Metrics for Herbie run

Date:	Monday, December 16th, 2024
Commit:	e7208c1b on no-localize
Hostname:	nightly with Racket 8.10
Seed:	2024351
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:	225 604.1 MB

sample2.2min (55.2%)

Memory

716.9MiB live, 125 573.5MiB allocated; 41.8s collecting garbage

Samples

30.6s	43 806×	2	valid
25.7s	147 776×	0	invalid
22.4s	96 622×	1	valid
16.8s	7 012×	5	exit
8.3s	87 510×	0	valid
2.4s	3 229×	3	valid
619.0ms	4 194×	0	exit
1.0ms	1×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5min

ival-pow: 16.1s (18.1% of total)

ival-tan: 13.5s (15.1% of total)

adjust: 8.7s (9.7% of total)

ival-mult: 6.5s (7.2% of total)

const: 5.2s (5.8% of total)

ival-log: 4.3s (4.8% of total)

ival-sub: 4.1s (4.6% of total)

ival-cos: 4.0s (4.4% of total)

ival-div: 3.8s (4.3% of total)

ival-add: 3.7s (4.2% of total)

ival-sin: 3.7s (4.2% of total)

ival-fabs: 2.9s (3.2% of total)

ival-<=: 2.2s (2.5% of total)

ival-expm1: 2.1s (2.3% of total)

ival-exp: 2.0s (2.3% of total)

ival-log1p: 1.3s (1.4% of total)

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

ival-<: 935.0ms (1% of total)

ival-and: 676.0ms (0.8% of total)

ival-fmin: 447.0ms (0.5% of total)

ival-neg: 382.0ms (0.4% of total)

exact: 377.0ms (0.4% of total)

ival-atan: 362.0ms (0.4% of total)

ival-cbrt: 334.0ms (0.4% of total)

ival->: 300.0ms (0.3% of total)

ival-assert: 162.0ms (0.2% of total)

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

Bogosity

rewrite22.6s (9.7%)

Memory

335.2MiB live, 21 420.8MiB allocated; 5.6s collecting garbage

Stop Event

224×	iter limit
109×	node limit

Counts

2 739 → 63 808

simplify21.9s (9.4%)

Memory

106.6MiB live, 18 112.3MiB allocated; 6.8s collecting garbage

Algorithm

137×	egg-herbie

Stop Event

130×	node limit
111×	iter limit
7×	saturated

Counts

9 182 → 9 016

derivations21.0s (9%)

Memory

423.4MiB live, 12 876.6MiB allocated; 2.5s collecting garbage

Stop Event

182×	iter limit
126×	node limit
25×	fuel
3×	done

Compiler

Compiled 7 665 to 1 771 computations (76.9% saved)

eval14.8s (6.3%)

Memory: 479.4MiB live, 19 420.1MiB allocated; 3.6s collecting garbage
Compiler: Compiled 3 495 253 to 384 314 computations (89% saved)

explain5.8s (2.5%)

Memory

12.9MiB live, 5 803.6MiB allocated; 1.0s collecting garbage

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`#f`	cancellation	4159	29
`log.f64`	`#f`	sensitivity	763	0
`/.f64`	`#f`	u/u	445	0
`sqrt.f64`	`#f`	oflow-rescue	362	0
`+.f64`	`#f`	cancellation	326	0
`/.f64`	`#f`	u/n	117	0
`pow.f64`	`(pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n))`	sensitivity	66	0
`sqrt.f64`	`#f`	uflow-rescue	26	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	24	0
↳	`(*.f64 b eps)`	underflow	148
↳	`(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))`	underflow	154
↳	`(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))`	underflow	148
↳	`(.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))`	underflow	232
↳	`(*.f64 a eps)`	underflow	154
`-.f64`	`#f`	nan-rescue	18	0
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	n/o	2	0
↳	`(*.f64 x x)`	overflow	61
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	0
`exp.f64`	`(exp.f64 (*.f64 a 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 -
+	5199	12
-	134	1823

Precision

0.9748734295893493

Recall

0.9976971790443293

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5199	8	4
-	134	21	1802

Precision?

0.9710928757926147

Recall?

0.9992323930147764

Freqs

test

number	freq
0	1835
1	4547
2	640
3	99
4	47

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

1.6s	2 810×	2	valid
1.2s	6 056×	1	valid
434.0ms	5 278×	0	valid
182.0ms	192×	3	valid

Compiler

Compiled 2 154 to 763 computations (64.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.8s

ival-tan: 677.0ms (24.1% of total)

adjust: 434.0ms (15.4% of total)

ival-log: 226.0ms (8% of total)

ival-cos: 209.0ms (7.4% of total)

ival-div: 208.0ms (7.4% of total)

ival-sin: 201.0ms (7.2% of total)

ival-sub: 154.0ms (5.5% of total)

ival-exp: 135.0ms (4.8% of total)

ival-sqrt: 108.0ms (3.8% of total)

ival-pow: 102.0ms (3.6% of total)

ival-mult: 95.0ms (3.4% of total)

ival-add: 92.0ms (3.3% of total)

ival-log1p: 65.0ms (2.3% of total)

ival-expm1: 27.0ms (1% of total)

ival-atan: 22.0ms (0.8% of total)

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

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

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

exact: 9.0ms (0.3% of total)

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

preprocess4.7s (2%)

Memory

-6.1MiB live, 4 722.5MiB allocated; 701ms collecting garbage

Algorithm

28×	egg-herbie

Stop Event

56×	iter limit
33×	saturated
23×	node limit

Compiler

Compiled 17 766 to 4 995 computations (71.9% saved)

prune4.1s (1.8%)

Memory: -310.5MiB live, 6 782.0MiB allocated; 1.6s collecting garbage
Counts: 92 964 → 1 761
Compiler: Compiled 90 057 to 49 056 computations (45.5% saved)

series4.0s (1.7%)

Memory

-134.8MiB live, 4 305.7MiB allocated; 887ms collecting garbage

Counts

2 739 → 9 182

Calls

501 calls:

Time	Variable		Point	Expression
143.0ms	x	@	-inf	((- (cbrt (+ x 1)) (cbrt x)) (/ (/ (/ 1/3 (cbrt x)) (pow x 1/4)) (pow (cbrt x) 1/4)) (/ (/ 1/3 (cbrt x)) (pow x 1/4)) (/ 1/3 (cbrt x)) 1/3 (cbrt x) x (pow x 1/4) 1/4 (pow (cbrt x) 1/4) (- (cbrt (+ x 1)) (cbrt x)) (* (pow x -2/3) 1/3) (pow x -2/3) -2/3 (- (cbrt (+ x 1)) (cbrt x)) (/ 1/3 (pow (cbrt x) 2)) (pow (cbrt x) 2) 2 (- (cbrt (+ x 1)) (cbrt x)) (* (cbrt (/ (exp (neg (log x))) x)) 1/3) (cbrt (/ (exp (neg (log x))) x)) (/ (exp (neg (log x))) x) (exp (neg (log x))) (neg (log x)) (log x) (- (cbrt (+ x 1)) (cbrt x)) (* (cbrt (/ (/ 1 x) (* (pow (pow x 1/4) 3) (pow x 1/4)))) 1/3) (cbrt (/ (/ 1 x) (* (pow (pow x 1/4) 3) (pow x 1/4)))) (/ (/ 1 x) (* (pow (pow x 1/4) 3) (pow x 1/4))) (/ 1 x) 1 (* (pow (pow x 1/4) 3) (pow x 1/4)) (pow (pow x 1/4) 3) 3)
89.0ms	eps	@	-inf	((- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (sin x) (pow (cos x) 2)) (sin x) x (pow (cos x) 2) (cos x) 2 1 -1/2 (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2)) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2) (/ -1 (pow (cos x) 2)) -1 (* (pow (sin x) 2) 1/6) 1/6 -1/6 eps (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 2) (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (cos (+ eps x)) (tan x) (- (tan (+ x eps)) (tan x)) (/ (- (pow (tan (+ eps x)) 2) (pow (tan x) 2)) (+ (tan x) (tan (+ eps x)))) (- (pow (tan (+ eps x)) 2) (pow (tan x) 2)) (pow (tan (+ eps x)) 2) (tan (+ eps x)) (pow (tan x) 2) (+ (tan x) (tan (+ eps x))))
83.0ms	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) b a (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ 1 a) 1 (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ 1 b) (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (+ (* (- (* (/ 1/2 b) (/ (pow (+ b a) 2) a)) (/ (* (* (+ b a) 1/2) (+ (* (* a a) b) (* (* b b) a))) (* (* (* a a) b) b))) eps) (+ (/ 1 b) (/ 1 a))) (- (* (/ 1/2 b) (/ (pow (+ b a) 2) a)) (/ (* (* (+ b a) 1/2) (+ (* (* a a) b) (* (* b b) a))) (* (* (* a a) b) b))) (* (/ 1/2 b) (/ (pow (+ b a) 2) a)) (/ 1/2 b) 1/2 (/ (pow (+ b a) 2) a) (pow (+ b a) 2) 2 (/ (* (* (+ b a) 1/2) (+ (* (* a a) b) (* (* b b) a))) (* (* (* a a) b) b)) (* (* (+ b a) 1/2) (+ (* (* a a) b) (* (* b b) a))) (* (+ b a) 1/2) (+ (* (* a a) b) (* (* b b) a)) (* a a) (* (* b b) a) (* b b) (* (* (* a a) b) b) (* (* a a) b) eps (+ (/ 1 b) (/ 1 a)) (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ (+ (* (* eps (- (/ (pow (exp a) eps) (- (exp (* a eps)) 1)) 1/2)) b) 1) b) (+ (* (* eps (- (/ (pow (exp a) eps) (- (exp (* a eps)) 1)) 1/2)) b) 1) (* eps (- (/ (pow (exp a) eps) (- (exp (* a eps)) 1)) 1/2)) (- (/ (pow (exp a) eps) (- (exp (* a eps)) 1)) 1/2) (/ (pow (exp a) eps) (- (exp (* a eps)) 1)) (pow (exp a) eps) (exp a) (- (exp (* a eps)) 1) (* a eps))
74.0ms	a	@	-inf	((- (exp (* x a)) 1) (* a x) a x (- (exp (* x a)) 1) (* (+ (* (* (* a a) x) 1/2) a) x) (+ (* (* (* a a) x) 1/2) a) (* (* a a) x) (* a a) 1/2 (- (exp (* a x)) 1) (exp (* a x)) (+ (* (+ (* (* 1/2 a) x) 1) (* x a)) 1) (* (* (* (* a a) x) 1/2) x) (* (* (* a a) x) 1/2) 1 (- (exp (* a x)) 1) (exp (* a x)) (+ (* (* (+ (* (* 1/2 a) x) 1) x) a) 1) (* (+ (* (* 1/2 a) x) 1) x) (+ (* (* 1/2 a) x) 1) (* 1/2 a) (- (exp (* x a)) 1) (* (+ (* (* (* x x) (+ (* (* 1/6 a) x) 1/2)) a) x) a) (+ (* (* (* x x) (+ (* (* 1/6 a) x) 1/2)) a) x) (* (* x x) (+ (* (* 1/6 a) x) 1/2)) (* x x) (+ (* (* 1/6 a) x) 1/2) (* 1/6 a) 1/6)
72.0ms	x	@	inf	((- (cbrt (+ x 1)) (cbrt x)) (* (cbrt (/ (/ 1 x) x)) 1/3) (cbrt (/ (/ 1 x) x)) (/ (/ 1 x) x) (/ 1 x) 1 x 1/3 (- (cbrt (+ x 1)) (cbrt x)) (cbrt (+ x 1)) (cbrt x) (- (cbrt (+ x 1)) (pow (pow x 1/6) 2)) (cbrt (+ x 1)) (+ x 1) (pow (pow x 1/6) 2) (pow x 1/6) 1/6 2 (- (pow (exp 1/3) (log (+ 1 x))) (cbrt x)) (pow (exp 1/3) (log (+ 1 x))) (exp 1/3) (log (+ 1 x)) (- (cbrt (+ x 1)) (cbrt (pow (exp 3) (log (cbrt x))))) (cbrt (pow (exp 3) (log (cbrt x)))) (pow (exp 3) (log (cbrt x))) (exp 3) 3 (log (cbrt x)))

regimes2.8s (1.2%)

Memory

-45.7MiB live, 3 508.7MiB allocated; 517ms collecting garbage

Counts

3 383 → 288

Calls

43 calls:

732.0ms	x
207.0ms	a
167.0ms	(/.f64 #s(literal 1 binary64) n)
136.0ms	eps
129.0ms	(-.f64 (cbrt.f64 (+.f64 x #s(literal 1 binary64))) (cbrt.f64 x))

Compiler

Compiled 2 002 to 1 864 computations (6.9% saved)

analyze2.0s (0.8%)

Memory

81.2MiB live, 2 327.7MiB allocated; 538ms collecting garbage

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 (0.5%)

Memory

-47.4MiB live, 748.2MiB allocated; 819ms collecting garbage

Algorithm

49×	binary-search
40×	left-value

Stop Event

46×	narrow-enough
3×	predicate-same

Samples

267.0ms	3 032×	0	valid
71.0ms	712×	0	invalid
52.0ms	430×	1	valid
23.0ms	90×	2	valid
1.0ms	15×	0	exit

Compiler

Compiled 15 858 to 12 493 computations (21.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 274.0ms

ival-mult: 100.0ms (36.5% of total)

ival-div: 32.0ms (11.7% of total)

ival-sub: 27.0ms (9.9% of total)

ival-add: 20.0ms (7.3% of total)

ival-pow: 19.0ms (6.9% of total)

ival-sqrt: 19.0ms (6.9% of total)

adjust: 16.0ms (5.8% of total)

ival-neg: 14.0ms (5.1% of total)

ival-cos: 11.0ms (4% of total)

ival-cbrt: 5.0ms (1.8% of total)

ival-true: 3.0ms (1.1% of total)

ival-exp: 2.0ms (0.7% of total)

ival-assert: 2.0ms (0.7% of total)

ival-expm1: 2.0ms (0.7% of total)

exact: 2.0ms (0.7% of total)

start1.0ms (0%)

Memory: 2.1MiB live, 2.1MiB allocated; 0ms collecting garbage

end0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

sample2.2min (55.2%)

rewrite22.6s (9.7%)

simplify21.9s (9.4%)

derivations21.0s (9%)

eval14.8s (6.3%)

explain5.8s (2.5%)

preprocess4.7s (2%)

prune4.1s (1.8%)

series4.0s (1.7%)

regimes2.8s (1.2%)

analyze2.0s (0.8%)

bsearch1.1s (0.5%)

start1.0ms (0%)

end0.0ms (0%)

Profiling