Metrics for Herbie run

Date:	Tuesday, July 9th, 2024
Commit:	05213bce on main
Hostname:	nightly with Racket 8.11.1
Seed:	2024191
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

simplify19.1min (20.8%)

Memory

525.9MiB live, 1 196 764.6MiB allocated

Algorithm

4 384×

egg-herbie

Rules

1 646 254×	`fma-define`
1 242 702×	`fmm-def`
882 322×	`distribute-lft-in`
840 496×	`times-frac`
814 065×	`associate-r`

Stop Event

2 880×	node limit
1 473×	saturated
31×	unsound

Counts

1 153 923 → 996 634

sample18.6min (20.3%)

Memory

4 859.7MiB live, 1 298 151.9MiB allocated

Samples

7.6min	3 884 732×	0	valid
2.7min	442 562×	1	valid
1.4min	32 981×	5	exit
1.3min	132 433×	2	valid
55.9s	317 658×	0	invalid
15.2s	14 989×	3	valid
8.5s	49 373×	0	exit
7.9s	28 154×	1	invalid
5.3s	20 309×	1	exit
1.4s	610×	4	exit
632.0ms	1 400×	2	invalid
440.0ms	41×	4	valid
335.0ms	125×	3	exit
296.0ms	1 277×	2	exit

Precisions

Click to see histograms. Total time spent on operations: 11.1min

ival-mult: 2.1min (19.2% of total)

ival-div: 1.0min (9.3% of total)

ival-sin: 58.7s (8.8% of total)

ival-add: 57.4s (8.6% of total)

ival-sub: 45.7s (6.9% of total)

ival-pow: 44.7s (6.7% of total)

const: 39.6s (5.9% of total)

ival-cos: 32.4s (4.9% of total)

ival-log: 25.1s (3.8% of total)

ival-tan: 24.8s (3.7% of total)

ival-exp: 24.0s (3.6% of total)

adjust: 23.1s (3.5% of total)

ival-sqrt: 20.8s (3.1% of total)

ival-<=: 14.1s (2.1% of total)

ival-pow2: 12.2s (1.8% of total)

ival-neg: 5.9s (0.9% of total)

ival-fabs: 5.0s (0.7% of total)

ival-hypot: 4.5s (0.7% of total)

exact: 3.8s (0.6% of total)

ival-<: 3.3s (0.5% of total)

ival-and: 2.8s (0.4% of total)

ival-true: 2.8s (0.4% of total)

ival-pi: 2.8s (0.4% of total)

ival-expm1: 2.2s (0.3% of total)

ival-asin: 2.0s (0.3% of total)

ival-assert: 1.9s (0.3% of total)

ival-acos: 1.7s (0.3% of total)

ival-atan2: 1.7s (0.3% of total)

ival-sinh: 1.5s (0.2% of total)

ival->: 1.5s (0.2% of total)

ival-log1p: 1.2s (0.2% of total)

ival-atan: 1.1s (0.2% of total)

ival-fmod: 916.0ms (0.1% of total)

ival->=: 720.0ms (0.1% of total)

ival-fmin: 690.0ms (0.1% of total)

ival-asinh: 654.0ms (0.1% of total)

ival-cbrt: 652.0ms (0.1% of total)

ival-if: 612.0ms (0.1% of total)

ival-==: 610.0ms (0.1% of total)

ival-floor: 585.0ms (0.1% of total)

ival-tanh: 530.0ms (0.1% of total)

ival-acosh: 320.0ms (0% of total)

ival-cosh: 303.0ms (0% of total)

ival-fmax: 302.0ms (0% of total)

ival-atanh: 270.0ms (0% of total)

ival-log2: 221.0ms (0% of total)

ival-or: 37.0ms (0% of total)

Bogosity

soundness11.9min (13.1%)

Memory

96.1MiB live, 660 973.4MiB allocated

Rules

659 248×	`fma-define`
483 914×	`log1p-expm1-u`
482 617×	`fmm-def`
395 998×	`associate-r`
377 744×	`times-frac`

Stop Event

1 923×	node limit
356×	fuel
186×	done
157×	saturated
25×	unsound

Compiler

Compiled 433 335 to 130 003 computations (70% saved)

rewrite8.3min (9.1%)

Memory

-529.0MiB live, 456 049.3MiB allocated

Algorithm

1 898×

batch-egg-rewrite

Rules

1 210 906×	`log1p-expm1-u`
913 798×	`expm1-log1p-u`
425 273×	`pow1`
407 230×	`add-exp-log`
388 450×	`add-log-exp`

Stop Event

1 883×	node limit
14×	unsound
1×	saturated

Counts

22 100 → 661 518

prune7.0min (7.6%)

Memory: -8 527.4MiB live, 589 263.3MiB allocated
Counts: 1 470 182 → 40 281
Compiler: Compiled 1 975 024 to 1 005 933 computations (49.1% saved)

localize5.9min (6.4%)

Memory

4 693.2MiB live, 429 203.3MiB allocated

Samples

1.9min	398 438×	0	valid
44.4s	42 818×	1	valid
28.1s	18 300×	2	valid
11.5s	3 668×	5	exit
10.2s	23 369×	0	invalid
3.6s	1 675×	3	valid
2.1s	4 735×	1	exit
2.1s	549×	4	exit
1.2s	802×	2	exit
1.0s	605×	1	invalid
1.0s	2 547×	0	exit
379.0ms	100×	3	exit
68.0ms	26×	4	valid
57.0ms	26×	2	invalid
5.0ms	6×	3	invalid

Compiler

Compiled 476 512 to 52 555 computations (89% saved)

Precisions

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

ival-mult: 44.0s (27.5% of total)

ival-div: 19.6s (12.2% of total)

ival-add: 14.8s (9.2% of total)

ival-pow: 9.0s (5.6% of total)

ival-sin: 8.6s (5.4% of total)

ival-sub: 8.1s (5.1% of total)

const: 6.9s (4.3% of total)

ival-cos: 6.8s (4.2% of total)

adjust: 6.7s (4.2% of total)

ival-log: 6.0s (3.7% of total)

ival-pow2: 4.5s (2.8% of total)

ival-sqrt: 4.1s (2.5% of total)

ival-exp: 3.5s (2.2% of total)

ival-tan: 2.7s (1.7% of total)

ival-hypot: 2.4s (1.5% of total)

ival-neg: 2.0s (1.3% of total)

ival-cbrt: 1.6s (1% of total)

ival-expm1: 1.6s (1% of total)

ival-log1p: 1.5s (1% of total)

ival-acos: 807.0ms (0.5% of total)

exact: 780.0ms (0.5% of total)

ival-atan2: 622.0ms (0.4% of total)

ival-asin: 535.0ms (0.3% of total)

ival-true: 423.0ms (0.3% of total)

ival-fabs: 306.0ms (0.2% of total)

ival-if: 294.0ms (0.2% of total)

ival-atan: 251.0ms (0.2% of total)

ival-fmod: 243.0ms (0.2% of total)

ival-pi: 228.0ms (0.1% of total)

ival-assert: 206.0ms (0.1% of total)

ival-fmax: 150.0ms (0.1% of total)

ival-copysign: 146.0ms (0.1% of total)

ival-cosh: 128.0ms (0.1% of total)

ival-floor: 94.0ms (0.1% of total)

ival-sinh: 85.0ms (0.1% of total)

ival-log2: 85.0ms (0.1% of total)

ival->=: 57.0ms (0% of total)

ival-e: 43.0ms (0% of total)

ival-tanh: 38.0ms (0% of total)

ival->: 16.0ms (0% of total)

ival-<: 8.0ms (0% of total)

eval5.5min (6%)

Memory: 7 221.7MiB live, 436 207.1MiB allocated
Compiler: Compiled 54 435 988 to 5 660 484 computations (89.6% saved)

regimes3.8min (4.2%)

Memory

-326.6MiB live, 312 706.0MiB allocated

Counts

109 555 → 9 042

Calls

1 224 calls:

19.3s	x
15.1s	y
12.4s	z
9.1s	t
8.5s	a

Compiler

Compiled 98 077 to 71 487 computations (27.1% saved)

series3.1min (3.4%)

Memory

1 436.5MiB live, 257 456.3MiB allocated

Counts

22 100 → 492 405

Calls

120135 calls:

Time	Variable		Point	Expression
652.0ms	base	@	0	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
469.0ms	dX.u	@	0	(log (+ 1 (log2 (sqrt (fmax (pow (sqrt (+ (* (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* dX.v (floor h)) (* dX.v (floor h))))) (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* dX.v (floor h)) (* dX.v (floor h)))))) (* (* (floor d) dX.w) (* (floor d) dX.w)))) 2) (pow (* dY.w (floor d)) 2))))))
463.0ms	t	@	inf	(log (+ 1 (* x (cos (* (+ (* y 2) 1) (* z (* t 1/16)))))))
416.0ms	y	@	-inf	(* 1/2 (* (/ y a) x))
389.0ms	b	@	inf	(log (+ 1 (sin b)))

preprocess2.4min (2.6%)

Memory

-2 675.1MiB live, 141 634.7MiB allocated

Algorithm

542×	egg-herbie

Rules

252 186×	`fma-define`
252 101×	`fmm-def`
106 305×	`unsub-neg`
100 734×	`sub-neg`
94 641×	`distribute-lft-in`

Stop Event

294×	saturated
248×	node limit

Compiler

Compiled 363 156 to 138 834 computations (61.8% saved)

bsearch2.3min (2.5%)

Memory

28.9MiB live, 148 468.4MiB allocated

Algorithm

4 031×	binary-search
606×	left-value

Stop Event

3 931×	narrow-enough
99×	predicate-same
1×	predicate-failed

Samples

1.3min	450 564×	0	valid
14.4s	33 458×	1	valid
2.6s	4 350×	2	valid
2.4s	17 881×	0	invalid
686.0ms	871×	5	exit
665.0ms	323×	3	valid
44.0ms	218×	1	invalid
7.0ms	62×	0	exit
7.0ms	19×	1	exit
2.0ms	7×	2	invalid

Compiler

Compiled 903 104 to 658 125 computations (27.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.2min

ival-mult: 21.0s (29.7% of total)

ival-div: 14.5s (20.6% of total)

ival-sub: 8.0s (11.4% of total)

ival-add: 6.4s (9.1% of total)

ival-sin: 4.1s (5.8% of total)

ival-cos: 3.6s (5.1% of total)

const: 2.1s (3% of total)

ival-log: 1.5s (2.1% of total)

adjust: 1.4s (2% of total)

ival-sqrt: 1.3s (1.9% of total)

ival-pow: 1.1s (1.6% of total)

ival-pow2: 934.0ms (1.3% of total)

ival-exp: 859.0ms (1.2% of total)

ival-neg: 677.0ms (1% of total)

ival-tan: 660.0ms (0.9% of total)

ival-hypot: 493.0ms (0.7% of total)

ival-true: 366.0ms (0.5% of total)

ival-atan2: 357.0ms (0.5% of total)

exact: 266.0ms (0.4% of total)

ival-assert: 191.0ms (0.3% of total)

ival-fabs: 143.0ms (0.2% of total)

ival-acos: 117.0ms (0.2% of total)

ival-cbrt: 97.0ms (0.1% of total)

ival-atan: 53.0ms (0.1% of total)

ival-pi: 50.0ms (0.1% of total)

ival-fmod: 37.0ms (0.1% of total)

ival-copysign: 15.0ms (0% of total)

ival-asin: 11.0ms (0% of total)

ival-tanh: 11.0ms (0% of total)

ival-if: 10.0ms (0% of total)

ival-sinh: 8.0ms (0% of total)

ival->=: 7.0ms (0% of total)

ival-log1p: 4.0ms (0% of total)

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

ival-expm1: 1.0ms (0% of total)

explain2.1min (2.3%)

Memory

1 744.8MiB live, 169 855.4MiB allocated

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`#f`	cancellation	8899	53
`sqrt.f64`	`#f`	oflow-rescue	5455	0
`log.f64`	`#f`	sensitivity	3456	11
`cos.f64`	`#f`	sensitivity	3244	5
`+.f64`	`#f`	cancellation	3114	119
`sin.f64`	`#f`	sensitivity	1975	5
`/.f64`	`#f`	o/n	1949	0
`/.f64`	`#f`	o/o	1733	0
`-.f64`	`#f`	nan-rescue	1300	0
`*.f64`	`#f`	*no**	1157	0
`log.f32`	`#f`	sensitivity	1152	54
`/.f64`	`#f`	u/u	1042	0
`sqrt.f64`	`#f`	uflow-rescue	986	0
`/.f64`	`#f`	n/o	978	0
`+.f64`	`#f`	nan-rescue	833	0
`/.f64`	`#f`	u/n	699	0
`sqrt.f32`	`#f`	oflow-rescue	526	0
`acos.f64`	`#f`	sensitivity	524	2
`*.f64`	`#f`	*nu**	467	0
`pow.f64`	`#f`	sensitivity	430	40
`tan.f64`	`#f`	sensitivity	420	0
`-.f32`	`#f`	cancellation	380	26
`/.f64`	`#f`	n/u	344	0
`-.f64`	(-.f64 (*.f64 #s(literal 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) t) #s(literal 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64))	oflow-left	220	0
`*.f64`	`#f`	*uo**	205	0
`cos.f32`	`(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) u1) (.f32 #s(literal 1/2 binary32) (PI.f32)))))))`	sensitivity	204	7
`exp.f64`	`#f`	sensitivity	202	34
`tan.f32`	`(tan.f32 (+.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))`	cancellation	199	12
`cos.f64`	`#f`	oflow-rescue	197	0
`pow.f64`	`#f`	oflow-rescue	150	0
`*.f64`	`#f`	*ou**	123	0
`asin.f64`	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))`	sensitivity	122	0
`/.f32`	`#f`	o/n	110	0
`log.f64`	`#f`	oflow-rescue	102	0
`cbrt.f64`	`#f`	oflow-rescue	81	0
`log.f64`	`#f`	uflow-rescue	79	0
`pow.f64`	`#f`	uflow-rescue	68	0
`cbrt.f64`	`#f`	uflow-rescue	45	0
`exp.f32`	`#f`	sensitivity	40	23
`sin.f64`	`#f`	oflow-rescue	35	0
`tan.f64`	`(tan.f64 (/.f64 x (*.f64 y #s(literal 2 binary64))))`	oflow-rescue	33	0
↳	`(/.f64 x (*.f64 y #s(literal 2 binary64)))`	overflow	33
`/.f32`	`#f`	u/n	27	0
`/.f32`	`#f`	n/o	11	0
`sqrt.f32`	`(sqrt.f32 (-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O))))))`	uflow-rescue	9	0
↳	`(*.f32 sinTheta_O sinTheta_O)`	underflow	270
↳	`(-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O)))))`	underflow	9
↳	`(/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_O))))`	underflow	135
↳	`(*.f32 eta eta)`	underflow	9
`/.f32`	`#f`	o/o	6	0
`*.f32`	`(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*nu**	2	0
`log.f32`	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`	oflow-rescue	2	0
↳	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`	overflow	2
↳	`(*.f32 x x)`	overflow	123
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	123
`*.f32`	`(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*uo**	1	0
↳	`(*.f32 u normAngle)`	underflow	3
↳	`(sin.f32 (*.f32 u normAngle))`	underflow	3
↳	`(/.f32 #s(literal 1 binary32) (sin.f32 normAngle))`	overflow	1
`sin.f32`	`(sin.f32 (.f32 (.f32 uy #s(literal 2 binary32)) (PI.f32)))`	cancellation	1	0
`*.f32`	`(.f32 (sin.f32 (.f32 (-.f32 #s(literal 1 binary32) u) normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*no**	1	0
`sin.f64`	`(sin.f64 (*.f64 (/.f64 angle #s(literal 180 binary64)) (PI.f64)))`	cancellation	1	0

Confusion

	Predicted +	Predicted -
+	30551	1160
-	6027	101014

Precision

0.8352288260703155

Recall

0.9634196335656396

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	30551	245	915
-	6027	399	100615

Precision?

0.8273601633442588

Recall?

0.9711456592349658

Freqs

test

number	freq
0	102174
1	30613
2	4895
3	601
4	298
5	103
6	39
7	22
8	5
9	2

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	338	3	3
-	11	4	183

Precision?

0.9578651685393258

Recall?

0.9912790697674418

Samples

26.5s	233 602×	0	valid
12.3s	31 908×	1	valid
7.2s	10 728×	2	valid
1.0s	1 146×	3	valid
13.0ms	90×	1	exit
12.0ms	8×	4	valid
11.0ms	22×	5	exit

Compiler

Compiled 106 238 to 25 502 computations (76% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.4s

ival-mult: 6.6s (20.9% of total)

ival-div: 3.5s (11.3% of total)

ival-add: 2.9s (9.3% of total)

ival-sin: 2.5s (7.9% of total)

ival-sub: 2.3s (7.4% of total)

ival-cos: 2.3s (7.3% of total)

ival-log: 1.9s (6.2% of total)

ival-tan: 1.3s (4.3% of total)

adjust: 1.3s (4.1% of total)

ival-sqrt: 1.2s (3.8% of total)

ival-exp: 1.1s (3.6% of total)

ival-pow: 655.0ms (2.1% of total)

ival-pow2: 651.0ms (2.1% of total)

const: 648.0ms (2.1% of total)

ival-atan2: 348.0ms (1.1% of total)

ival-asin: 307.0ms (1% of total)

ival-hypot: 254.0ms (0.8% of total)

ival-true: 240.0ms (0.8% of total)

ival-neg: 226.0ms (0.7% of total)

exact: 199.0ms (0.6% of total)

ival-pi: 158.0ms (0.5% of total)

ival-assert: 112.0ms (0.4% of total)

ival-acos: 110.0ms (0.4% of total)

ival-atan: 73.0ms (0.2% of total)

ival-log1p: 73.0ms (0.2% of total)

ival-fabs: 59.0ms (0.2% of total)

ival-sinh: 53.0ms (0.2% of total)

ival-floor: 41.0ms (0.1% of total)

ival-cbrt: 35.0ms (0.1% of total)

ival-fmod: 29.0ms (0.1% of total)

ival-expm1: 26.0ms (0.1% of total)

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

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

ival-log2: 14.0ms (0% of total)

ival-copysign: 12.0ms (0% of total)

ival-cosh: 10.0ms (0% of total)

ival->=: 6.0ms (0% of total)

ival-tanh: 6.0ms (0% of total)

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

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

analyze1.4min (1.5%)

Memory

-279.8MiB live, 109 492.1MiB allocated

Algorithm

545×	search
2×	random

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	84.4%	15.6%	0%	0%	0%	0
39.8%	33.6%	50.8%	15.6%	0%	0%	0%	1
45.9%	38.4%	45.3%	15.6%	0%	0.8%	0%	2
54.5%	44.5%	37.2%	15.6%	0%	2.8%	0%	3
61.4%	49.5%	31.1%	15.6%	0%	3.8%	0%	4
67.7%	54.3%	25.9%	15.6%	0%	4.3%	0%	5
71.6%	57.1%	22.7%	15.6%	0%	4.7%	0%	6
75.5%	59.8%	19.4%	15.6%	0%	5.2%	0%	7
77.5%	61.1%	17.7%	15.6%	0%	5.6%	0%	8
80.1%	62.9%	15.6%	15.6%	0%	5.9%	0%	9
81.7%	63.9%	14.3%	15.6%	0%	6.2%	0%	10
83.9%	65.5%	12.6%	15.6%	0%	6.4%	0%	11
85%	66.2%	11.6%	15.6%	0%	6.6%	0%	12

Compiler

Compiled 12 512 to 7 841 computations (37.3% saved)

end4.0ms (0%)

Memory: -29.3MiB live, 9.0MiB allocated

simplify19.1min (20.8%)

sample18.6min (20.3%)

soundness11.9min (13.1%)

rewrite8.3min (9.1%)

prune7.0min (7.6%)

localize5.9min (6.4%)

eval5.5min (6%)

regimes3.8min (4.2%)

series3.1min (3.4%)

preprocess2.4min (2.6%)

bsearch2.3min (2.5%)

explain2.1min (2.3%)

analyze1.4min (1.5%)

end4.0ms (0%)

Profiling