Metrics for Herbie run

Date:	Thursday, May 30th, 2024
Commit:	d3c34d85 on main
Hostname:	nightly with Racket 8.11.1
Seed:	2024151
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 (25.1%)

Algorithm

270×	egg-herbie

Rules

211492×	`fma-define`
118146×	`associate-r`
118116×	`*-commutative`
116842×	`distribute-lft-in`
112944×	`fmm-def`

Stop Event

70×	saturated
200×	node limit

Counts

100443 → 71523

sample1.6min (16.1%)

Results

1.2min	247629×	0	valid
1.5s	8174×	0	invalid
1.3s	2101×	0	precondition
10.0ms	51×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.0min

ival-mult: 13.1s (21.4% of total)

ival-<=: 10.1s (16.6% of total)

...c/correct-round.rkt:121:19: 9.2s (15.1% of total)

ival-div: 4.9s (8% of total)

ival-sub: 2.4s (3.9% of total)

ival-sin: 2.3s (3.7% of total)

ival-log: 2.1s (3.5% of total)

ival-add: 2.1s (3.5% of total)

ival-fabs: 2.1s (3.5% of total)

ival-sqrt: 1.9s (3.2% of total)

ival-and: 1.6s (2.6% of total)

ival-exp: 1.1s (1.8% of total)

ival-cos: 1.1s (1.8% of total)

ival-pi: 1.0s (1.7% of total)

ival-floor: 912.0ms (1.5% of total)

ival-fmax: 835.0ms (1.4% of total)

ival-neg: 661.0ms (1.1% of total)

ival-<: 551.0ms (0.9% of total)

ival-log2: 450.0ms (0.7% of total)

const: 448.0ms (0.7% of total)

ival-if: 382.0ms (0.6% of total)

ival-tan: 369.0ms (0.6% of total)

ival-asin: 314.0ms (0.5% of total)

ival->: 293.0ms (0.5% of total)

ival-==: 194.0ms (0.3% of total)

ival-sinh: 193.0ms (0.3% of total)

ival-atan: 119.0ms (0.2% of total)

ival->=: 95.0ms (0.2% of total)

backward-pass: 69.0ms (0.1% of total)

Bogosity

soundness1.5min (15%)

Rules

102328×	`fma-define`
67508×	`associate-r`
62338×	`*-commutative`
59560×	`times-frac`
54026×	`fmm-def`

Stop Event

8×	saturated
164×	node limit
29×	fuel
1×	done

Compiler

Compiled 58531 to 12386 computations (78.8% saved)

prune44.7s (7.6%)

Counts: 143910 → 4069
Compiler: Compiled 353138 to 130878 computations (62.9% saved)

localize42.5s (7.2%)

Results

18.8s	26734×	0	valid
5.6s	903×	5	exit
1.9s	1796×	0	invalid
1.1s	747×	1	valid
343.0ms	540×	0	unsamplable

Compiler

Compiled 130431 to 5690 computations (95.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.3s

ival-mult: 4.5s (27.3% of total)

ival-pow: 2.0s (12.3% of total)

ival-div: 1.9s (11.8% of total)

ival-add: 1.7s (10.3% of total)

ival-sqrt: 1.0s (6.2% of total)

ival-sin: 770.0ms (4.7% of total)

ival-log: 725.0ms (4.4% of total)

backward-pass: 539.0ms (3.3% of total)

ival-tan: 465.0ms (2.8% of total)

ival-sub: 447.0ms (2.7% of total)

ival-exp: 400.0ms (2.4% of total)

...c/correct-round.rkt:121:19: 277.0ms (1.7% of total)

ival-atan: 233.0ms (1.4% of total)

ival-neg: 201.0ms (1.2% of total)

ival-fmax: 167.0ms (1% of total)

ival-if: 151.0ms (0.9% of total)

ival-pi: 128.0ms (0.8% of total)

ival-cos: 128.0ms (0.8% of total)

const: 100.0ms (0.6% of total)

ival-floor: 94.0ms (0.6% of total)

ival-log2: 91.0ms (0.6% of total)

ival-cbrt: 81.0ms (0.5% of total)

ival-asin: 70.0ms (0.4% of total)

ival->=: 43.0ms (0.3% of total)

ival->: 41.0ms (0.3% of total)

ival-fabs: 39.0ms (0.2% of total)

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

ival-<: 13.0ms (0.1% of total)

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

analyze34.4s (5.8%)

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%	0%	6
69.5%	1.8%	0.8%	97.4%	0%	0%	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 2668 to 1046 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.2s

ival-mult: 5.5s (23.7% of total)

ival-<=: 4.0s (17.3% of total)

...c/correct-round.rkt:121:19: 2.4s (10.6% of total)

ival-fabs: 1.8s (7.9% of total)

ival-div: 1.8s (7.9% of total)

ival-add: 951.0ms (4.1% of total)

ival-floor: 839.0ms (3.6% of total)

ival-sin: 717.0ms (3.1% of total)

ival-sqrt: 673.0ms (2.9% of total)

ival-fmax: 668.0ms (2.9% of total)

ival-and: 665.0ms (2.9% of total)

ival-sub: 525.0ms (2.3% of total)

ival-==: 405.0ms (1.7% of total)

ival-if: 385.0ms (1.7% of total)

ival-log: 321.0ms (1.4% of total)

ival-cos: 247.0ms (1.1% of total)

ival->: 202.0ms (0.9% of total)

ival-log2: 173.0ms (0.7% of total)

const: 132.0ms (0.6% of total)

ival-exp: 131.0ms (0.6% of total)

ival-tan: 113.0ms (0.5% of total)

ival-neg: 90.0ms (0.4% of total)

ival->=: 84.0ms (0.4% of total)

ival-pi: 75.0ms (0.3% of total)

ival-<: 63.0ms (0.3% of total)

ival-atan: 38.0ms (0.2% of total)

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

backward-pass: 20.0ms (0.1% of total)

ival-asin: 17.0ms (0.1% of total)

rewrite30.9s (5.2%)

Algorithm

120×	batch-egg-rewrite

Rules

65897×	`log1p-expm1-u`
51393×	`expm1-log1p-u`
37041×	`pow1`
35764×	`log-prod`
35276×	`add-exp-log`

Stop Event

120×	node limit

Counts

1945 → 43714

series30.3s (5.1%)

Counts

1945 → 56729

Calls

13830 calls:

Time	Variable		Point	Expression
333.0ms	w	@	-inf	(log (+ 1 (log2 (sqrt (fmax (pow (* dX.w (floor d)) 2) (pow (sqrt (+ (* (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor d) dY.w) (* (floor d) dY.w)))) (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor d) dY.w) (* (floor d) dY.w))))) (* (* (floor h) dY.v) (* (floor h) dY.v)))) 2))))))
318.0ms	dY.u	@	-inf	(log (+ 1 (log2 (if (> (/ (fmax (pow (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v)))) 2) (pow (sqrt (+ (* (* (floor h) dY.v) (* (floor h) dY.v)) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2)) (fabs (* (* (floor w) (floor h)) (- (* dX.u dY.v) (* dX.v dY.u))))) (floor maxAniso)) (/ (sqrt (fmax (pow (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v)))) 2) (pow (sqrt (+ (* (* (floor h) dY.v) (* (floor h) dY.v)) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2))) (floor maxAniso)) (/ (fabs (* (* (floor w) (floor h)) (- (* dX.u dY.v) (* dX.v dY.u)))) (sqrt (fmax (pow (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v)))) 2) (pow (sqrt (+ (* (* (floor h) dY.v) (* (floor h) dY.v)) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2))))))))
303.0ms	uy	@	inf	(log (* yi (sin (* (* uy 2) (PI)))))
286.0ms	r	@	inf	(* (/ 1/8 (* s (PI))) (+ (/ (exp (/ r (neg s))) r) (/ (sqrt 1) r)))
284.0ms	d	@	0	(log (log2 (sqrt (fmax (pow (sqrt (+ (* (* dX.w (floor d)) (* dX.w (floor d))) (* (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)))))))) 2) (pow (sqrt (+ (* (* (floor d) dY.w) (* (floor d) dY.w)) (* (* (floor w) dY.u) (* (floor w) dY.u)))) 2)))))

eval29.8s (5%)

Compiler: Compiled 13668995 to 597743 computations (95.6% saved)

regimes28.8s (4.9%)

Counts

9900 → 392

Calls

145 calls:

912.0ms	s
811.0ms	cosTheta_i
677.0ms	dY.u
674.0ms	dX.v
672.0ms	u2

Compiler

Compiled 14153 to 9708 computations (31.4% saved)

explain9.2s (1.6%)

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f32`	`#f`	sensitivity	1019	87
`-.f32`	`#f`	cancellation	397	39
`sqrt.f32`	`#f`	oflow-rescue	372	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	187	14
`tan.f32`	`(tan.f32 (+.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))`	cancellation	174	20
`/.f32`	`#f`	o/n	134	0
`exp.f32`	`#f`	sensitivity	31	15
`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	16	0
↳	`(*.f32 sinTheta_O sinTheta_O)`	underflow	292
↳	`(-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O)))))`	underflow	16
↳	`(/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_O))))`	underflow	146
↳	`(*.f32 eta eta)`	underflow	16
`/.f32`	`#f`	u/n	16	0
`/.f32`	`#f`	o/o	12	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	6	0
↳	`(/.f32 sin2phi (*.f32 alphay alphay))`	overflow	12
↳	`(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))`	overflow	12
`sin.f32`	`#f`	cancellation	4	2
`*.f32`	`(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*nu**	1	0

Confusion

	Predicted +	Predicted -
+	1662	61
-	390	5567

Precision

0.8099415204678363

Recall

0.9645966337782936

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1662	40	21
-	390	119	5448

Precision?

0.7697874265038445

Recall?

0.987811955890888

Freqs

test

number	freq
0	5628
1	1747
2	293
3	12

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	21	1	0
-	6	0	2

Precision?

0.7857142857142857

Recall?

1.0

Results

3.5s	15294×	0	valid
38.0ms	66×	1	valid

Compiler

Compiled 18444 to 2196 computations (88.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.7s

ival-mult: 612.0ms (35.7% of total)

ival-div: 232.0ms (13.5% of total)

ival-exp: 99.0ms (5.8% of total)

ival-sub: 95.0ms (5.5% of total)

ival-add: 92.0ms (5.4% of total)

ival-log: 92.0ms (5.4% of total)

ival-sin: 77.0ms (4.5% of total)

ival-sqrt: 73.0ms (4.3% of total)

ival-floor: 50.0ms (2.9% of total)

ival-cos: 46.0ms (2.7% of total)

ival-neg: 37.0ms (2.2% of total)

const: 29.0ms (1.7% of total)

ival-pi: 27.0ms (1.6% of total)

...c/correct-round.rkt:121:19: 27.0ms (1.6% of total)

ival-fmax: 19.0ms (1.1% of total)

ival-tan: 19.0ms (1.1% of total)

ival-if: 17.0ms (1% of total)

ival-log2: 16.0ms (0.9% of total)

ival-fabs: 10.0ms (0.6% of total)

ival-atan: 9.0ms (0.5% of total)

ival-sinh: 8.0ms (0.5% of total)

backward-pass: 7.0ms (0.4% of total)

ival->=: 7.0ms (0.4% of total)

ival->: 6.0ms (0.4% of total)

ival-asin: 6.0ms (0.4% of total)

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

preprocess9.1s (1.5%)

Algorithm

30×	egg-herbie

Rules

30620×	`fma-define`
21784×	`fmm-def`
14698×	`distribute-lft-neg-in`
14266×	`unsub-neg`
11858×	`distribute-rgt-neg-in`

Stop Event

11×	saturated
19×	node limit

Compiler

Compiled 50156 to 16198 computations (67.7% saved)

bsearch40.0ms (0%)

Algorithm

50×	binary-search
21×	left-value

Stop Event

50×	narrow-enough

Compiler

Compiled 3587 to 1648 computations (54.1% saved)

Herbie run

simplify2.5min (25.1%)

sample1.6min (16.1%)

soundness1.5min (15%)

prune44.7s (7.6%)

localize42.5s (7.2%)

analyze34.4s (5.8%)

rewrite30.9s (5.2%)

series30.3s (5.1%)

eval29.8s (5%)

regimes28.8s (4.9%)

explain9.2s (1.6%)

preprocess9.1s (1.5%)

bsearch40.0ms (0%)

end0.0ms (0%)

Profiling