Metrics for Herbie run

Date:	Thursday, June 13th, 2024
Commit:	63d27371 on web-cleanup
Hostname:	nightly with Racket 8.11.1
Seed:	2024165
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

sample22.3min (23.2%)

Samples

8.4min	3 840 064×	0	valid
3.2min	58 547×	5	exit
3.2min	483 300×	1	valid
1.3min	129 533×	2	valid
1.3min	377 366×	0	invalid
30.1s	19 626×	3	valid
9.2s	2 253×	4	valid
7.9s	26 595×	1	invalid
2.1s	2 822×	2	invalid
143.0ms	13×	5	valid
14.0ms	26×	3	invalid

Precisions

Click to see histograms. Total time spent on operations: 13.6min

ival-pow: 2.5min (18.6% of total)

ival-mult: 2.4min (17.3% of total)

ival-sin: 1.3min (9.3% of total)

ival-div: 1.1min (8.3% of total)

ival-add: 57.2s (7% of total)

ival-sub: 55.2s (6.7% of total)

ival-cos: 37.6s (4.6% of total)

...in/eval/compile.rkt:71:19: 35.3s (4.3% of total)

adjust: 34.0s (4.2% of total)

ival-exp: 30.7s (3.8% of total)

ival-log: 27.5s (3.4% of total)

ival-sqrt: 22.4s (2.7% of total)

ival-tan: 19.5s (2.4% of total)

ival-<=: 14.3s (1.7% of total)

ival-neg: 7.8s (1% of total)

ival-fabs: 4.0s (0.5% of total)

ival-<: 3.8s (0.5% of total)

ival-and: 3.3s (0.4% of total)

ival-true: 3.3s (0.4% of total)

...in/eval/compile.rkt:70:19: 2.9s (0.4% of total)

ival-assert: 2.7s (0.3% of total)

ival-acos: 2.7s (0.3% of total)

ival-pi: 2.4s (0.3% of total)

ival-atan2: 2.1s (0.3% of total)

ival-asin: 1.8s (0.2% of total)

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

ival-atan: 1.3s (0.2% of total)

ival-floor: 1.1s (0.1% of total)

ival-fmod: 1.0s (0.1% of total)

ival-sinh: 726.0ms (0.1% of total)

ival-log2: 558.0ms (0.1% of total)

ival-cosh: 556.0ms (0.1% of total)

ival-cbrt: 513.0ms (0.1% of total)

ival-==: 510.0ms (0.1% of total)

ival-hypot: 422.0ms (0.1% of total)

ival-fmin: 409.0ms (0% of total)

ival-if: 336.0ms (0% of total)

ival-fmax: 311.0ms (0% of total)

ival-acosh: 279.0ms (0% of total)

ival->=: 268.0ms (0% of total)

ival-asinh: 250.0ms (0% of total)

ival-fma: 241.0ms (0% of total)

ival-tanh: 174.0ms (0% of total)

ival-atanh: 139.0ms (0% of total)

ival-or: 46.0ms (0% of total)

Bogosity

simplify19.0min (19.8%)

Algorithm

4 360×

egg-herbie

Rules

1 669 971×	`fma-define`
1 272 933×	`fmm-def`
889 389×	`distribute-lft-in`
848 175×	`times-frac`
818 299×	`associate-r`

Stop Event

2 882×	node limit
1 446×	saturated
32×	unsound

Counts

1 145 198 → 989 402

soundness12.2min (12.7%)

Rules

659 778×	`fma-define`
490 122×	`log1p-expm1-u`
489 571×	`fmm-def`
413 647×	`associate-r`
392 117×	`times-frac`

Stop Event

1 958×	node limit
359×	fuel
183×	done
156×	saturated
24×	unsound

Compiler

Compiled 465 123 to 134 424 computations (71.1% saved)

rewrite8.2min (8.6%)

Algorithm

1 887×

batch-egg-rewrite

Rules

1 217 382×	`log1p-expm1-u`
910 523×	`expm1-log1p-u`
424 314×	`pow1`
402 138×	`add-exp-log`
385 554×	`add-log-exp`

Stop Event

1 872×	node limit
13×	unsound
2×	saturated

Counts

21 808 → 659 951

localize7.0min (7.3%)

Samples

2.3min	392 703×	0	valid
57.1s	46 119×	1	valid
51.3s	9 540×	5	exit
25.6s	14 350×	2	valid
15.4s	28 511×	0	invalid
6.4s	2 072×	3	valid
1.7s	874×	1	invalid
745.0ms	133×	4	valid
122.0ms	28×	2	invalid
13.0ms	3×	5	valid
5.0ms	3×	3	invalid

Compiler

Compiled 456 998 to 51 156 computations (88.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0min

ival-mult: 37.9s (20.7% of total)

ival-div: 20.9s (11.4% of total)

ival-pow: 18.5s (10.1% of total)

adjust: 15.3s (8.4% of total)

ival-add: 12.9s (7.1% of total)

ival-sin: 10.6s (5.8% of total)

ival-cos: 8.9s (4.8% of total)

ival-log: 8.2s (4.5% of total)

ival-sub: 8.2s (4.5% of total)

ival-tan: 7.7s (4.2% of total)

...in/eval/compile.rkt:71:19: 6.3s (3.5% of total)

ival-sqrt: 4.8s (2.6% of total)

ival-fma: 4.7s (2.6% of total)

ival-exp: 3.1s (1.7% of total)

ival-hypot: 2.4s (1.3% of total)

ival-log1p: 1.9s (1% of total)

ival-neg: 1.8s (1% of total)

ival-expm1: 1.7s (0.9% of total)

ival-cbrt: 1.5s (0.8% of total)

ival-atan2: 598.0ms (0.3% of total)

...in/eval/compile.rkt:70:19: 566.0ms (0.3% of total)

ival-atan: 560.0ms (0.3% of total)

ival-fmod: 532.0ms (0.3% of total)

ival-true: 476.0ms (0.3% of total)

ival-acos: 403.0ms (0.2% of total)

ival-asin: 402.0ms (0.2% of total)

ival-pi: 343.0ms (0.2% of total)

ival-if: 343.0ms (0.2% of total)

ival-assert: 315.0ms (0.2% of total)

ival-fabs: 225.0ms (0.1% of total)

ival-fmax: 171.0ms (0.1% of total)

ival-e: 131.0ms (0.1% of total)

ival-copysign: 126.0ms (0.1% of total)

ival-log2: 98.0ms (0.1% of total)

ival-floor: 93.0ms (0.1% of total)

ival-sinh: 68.0ms (0% of total)

ival-cosh: 63.0ms (0% of total)

ival->=: 39.0ms (0% of total)

ival->: 21.0ms (0% of total)

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

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

prune6.4min (6.7%)

Counts: 1 456 375 → 40 131
Compiler: Compiled 1 945 045 to 989 458 computations (49.1% saved)

eval5.2min (5.4%)

Compiler: Compiled 50 469 743 to 5 561 256 computations (89% saved)

regimes3.9min (4.1%)

Counts

108 616 → 9 151

Calls

1 224 calls:

19.0s	x
14.4s	y
11.0s	z
9.2s	t
8.9s	a

Compiler

Compiled 99 144 to 72 396 computations (27% saved)

series3.1min (3.2%)

Counts

21 808 → 485 247

Calls

118155 calls:

Time	Variable		Point	Expression
958.0ms	x-scale	@	inf	(log (* (* 1/4 a) (* x-scale 4)))
715.0ms	h	@	-inf	(pow (fmax (pow (sqrt (+ (* (* (floor d) dX.w) (* (floor d) dX.w)) (* (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v)))) (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))))))) 2) (pow (sqrt (+ (* (* (floor d) dY.w) (* (floor d) dY.w)) (* (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))))) 2)) 1/4)
595.0ms	x	@	-inf	(* x (* 2 (log (sqrt x))))
529.0ms	y	@	0	(* x (pow (sqrt (- (log (neg x)) (log (neg y)))) 2))
510.0ms	z	@	0	(/ (log (+ 1 (* y (- (exp z) 1)))) (* t x))

preprocess2.4min (2.6%)

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 380 838 to 145 636 computations (61.8% saved)

bsearch2.4min (2.5%)

Algorithm

4 111×	binary-search
610×	left-value

Stop Event

4 012×	narrow-enough
93×	predicate-same
6×	predicate-failed

Samples

1.3min	463 493×	0	valid
15.1s	30 005×	1	valid
3.2s	24 144×	0	invalid
3.0s	1 176×	3	valid
2.2s	4 308×	2	valid
106.0ms	239×	1	invalid
44.0ms	26×	4	valid
12.0ms	41×	2	invalid
1.0ms	2×	5	exit

Compiler

Compiled 953 971 to 695 320 computations (27.1% saved)

Precisions

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

ival-mult: 22.8s (32.5% of total)

ival-div: 8.5s (12.2% of total)

ival-sub: 8.2s (11.7% of total)

ival-add: 7.1s (10.1% of total)

ival-sin: 4.3s (6.2% of total)

ival-cos: 3.9s (5.6% of total)

ival-pow: 2.9s (4.2% of total)

ival-log: 2.7s (3.8% of total)

...in/eval/compile.rkt:71:19: 2.6s (3.6% of total)

ival-sqrt: 1.8s (2.6% of total)

adjust: 1.2s (1.7% of total)

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

ival-tan: 679.0ms (1% of total)

ival-true: 441.0ms (0.6% of total)

ival-neg: 373.0ms (0.5% of total)

ival-assert: 295.0ms (0.4% of total)

ival-atan2: 285.0ms (0.4% of total)

ival-fabs: 247.0ms (0.4% of total)

...in/eval/compile.rkt:70:19: 201.0ms (0.3% of total)

ival-atan: 115.0ms (0.2% of total)

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

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

ival->=: 21.0ms (0% of total)

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

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

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

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

ival-cbrt: 9.0ms (0% of total)

ival-if: 9.0ms (0% of total)

ival-tanh: 7.0ms (0% of total)

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

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

explain2.4min (2.5%)

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`#f`	cancellation	8904	47
`sqrt.f64`	`#f`	oflow-rescue	5301	0
`log.f64`	`#f`	sensitivity	3490	2
`cos.f64`	`#f`	sensitivity	3348	3
`+.f64`	`#f`	cancellation	3114	118
`sin.f64`	`#f`	sensitivity	2054	4
`/.f64`	`#f`	o/o	1902	0
`/.f64`	`#f`	o/n	1899	0
`-.f64`	`#f`	nan-rescue	1435	0
`log.f32`	`#f`	sensitivity	1138	75
`/.f64`	`#f`	u/u	1010	0
`*.f64`	`#f`	*no**	1009	0
`/.f64`	`#f`	n/o	976	0
`sqrt.f64`	`#f`	uflow-rescue	886	0
`+.f64`	`#f`	nan-rescue	856	0
`/.f64`	`#f`	u/n	792	0
`sqrt.f32`	`#f`	oflow-rescue	569	0
`acos.f64`	`#f`	sensitivity	527	2
`*.f64`	`#f`	*nu**	452	0
`tan.f64`	`#f`	sensitivity	421	2
`pow.f64`	`#f`	sensitivity	395	49
`-.f32`	`#f`	cancellation	395	33
`/.f64`	`#f`	n/u	323	0
`exp.f64`	`#f`	sensitivity	218	28
`cos.f64`	`#f`	oflow-rescue	217	0
`-.f64`	(-.f64 (*.f64 #s(literal 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) t) #s(literal 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64))	oflow-left	216	0
`*.f64`	`#f`	*uo**	195	0
`cos.f32`	`#f`	sensitivity	194	19
`tan.f32`	`(tan.f32 (+.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))`	cancellation	189	16
`pow.f64`	`#f`	oflow-rescue	153	0
`*.f64`	`#f`	*ou**	149	0
`/.f32`	`#f`	o/n	130	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	113	0
`log.f64`	`#f`	oflow-rescue	102	0
`cbrt.f64`	`#f`	oflow-rescue	84	0
`pow.f64`	`#f`	uflow-rescue	68	0
`log.f64`	`#f`	uflow-rescue	63	0
`exp.f32`	`#f`	sensitivity	37	14
`cbrt.f64`	`#f`	uflow-rescue	35	0
`sin.f64`	`#f`	oflow-rescue	31	0
`tan.f64`	`(tan.f64 (/.f64 x (*.f64 y #s(literal 2 binary64))))`	oflow-rescue	28	0
↳	`(/.f64 x (*.f64 y #s(literal 2 binary64)))`	overflow	28
`/.f32`	`#f`	u/n	23	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	18	0
↳	`(*.f32 sinTheta_O sinTheta_O)`	underflow	276
↳	`(-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O)))))`	underflow	18
↳	`(/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_O))))`	underflow	138
↳	`(*.f32 eta eta)`	underflow	18
`/.f32`	`#f`	o/o	14	0
`log.f32`	`#f`	oflow-rescue	7	0
`/.f32`	`#f`	n/o	6	0
`*.f32`	`(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*nu**	4	0
`*.f32`	`(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*uo**	1	0
↳	`(*.f32 u normAngle)`	underflow	5
↳	`(sin.f32 (*.f32 u normAngle))`	underflow	5
↳	`(/.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

Confusion

	Predicted +	Predicted -
+	30605	1177
-	5901	101069

Precision

0.8383553388484085

Recall

0.9629664590019508

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	30605	252	925
-	5901	393	100676

Precision?

0.8305832952006675

Recall?

0.9708954754263419

Freqs

test

number	freq
0	102246
1	30584
2	4756
3	600
4	333
5	145
6	66
7	15
8	4
9	3

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	338	2	5
-	10	2	185

Precision?

0.9659090909090909

Recall?

0.9855072463768116

Samples

34.6s	230 824×	0	valid
14.6s	34 548×	1	valid
7.5s	10 498×	2	valid
2.3s	1 390×	3	valid
642.0ms	98×	5	exit
527.0ms	146×	4	valid

Compiler

Compiled 106 238 to 25 504 computations (76% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.9s

ival-mult: 8.1s (23.9% of total)

ival-div: 3.9s (11.5% of total)

ival-sin: 2.9s (8.6% of total)

ival-add: 2.9s (8.5% of total)

ival-sub: 2.5s (7.5% of total)

ival-cos: 2.2s (6.6% of total)

adjust: 2.1s (6.2% of total)

ival-log: 1.9s (5.7% of total)

ival-pow: 1.5s (4.4% of total)

ival-exp: 1.2s (3.5% of total)

ival-tan: 1.1s (3.2% of total)

ival-sqrt: 906.0ms (2.7% of total)

...in/eval/compile.rkt:71:19: 553.0ms (1.6% of total)

ival-neg: 379.0ms (1.1% of total)

ival-pi: 352.0ms (1% of total)

ival-true: 269.0ms (0.8% of total)

ival-assert: 170.0ms (0.5% of total)

ival-atan2: 136.0ms (0.4% of total)

...in/eval/compile.rkt:70:19: 132.0ms (0.4% of total)

ival-floor: 111.0ms (0.3% of total)

ival-asin: 100.0ms (0.3% of total)

ival-acos: 82.0ms (0.2% of total)

ival-atan: 66.0ms (0.2% of total)

ival-fabs: 58.0ms (0.2% of total)

ival-cbrt: 42.0ms (0.1% of total)

ival-fmod: 42.0ms (0.1% of total)

ival-sinh: 30.0ms (0.1% of total)

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

ival-cosh: 19.0ms (0.1% of total)

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

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

ival-log2: 16.0ms (0% of total)

ival-copysign: 13.0ms (0% of total)

ival-fma: 13.0ms (0% of total)

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

ival-log1p: 8.0ms (0% of total)

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

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

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

analyze1.6min (1.6%)

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
38.9%	32.9%	51.6%	15.6%	0%	0%	0%	1
44.8%	37.5%	46.2%	15.6%	0%	0.8%	0%	2
54%	44.1%	37.5%	15.6%	0%	2.8%	0%	3
60.9%	49.1%	31.6%	15.6%	0%	3.8%	0%	4
67.1%	53.8%	26.4%	15.6%	0%	4.2%	0%	5
71%	56.7%	23.1%	15.6%	0%	4.6%	0%	6
75%	59.4%	19.8%	15.6%	0%	5.2%	0.1%	7
77%	60.7%	18.1%	15.6%	0%	5.5%	0.1%	8
79.6%	62.5%	16%	15.6%	0%	5.8%	0.1%	9
81.1%	63.5%	14.8%	15.6%	0%	6.1%	0.1%	10
83.4%	65.1%	13%	15.6%	0%	6.3%	0.1%	11
84.5%	65.8%	12.1%	15.6%	0%	6.5%	0.1%	12

Compiler

Compiled 12 512 to 7 913 computations (36.8% saved)

Herbie run

sample22.3min (23.2%)

simplify19.0min (19.8%)

soundness12.2min (12.7%)

rewrite8.2min (8.6%)

localize7.0min (7.3%)

prune6.4min (6.7%)

eval5.2min (5.4%)

regimes3.9min (4.1%)

series3.1min (3.2%)

preprocess2.4min (2.6%)

bsearch2.4min (2.5%)

explain2.4min (2.5%)

analyze1.6min (1.6%)

end3.0ms (0%)

Profiling