cbrt x) 2) (cbrt x)) 1)) (cbrt x)) (cbrt (+ (* (pow (cbrt x) 2) (cbrt x)) 1)) (pow (cbrt x) 2) (cbrt (/ (/ 1 x) x)) (pow x 1/6))
68.0ms	eps	@	inf	((* (- (/ x eps) -1/2) eps) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* (+ (* (+ (* 1/4 eps) (* 1/6 x)) x) -1) x) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (* (neg (* eps eps)) (/ -1 eps)) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (* (neg (* eps eps)) (/ -1 eps))))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (* (neg (* eps eps)) (/ -1 eps))))) (sin (* 1/2 (+ (* 2 x) eps))) (* 1/6 x) (+ (* 1/4 eps) (* 1/6 x)) (* eps (+ (* 1/4 (* x x)) -1/2)) (sin (* 1/2 (+ (* 2 x) eps))))

bsearch1.7s (0.6%)

Memory

-92.8MiB live, 1 334.2MiB allocated

Algorithm

74×	binary-search
32×	left-value

Stop Event

72×	narrow-enough
2×	predicate-same

Samples

586.0ms	387×	2	valid
361.0ms	3 727×	0	valid
104.0ms	619×	1	valid
65.0ms	849×	0	invalid
1.0ms	14×	0	exit
1.0ms	3×	3	valid

Compiler

Compiled 24 094 to 18 853 computations (21.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 918.0ms

ival-add: 479.0ms (52.2% of total)

ival-pow: 108.0ms (11.8% of total)

ival-div: 80.0ms (8.7% of total)

ival-mult: 79.0ms (8.6% of total)

ival-sub: 45.0ms (4.9% of total)

adjust: 31.0ms (3.4% of total)

ival-sqrt: 26.0ms (2.8% of total)

ival-neg: 18.0ms (2% of total)

ival-cos: 17.0ms (1.9% of total)

ival-sin: 14.0ms (1.5% of total)

ival-cbrt: 6.0ms (0.7% of total)

ival-expm1: 4.0ms (0.4% of total)

ival-true: 4.0ms (0.4% of total)

exact: 3.0ms (0.3% of total)

ival-exp: 2.0ms (0.2% of total)

ival-assert: 2.0ms (0.2% of total)

analyze1.7s (0.6%)

Memory

61.3MiB live, 1 932.6MiB 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)

start1.0ms (0%)

Memory: 1.8MiB live, 1.8MiB allocated

end0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated

sample1.9min (43%)

simplify37.9s (14.1%)

soundness30.3s (11.3%)

rewrite23.4s (8.7%)

localize22.2s (8.3%)

eval13.4s (5%)

explain6.2s (2.3%)

preprocess4.6s (1.7%)

prune4.2s (1.6%)

regimes3.9s (1.4%)

series3.8s (1.4%)

bsearch1.7s (0.6%)

analyze1.7s (0.6%)

start1.0ms (0%)

end0.0ms (0%)

Profiling