Metrics for Herbie run

Date:	Thursday, June 27th, 2024
Commit:	1ed5d077 on no-const-taylor
Hostname:	nightly with Racket 8.11.1
Seed:	2024179
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

simplify2.8min (24.7%)

Memory

999.5MiB live, 235 294.8MiB allocated

Algorithm

267×	egg-herbie

Rules

201 656×	`fma-define`
125 450×	`fmm-def`
123 982×	`*-commutative`
119 024×	`distribute-lft-in`
104 624×	`distribute-rgt-in`

Stop Event

203×	node limit
64×	saturated

Counts

111 052 → 77 108

prune1.6min (14.1%)

Memory: 208.9MiB live, 151 603.2MiB allocated
Counts: 149 400 → 3 438
Compiler: Compiled 336 030 to 124 818 computations (62.9% saved)

soundness1.5min (13.5%)

Memory

56.3MiB live, 101 236.1MiB allocated

Rules

83 738×	`fma-define`
58 358×	`*-commutative`
51 996×	`associate-r`
44 006×	`distribute-lft-in`
43 628×	`fmm-def`

Stop Event

150×	node limit
28×	fuel
7×	saturated
2×	done

Compiler

Compiled 48 995 to 10 372 computations (78.8% saved)

series1.3min (11.8%)

Memory

928.3MiB live, 108 956.4MiB allocated

Counts

2 133 → 63 324

Calls

15336 calls:

Time	Variable		Point	Expression
4.4s	h	@	inf	(* (log (fmax (+ (pow (* (floor d) dX.w) 2) (/ (- (pow (* (floor w) dX.u) 4) (pow (* (floor h) dX.v) 4)) (- (pow (* (floor w) dX.u) 2) (pow (* (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))) 1/2)
1.6s	dX.w	@	inf	(log (log2 (sqrt (fmax (+ (pow (* (floor d) dX.w) 2) (/ (- (pow (* (floor w) dX.u) 4) (pow (* (floor h) dX.v) 4)) (- (pow (* (floor w) dX.u) 2) (pow (* (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)))))
1.1s	w	@	-inf	(log (+ 1 (pow (log2 (sqrt (fmax (+ (pow (* dX.w (floor d)) 2) (/ (- (pow (* dX.u (floor w)) 4) (pow (* dX.v (floor h)) 4)) (- (pow (* dX.u (floor w)) 2) (pow (* dX.v (floor h)) 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)))) 3)))
928.0ms	h	@	inf	(* (log (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))) 1/2)
912.0ms	cosTheta_O	@	-inf	(* (/ 1/2 v) (pow (exp (- (+ (* cosTheta_O cosTheta_i) (* v 6931/10000)) (+ (* sinTheta_O sinTheta_i) 1))) (/ 1 v)))

sample1.3min (11.7%)

Memory

643.4MiB live, 100 760.9MiB allocated

Samples

57.8s	247 633×	0	valid
1.9s	10 721×	0	invalid
6.0ms	47×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 47.3s

ival-mult: 11.3s (23.9% of total)

...in/eval/compile.rkt:77:19: 7.4s (15.7% of total)

ival-<=: 6.4s (13.5% of total)

ival-div: 4.3s (9.2% of total)

ival-sub: 2.2s (4.6% of total)

ival-sin: 2.0s (4.2% of total)

ival-add: 1.8s (3.7% of total)

ival-sqrt: 1.5s (3.2% of total)

ival-log: 1.4s (3% of total)

ival-fabs: 1.3s (2.7% of total)

ival-and: 1.2s (2.5% of total)

ival-exp: 1.1s (2.3% of total)

ival-cos: 869.0ms (1.8% of total)

ival-floor: 754.0ms (1.6% of total)

ival-pi: 510.0ms (1.1% of total)

ival-neg: 502.0ms (1.1% of total)

ival-tan: 469.0ms (1% of total)

ival-fmax: 381.0ms (0.8% of total)

...in/eval/compile.rkt:76:19: 345.0ms (0.7% of total)

ival->: 259.0ms (0.5% of total)

ival-log2: 243.0ms (0.5% of total)

ival-if: 223.0ms (0.5% of total)

ival-sinh: 207.0ms (0.4% of total)

ival-atan: 175.0ms (0.4% of total)

ival-<: 165.0ms (0.3% of total)

ival-asin: 143.0ms (0.3% of total)

ival-assert: 97.0ms (0.2% of total)

ival-==: 97.0ms (0.2% of total)

ival->=: 50.0ms (0.1% of total)

adjust: 1.0ms (0% of total)

Bogosity

localize36.6s (5.4%)

Memory

-211.1MiB live, 52 740.5MiB allocated

Samples

13.8s	27 321×	0	valid
3.7s	538×	5	exit
820.0ms	1 378×	0	invalid
452.0ms	542×	1	valid
226.0ms	685×	0	exit

Compiler

Compiled 116 806 to 6 246 computations (94.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.7s

ival-mult: 3.8s (26.2% of total)

ival-add: 1.8s (12.4% of total)

ival-div: 1.7s (11.7% of total)

ival-pow: 995.0ms (6.8% of total)

ival-log: 802.0ms (5.5% of total)

ival-hypot: 613.0ms (4.2% of total)

...in/eval/compile.rkt:77:19: 561.0ms (3.8% of total)

ival-sqrt: 506.0ms (3.4% of total)

ival-pow2: 493.0ms (3.4% of total)

ival-sub: 476.0ms (3.2% of total)

ival-sin: 473.0ms (3.2% of total)

ival-cos: 315.0ms (2.1% of total)

ival-exp: 266.0ms (1.8% of total)

ival-log1p: 239.0ms (1.6% of total)

adjust: 217.0ms (1.5% of total)

ival-log2: 211.0ms (1.4% of total)

ival-expm1: 157.0ms (1.1% of total)

ival-neg: 146.0ms (1% of total)

ival-fmax: 142.0ms (1% of total)

ival-if: 130.0ms (0.9% of total)

ival-floor: 89.0ms (0.6% of total)

ival-tan: 85.0ms (0.6% of total)

ival-pi: 68.0ms (0.5% of total)

ival-cbrt: 65.0ms (0.4% of total)

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

...in/eval/compile.rkt:76:19: 44.0ms (0.3% of total)

ival-fabs: 30.0ms (0.2% of total)

ival-true: 30.0ms (0.2% of total)

ival->: 20.0ms (0.1% of total)

ival->=: 20.0ms (0.1% of total)

ival-atan: 16.0ms (0.1% of total)

ival-sinh: 14.0ms (0.1% of total)

ival-assert: 14.0ms (0.1% of total)

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

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

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

rewrite31.5s (4.7%)

Memory

62.4MiB live, 35 899.6MiB allocated

Algorithm

118×	batch-egg-rewrite

Rules

60 682×	`log1p-expm1-u`
52 801×	`expm1-log1p-u`
39 837×	`pow1`
37 550×	`log-prod`
36 901×	`add-exp-log`

Stop Event

118×	node limit

Counts

2 133 → 47 728

eval31.4s (4.7%)

Memory: 959.2MiB live, 52 729.5MiB allocated
Compiler: Compiled 15 485 805 to 704 283 computations (95.5% saved)

analyze20.1s (3%)

Memory

-219.7MiB live, 29 541.5MiB allocated

Algorithm

30×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	2.6%	97.4%	0%	0%	0%	0
0%	0%	2.6%	97.4%	0%	0%	0%	1
7.8%	0.2%	2.4%	97.4%	0%	0%	0%	2
8.5%	0.2%	2.4%	97.4%	0%	0%	0%	3
12.8%	0.3%	2.3%	97.4%	0%	0%	0%	4
47%	1.2%	1.4%	97.4%	0%	0%	0%	5
51.8%	1.3%	1.2%	97.4%	0%	0.1%	0%	6
69.5%	1.8%	0.8%	97.4%	0%	0.1%	0%	7
71.6%	1.8%	0.7%	97.4%	0%	0.1%	0%	8
81.1%	2.1%	0.5%	97.4%	0%	0.1%	0%	9
82.6%	2.1%	0.4%	97.4%	0%	0.1%	0%	10
88.3%	2.2%	0.3%	97.4%	0%	0.1%	0%	11
89.1%	2.2%	0.3%	97.4%	0%	0.1%	0%	12

Compiler

Compiled 2 586 to 1 076 computations (58.4% saved)

regimes18.8s (2.8%)

Memory

-347.0MiB live, 24 393.5MiB allocated

Counts

5 893 → 201

Calls

145 calls:

1.1s	(log2.f32 (sqrt.f32 (fmax.f32 (+.f32 (+.f32 (.f32 (.f32 (floor.f32 w) dX.u) (.f32 (floor.f32 w) dX.u)) (.f32 (.f32 (floor.f32 h) dX.v) (.f32 (floor.f32 h) dX.v))) (.f32 (.f32 (floor.f32 d) dX.w) (.f32 (floor.f32 d) dX.w))) (+.f32 (+.f32 (.f32 (.f32 (floor.f32 w) dY.u) (.f32 (floor.f32 w) dY.u)) (.f32 (.f32 (floor.f32 h) dY.v) (.f32 (floor.f32 h) dY.v))) (.f32 (.f32 (floor.f32 d) dY.w) (.f32 (floor.f32 d) dY.w))))))
618.0ms	s
567.0ms	uy
377.0ms	r
366.0ms	cosTheta_i

Compiler

Compiled 10 931 to 7 088 computations (35.2% saved)

explain9.4s (1.4%)

Memory

-381.0MiB live, 13 486.6MiB allocated

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f32`	`#f`	sensitivity	995	77
`-.f32`	`#f`	cancellation	396	30
`sqrt.f32`	`#f`	oflow-rescue	346	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	9
`tan.f32`	`(tan.f32 (+.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))`	cancellation	197	12
`/.f32`	`#f`	o/n	144	0
`exp.f32`	`#f`	sensitivity	50	15
`/.f32`	`#f`	u/n	16	0
`/.f32`	`#f`	o/o	12	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	10	0
↳	`(*.f32 sinTheta_O sinTheta_O)`	underflow	288
↳	`(-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O)))))`	underflow	10
↳	`(/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_O))))`	underflow	144
↳	`(*.f32 eta eta)`	underflow	10
`/.f32`	`#f`	n/o	8	0
`*.f32`	`(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*nu**	2	0
`*.f32`	`(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))`	*no**	1	0

Confusion

	Predicted +	Predicted -
+	1626	73
-	403	5578

Precision

0.8013799901429276

Recall

0.9570335491465568

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1626	44	29
-	403	97	5481

Precision?

0.7695852534562212

Recall?

0.9829311359623308

Freqs

test

number	freq
0	5651
1	1689
2	328
3	12

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	20	1	2
-	4	1	2

Precision?

0.8076923076923077

Recall?

0.9130434782608695

Samples

2.6s	15 320×	0	valid
14.0ms	40×	1	valid

Compiler

Compiled 18 280 to 2 256 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.8s

ival-mult: 507.0ms (27.5% of total)

ival-exp: 449.0ms (24.4% of total)

ival-div: 214.0ms (11.6% of total)

ival-add: 82.0ms (4.5% of total)

ival-log: 82.0ms (4.5% of total)

ival-sub: 78.0ms (4.2% of total)

ival-sin: 76.0ms (4.1% of total)

ival-sqrt: 64.0ms (3.5% of total)

ival-floor: 45.0ms (2.4% of total)

ival-cos: 45.0ms (2.4% of total)

ival-neg: 28.0ms (1.5% of total)

ival-pi: 23.0ms (1.2% of total)

...in/eval/compile.rkt:77:19: 23.0ms (1.2% of total)

ival-tan: 18.0ms (1% of total)

ival-fmax: 17.0ms (0.9% of total)

ival-log2: 14.0ms (0.8% of total)

ival-true: 14.0ms (0.8% of total)

ival-if: 13.0ms (0.7% of total)

...in/eval/compile.rkt:76:19: 8.0ms (0.4% of total)

ival-fabs: 8.0ms (0.4% of total)

ival-assert: 7.0ms (0.4% of total)

ival-atan: 7.0ms (0.4% of total)

ival-sinh: 6.0ms (0.3% of total)

ival-asin: 5.0ms (0.3% of total)

ival->: 3.0ms (0.2% of total)

ival->=: 3.0ms (0.2% of total)

ival-<: 2.0ms (0.1% of total)

adjust: 1.0ms (0.1% of total)

preprocess8.0s (1.2%)

Memory

10.0MiB live, 9 528.0MiB allocated

Algorithm

30×	egg-herbie

Rules

30 620×	`fma-define`
21 784×	`fmm-def`
14 698×	`distribute-lft-neg-in`
14 266×	`unsub-neg`
11 858×	`distribute-rgt-neg-in`

Stop Event

19×	node limit
11×	saturated

Compiler

Compiled 37 312 to 13 650 computations (63.4% saved)

end6.5s (1%)

Memory: -45.7MiB live, 3 325.7MiB allocated

bsearch4.0ms (0%)

Memory

14.2MiB live, 14.2MiB allocated

Algorithm

1×	left-value
1×	binary-search

Stop Event

1×	narrow-enough

Compiler

Compiled 87 to 56 computations (35.6% saved)

simplify2.8min (24.7%)

prune1.6min (14.1%)

soundness1.5min (13.5%)

series1.3min (11.8%)

sample1.3min (11.7%)

localize36.6s (5.4%)

rewrite31.5s (4.7%)

eval31.4s (4.7%)

analyze20.1s (3%)

regimes18.8s (2.8%)

explain9.4s (1.4%)

preprocess8.0s (1.2%)

end6.5s (1%)

bsearch4.0ms (0%)

Profiling