Metrics for Herbie run

Date:	Tuesday, June 18th, 2024
Commit:	2f9055fd on zane-job-abstraction3
Hostname:	nightly with Racket 8.11.1
Seed:	2024170
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

simplify2.5min (28%)

Algorithm

243×	egg-herbie

Rules

194190×	`fma-define`
115288×	`distribute-lft-in`
102302×	`*-commutative`
102004×	`times-frac`
98384×	`fmm-def`

Stop Event

57×	saturated
186×	node limit

Counts

93799 → 64962

soundness1.5min (17.5%)

Rules

87784×	`fma-define`
59370×	`associate-r`
55984×	`*-commutative`
53122×	`times-frac`
50968×	`distribute-lft-in`

Stop Event

7×	saturated
143×	node limit
27×	fuel

Compiler

Compiled 49750 to 10118 computations (79.7% saved)

sample1.2min (13.2%)

Results

52.8s	222853×	0	valid
10.0ms	69×	0	invalid
8.0ms	59×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 43.5s

ival-mult: 9.4s (21.6% of total)

...in/eval/compile.rkt:77:19: 6.1s (14% of total)

ival-<=: 5.1s (11.6% of total)

ival-div: 4.5s (10.2% of total)

ival-fabs: 2.1s (4.9% of total)

ival-log: 1.8s (4.2% of total)

ival-sub: 1.7s (3.9% of total)

ival-sin: 1.6s (3.7% of total)

ival-add: 1.5s (3.5% of total)

ival-sqrt: 1.2s (2.8% of total)

ival-and: 1.2s (2.7% of total)

ival-exp: 1.1s (2.5% of total)

ival-floor: 1.1s (2.4% of total)

ival-cos: 1.0s (2.3% of total)

ival-pi: 769.0ms (1.8% of total)

ival-neg: 544.0ms (1.2% of total)

ival-fmax: 472.0ms (1.1% of total)

ival-==: 407.0ms (0.9% of total)

ival-tan: 382.0ms (0.9% of total)

...in/eval/compile.rkt:76:19: 271.0ms (0.6% of total)

ival-<: 256.0ms (0.6% of total)

ival-log2: 239.0ms (0.5% of total)

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

ival->: 181.0ms (0.4% of total)

ival-atan: 157.0ms (0.4% of total)

ival-assert: 116.0ms (0.3% of total)

ival-sinh: 86.0ms (0.2% of total)

ival->=: 60.0ms (0.1% of total)

adjust: 1.0ms (0% of total)

Bogosity

prune36.9s (7%)

Counts: 128504 → 3690
Compiler: Compiled 331898 to 124513 computations (62.5% saved)

localize31.6s (6%)

Results

12.2s	24948×	0	valid
2.8s	623×	5	exit
878.0ms	1458×	0	invalid
717.0ms	619×	1	valid

Compiler

Compiled 103565 to 5339 computations (94.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.8s

ival-mult: 3.6s (28.2% of total)

ival-div: 1.7s (13.1% of total)

ival-pow: 895.0ms (7% of total)

ival-add: 783.0ms (6.1% of total)

ival-pow2: 696.0ms (5.4% of total)

ival-sin: 556.0ms (4.3% of total)

ival-sqrt: 455.0ms (3.6% of total)

ival-hypot: 443.0ms (3.5% of total)

ival-sub: 384.0ms (3% of total)

ival-exp: 340.0ms (2.7% of total)

ival-log: 319.0ms (2.5% of total)

adjust: 280.0ms (2.2% of total)

ival-log1p: 272.0ms (2.1% of total)

...in/eval/compile.rkt:77:19: 266.0ms (2.1% of total)

ival-cbrt: 237.0ms (1.9% of total)

ival-tan: 231.0ms (1.8% of total)

ival-cos: 224.0ms (1.8% of total)

ival-fmax: 160.0ms (1.3% of total)

ival-log2: 153.0ms (1.2% of total)

ival-neg: 140.0ms (1.1% of total)

ival-if: 126.0ms (1% of total)

ival-floor: 115.0ms (0.9% of total)

ival-expm1: 104.0ms (0.8% of total)

ival-atan: 81.0ms (0.6% of total)

ival-pi: 61.0ms (0.5% of total)

...in/eval/compile.rkt:76:19: 38.0ms (0.3% of total)

ival-fabs: 35.0ms (0.3% of total)

ival->=: 27.0ms (0.2% of total)

ival-true: 27.0ms (0.2% of total)

ival->: 22.0ms (0.2% of total)

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

ival-sinh: 11.0ms (0.1% of total)

ival-<: 9.0ms (0.1% of total)

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

series31.5s (6%)

Counts

1797 → 53453

Calls

12897 calls:

Time	Variable		Point	Expression
413.0ms	h	@	inf	(* (log (fmax (pow (sqrt (+ (* (* dX.v (floor h)) (* dX.v (floor h))) (* (* dX.w (floor d)) (* dX.w (floor d))))) 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)
348.0ms	dX.v	@	0	(if (< (if (> (/ (fmax (+ (* (floor w) (* (* dX.u dX.u) (floor w))) (* dX.v (* dX.v (* (floor h) (floor h))))) (+ (* (floor w) (* (* dY.u dY.u) (floor w))) (* (* (floor h) (floor h)) (* dY.v dY.v)))) (fabs (* (floor w) (+ (* dY.v (* dX.u (floor h))) (* (* (floor h) (neg dX.v)) dY.u))))) (floor maxAniso)) (/ (sqrt (fmax (+ (* (floor w) (* (* dX.u dX.u) (floor w))) (* dX.v (* dX.v (* (floor h) (floor h))))) (+ (* (floor w) (* (* dY.u dY.u) (floor w))) (* (* (floor h) (floor h)) (* dY.v dY.v))))) (floor maxAniso)) (/ (fabs (* (floor w) (+ (* dY.v (* dX.u (floor h))) (* (* (floor h) (neg dX.v)) dY.u)))) (sqrt (fmax (+ (* (floor w) (* (* dX.u dX.u) (floor w))) (* dX.v (* dX.v (* (floor h) (floor h))))) (+ (* (floor w) (* (* dY.u dY.u) (floor w))) (* (* (floor h) (floor h)) (* dY.v dY.v))))))) 1) (fmax 1 (* (if (> (/ (fmax (pow (sqrt (+ (* (* (floor h) dX.v) (* (floor h) dX.v)) (* (* dX.u (floor w)) (* dX.u (floor w))))) 2) (pow (sqrt (+ (* (* dY.v (floor h)) (* dY.v (floor h))) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2)) (* (floor h) (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u))))) (floor maxAniso)) (/ (sqrt (fmax (pow (sqrt (+ (* (* (floor h) dX.v) (* (floor h) dX.v)) (* (* dX.u (floor w)) (* dX.u (floor w))))) 2) (pow (sqrt (+ (* (* dY.v (floor h)) (* dY.v (floor h))) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2))) (floor maxAniso)) (/ (* (floor h) (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u)))) (sqrt (fmax (pow (sqrt (+ (* (* (floor h) dX.v) (* (floor h) dX.v)) (* (* dX.u (floor w)) (* dX.u (floor w))))) 2) (pow (sqrt (+ (* (* dY.v (floor h)) (* dY.v (floor h))) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2))))) (if (> (/ (fmax (pow (sqrt (+ (* (* (floor h) dX.v) (* (floor h) dX.v)) (* (* dX.u (floor w)) (* dX.u (floor w))))) 2) (pow (sqrt (+ (* (* dY.v (floor h)) (* dY.v (floor h))) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2)) (* (floor h) (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u))))) (floor maxAniso)) (floor maxAniso) (/ (fmax (pow (sqrt (+ (* (* (floor h) dX.v) (* (floor h) dX.v)) (* (* dX.u (floor w)) (* dX.u (floor w))))) 2) (pow (sqrt (+ (* (* dY.v (floor h)) (* dY.v (floor h))) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2)) (* (floor h) (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u)))))))) (if (> (/ (fmax (+ (* (floor w) (* (* dX.u dX.u) (floor w))) (* dX.v (* dX.v (* (floor h) (floor h))))) (+ (* (floor w) (* (* dY.u dY.u) (floor w))) (* (* (floor h) (floor h)) (* dY.v dY.v)))) (fabs (* (floor w) (+ (* dY.v (* dX.u (floor h))) (* (* (floor h) (neg dX.v)) dY.u))))) (floor maxAniso)) (floor maxAniso) (/ (fmax (+ (* (floor w) (* (* dX.u dX.u) (floor w))) (* dX.v (* dX.v (* (floor h) (floor h))))) (+ (* (floor w) (* (* dY.u dY.u) (floor w))) (* (* (floor h) (floor h)) (* dY.v dY.v)))) (fabs (* (floor w) (+ (* dY.v (* dX.u (floor h))) (* (* (floor h) (neg dX.v)) dY.u)))))))
336.0ms	s	@	0	(* s (- (log (+ 1 (* u 4))) (log (+ 1 (* (pow u 2) -16)))))
334.0ms	dX.v	@	0	(if (>= (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (* (/ 1 (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (pow dX.v 2) (pow (floor h) 2))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))))) (* (floor w) dX.u)) (* (/ 1 (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))))) (* (floor w) dY.u)))
302.0ms	h	@	-inf	(log2 (if (> (/ (fmax (pow (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* dX.v (floor h)) (* dX.v (floor h))))) 2) (pow (sqrt (+ (* (* (floor h) dY.v) (* (floor h) dY.v)) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2)) (* (floor w) (* (floor h) (* dX.v (neg dY.u))))) (floor maxAniso)) (/ (sqrt (fmax (pow (sqrt (+ (* (* (floor h) dX.v) (* (floor h) dX.v)) (* (* dX.u (floor w)) (* dX.u (floor w))))) 2) (pow (sqrt (+ (* (* dY.v (floor h)) (* dY.v (floor h))) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2))) (floor maxAniso)) (* dX.u (* (sqrt (/ 1 (fmax (pow (sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* dX.v (floor h)) (* dX.v (floor h))))) 2) (pow (sqrt (+ (* (* (floor h) dY.v) (* (floor h) dY.v)) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2)))) (* (floor w) (* (floor h) dY.v))))))

rewrite27.3s (5.2%)

Algorithm

108×	batch-egg-rewrite

Rules

54398×	`log1p-expm1-u`
45555×	`expm1-log1p-u`
33503×	`pow1`
33076×	`log-prod`
32210×	`add-exp-log`

Stop Event

108×	node limit

Counts

1797 → 40346

eval25.0s (4.8%)

Compiler: Compiled 11858095 to 538073 computations (95.5% saved)

analyze24.8s (4.7%)

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
0%	0%	2.6%	97.4%	0%	0%	0%	2
0%	0%	2.6%	97.4%	0%	0%	0%	3
0.6%	0%	2.6%	97.4%	0%	0%	0%	4
16.9%	0.4%	2.2%	97.4%	0%	0%	0%	5
17.3%	0.5%	2.2%	97.4%	0%	0%	0%	6
30.4%	0.8%	1.8%	97.4%	0%	0%	0%	7
33.6%	0.9%	1.7%	97.4%	0%	0%	0%	8
41.4%	1.1%	1.5%	97.4%	0%	0%	0%	9
43.7%	1.2%	1.5%	97.4%	0%	0%	0%	10
47.2%	1.2%	1.4%	97.4%	0%	0%	0%	11
48.5%	1.3%	1.4%	97.4%	0%	0%	0%	12

Compiler

Compiled 2586 to 1076 computations (58.4% saved)

regimes24.1s (4.6%)

Counts

8214 → 360

Calls

131 calls:

757.0ms	u1
715.0ms	(floor.f32 w)
649.0ms	u
634.0ms	(floor.f32 h)
604.0ms	(.f32 (.f32 uy #s(literal 2 binary32)) (PI.f32))

Compiler

Compiled 13330 to 9270 computations (30.5% saved)

preprocess8.2s (1.6%)

Algorithm

27×	egg-herbie

Rules

27386×	`fma-define`
17798×	`fmm-def`
13540×	`distribute-lft-neg-in`
12704×	`unsub-neg`
11034×	`associate-r`

Stop Event

11×	saturated
16×	node limit

Compiler

Compiled 53258 to 14994 computations (71.8% saved)

explain7.7s (1.5%)

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f32`	`#f`	sensitivity	1017	81
`-.f32`	`#f`	cancellation	407	28
`sqrt.f32`	`#f`	oflow-rescue	312	0
`cos.f32`	`#f`	sensitivity	181	13
`tan.f32`	`(tan.f32 (+.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))`	cancellation	179	18
`/.f32`	`#f`	o/n	110	0
`exp.f32`	`#f`	sensitivity	25	16
`/.f32`	`#f`	o/o	6	0
`/.f32`	`#f`	u/n	3	0
`/.f32`	`(/.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))`	n/o	1	0
↳	`(/.f32 sin2phi (*.f32 alphay alphay))`	overflow	11
↳	`(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))`	overflow	11

Confusion

	Predicted +	Predicted -
+	1610	42
-	350	4910

Precision

0.8214285714285714

Recall

0.9745762711864406

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1610	30	12
-	350	112	4798

Precision?

0.780209324452902

Recall?

0.9927360774818402

Freqs

test

number	freq
0	4952
1	1685
2	269
3	6

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	17	1	2
-	4	1	2

Precision?

0.782608695652174

Recall?

0.9

Results

2.2s	13780×	0	valid
18.0ms	44×	1	valid

Compiler

Compiled 17450 to 2040 computations (88.3% saved)

Precisions

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

ival-mult: 491.0ms (36.8% of total)

ival-div: 174.0ms (13% of total)

ival-add: 76.0ms (5.7% of total)

ival-log: 73.0ms (5.5% of total)

ival-sin: 67.0ms (5% of total)

ival-sub: 64.0ms (4.8% of total)

ival-sqrt: 61.0ms (4.6% of total)

ival-cos: 45.0ms (3.4% of total)

ival-floor: 43.0ms (3.2% of total)

ival-exp: 42.0ms (3.1% of total)

ival-neg: 34.0ms (2.5% of total)

ival-pi: 21.0ms (1.6% of total)

ival-tan: 19.0ms (1.4% of total)

ival-fmax: 18.0ms (1.3% of total)

...in/eval/compile.rkt:77:19: 17.0ms (1.3% of total)

ival-log2: 16.0ms (1.2% of total)

ival-if: 14.0ms (1% of total)

ival-true: 14.0ms (1% of total)

ival-assert: 9.0ms (0.7% of total)

ival-fabs: 9.0ms (0.7% of total)

...in/eval/compile.rkt:76:19: 8.0ms (0.6% of total)

ival-atan: 7.0ms (0.5% of total)

ival-sinh: 5.0ms (0.4% of total)

ival->=: 4.0ms (0.3% of total)

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

adjust: 1.0ms (0.1% of total)

ival-<: 1.0ms (0.1% of total)

bsearch36.0ms (0%)

Algorithm

62×	binary-search
18×	left-value

Stop Event

62×	narrow-enough

Compiler

Compiled 3599 to 1823 computations (49.3% saved)

Herbie run

simplify2.5min (28%)

soundness1.5min (17.5%)

sample1.2min (13.2%)

prune36.9s (7%)

localize31.6s (6%)

series31.5s (6%)

rewrite27.3s (5.2%)

eval25.0s (4.8%)

analyze24.8s (4.7%)

regimes24.1s (4.6%)

preprocess8.2s (1.6%)

explain7.7s (1.5%)

bsearch36.0ms (0%)

end0.0ms (0%)

Profiling