Metrics for Herbie run

Date:	Thursday, May 23rd, 2024
Commit:	6b737c7e on explanations-trifurcate
Hostname:	nightly with Racket 8.11.1
Seed:	2024144
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

simplify2.4min (22.1%)

Algorithm

268×	egg-herbie

Rules

215708×	`fma-define`
120276×	`times-frac`
120022×	`distribute-lft-in`
118514×	`*-commutative`
113718×	`fma-neg`

Stop Event

65×	saturated
203×	node limit

Counts

102538 → 73426

soundness1.5min (14.3%)

Rules

107976×	`fma-define`
70784×	`times-frac`
69616×	`*-commutative`
65470×	`associate-r`
56456×	`distribute-lft-in`

Stop Event

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

Compiler

Compiled 62999 to 12855 computations (79.6% saved)

sample1.5min (14.2%)

Results

1.2min	247632×	0	valid
1.4s	8365×	0	invalid
703.0ms	2120×	0	precondition
9.0ms	48×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 59.2s

ival-mult: 12.7s (21.5% of total)

ival-<=: 11.3s (19.1% of total)

...c/correct-round.rkt:121:19: 9.7s (16.4% of total)

ival-div: 4.5s (7.5% of total)

ival-sub: 2.2s (3.7% of total)

ival-sin: 2.1s (3.6% of total)

ival-add: 2.0s (3.3% of total)

ival-fabs: 1.9s (3.1% of total)

ival-log: 1.7s (2.9% of total)

ival-sqrt: 1.7s (2.9% of total)

ival-and: 1.6s (2.7% of total)

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

ival-exp: 993.0ms (1.7% of total)

ival-floor: 927.0ms (1.6% of total)

ival-cos: 895.0ms (1.5% of total)

ival-pi: 805.0ms (1.4% of total)

const: 454.0ms (0.8% of total)

ival-tan: 433.0ms (0.7% of total)

ival-if: 405.0ms (0.7% of total)

ival-fmax: 326.0ms (0.6% of total)

ival-<: 291.0ms (0.5% of total)

ival->: 260.0ms (0.4% of total)

ival-log2: 255.0ms (0.4% of total)

ival-==: 175.0ms (0.3% of total)

ival-asin: 161.0ms (0.3% of total)

ival-atan: 118.0ms (0.2% of total)

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

ival->=: 79.0ms (0.1% of total)

backward-pass: 73.0ms (0.1% of total)

Bogosity

prune58.4s (9.1%)

Counts: 152282 → 4062
Compiler: Compiled 362196 to 132286 computations (63.5% saved)

end44.7s (6.9%)

localize44.0s (6.8%)

Results

18.8s	26010×	0	valid
7.4s	784×	5	exit
2.2s	1993×	0	invalid
1.0s	518×	1	valid
623.0ms	1159×	0	unsamplable

Compiler

Compiled 103174 to 5501 computations (94.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.1s

ival-mult: 4.4s (24.3% of total)

ival-div: 2.9s (16% of total)

ival-pow: 1.8s (9.9% of total)

ival-expm1: 1.6s (8.9% of total)

ival-add: 717.0ms (4% of total)

ival-log: 581.0ms (3.2% of total)

ival-sqrt: 573.0ms (3.2% of total)

ival-sin: 550.0ms (3% of total)

backward-pass: 529.0ms (2.9% of total)

...c/correct-round.rkt:121:19: 478.0ms (2.6% of total)

ival-tan: 409.0ms (2.3% of total)

ival-fma: 379.0ms (2.1% of total)

ival-cos: 375.0ms (2.1% of total)

ival-sub: 341.0ms (1.9% of total)

ival-log1p: 315.0ms (1.7% of total)

ival-exp: 312.0ms (1.7% of total)

ival-neg: 300.0ms (1.7% of total)

ival-hypot: 278.0ms (1.5% of total)

ival-fmax: 270.0ms (1.5% of total)

ival-atan: 171.0ms (0.9% of total)

ival-if: 147.0ms (0.8% of total)

ival-pi: 120.0ms (0.7% of total)

ival-floor: 102.0ms (0.6% of total)

const: 100.0ms (0.6% of total)

ival-log2: 92.0ms (0.5% of total)

ival-cbrt: 49.0ms (0.3% of total)

ival-asin: 48.0ms (0.3% of total)

ival->: 44.0ms (0.2% of total)

ival->=: 40.0ms (0.2% of total)

ival-fabs: 36.0ms (0.2% of total)

ival-<: 15.0ms (0.1% of total)

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

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

eval33.7s (5.2%)

Compiler: Compiled 17062972 to 625865 computations (96.3% saved)

rewrite32.4s (5%)

Algorithm

119×	batch-egg-rewrite

Rules

60454×	`log1p-expm1-u`
48868×	`expm1-log1p-u`
37013×	`pow1`
36414×	`log-prod`
35796×	`add-exp-log`

Stop Event

119×	node limit

Counts

2012 → 46024

analyze32.0s (5%)

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: 22.0s

ival-mult: 5.2s (23.5% of total)

ival-<=: 4.1s (18.6% of total)

...c/correct-round.rkt:121:19: 2.6s (11.8% of total)

ival-fabs: 1.7s (7.6% of total)

ival-div: 1.4s (6.5% of total)

ival-add: 1.2s (5.5% of total)

ival-floor: 713.0ms (3.2% of total)

ival-sqrt: 685.0ms (3.1% of total)

ival-and: 677.0ms (3.1% of total)

ival-fmax: 554.0ms (2.5% of total)

ival-sub: 464.0ms (2.1% of total)

ival-sin: 434.0ms (2% of total)

ival-if: 429.0ms (2% of total)

ival-==: 260.0ms (1.2% of total)

ival-cos: 229.0ms (1% of total)

ival-log2: 212.0ms (1% of total)

ival->: 196.0ms (0.9% of total)

ival-log: 185.0ms (0.8% of total)

const: 134.0ms (0.6% of total)

ival-<: 109.0ms (0.5% of total)

ival-tan: 104.0ms (0.5% of total)

ival-pi: 86.0ms (0.4% of total)

ival-exp: 85.0ms (0.4% of total)

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

ival-neg: 78.0ms (0.4% of total)

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

ival-sinh: 31.0ms (0.1% of total)

backward-pass: 23.0ms (0.1% of total)

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

regimes29.6s (4.6%)

Counts

9655 → 401

Calls

145 calls:

894.0ms	dY.u
801.0ms	ux
786.0ms	maxCos
756.0ms	s
752.0ms	uy

Compiler

Compiled 14799 to 10226 computations (30.9% saved)

series26.1s (4%)

Counts

2012 → 56514

Calls

14022 calls:

Time	Variable		Point	Expression
247.0ms	c	@	0	(sqrt (* c (+ 1 (+ (/ (pow (PI) -1/2) (* cosTheta c)) (- (/ 1 c) (/ (pow (PI) -1/2) c))))))
163.0ms	ux	@	-inf	(- 1 (* (+ (- 1 ux) (* ux maxCos)) (+ (- 1 ux) (* ux maxCos))))
159.0ms	dX.v	@	0	(if (>= (+ (* (floor w) (* (* dX.u dX.u) (floor w))) (* (floor h) (* (floor h) (* dX.v dX.v)))) (+ (* (floor h) (* dY.v (* (floor h) dY.v))) (* dY.u (* dY.u (* (floor w) (floor w)))))) (/ (* (floor h) dX.v) (sqrt (fmax (+ (* (floor w) (* (* dX.u dX.u) (floor w))) (* (floor h) (* (floor h) (* dX.v dX.v)))) (+ (* (floor h) (* dY.v (* (floor h) dY.v))) (* dY.u (* dY.u (* (floor w) (floor w)))))))) (/ (* (floor h) dY.v) (sqrt (fmax (+ (* (floor w) (* (* dX.u dX.u) (floor w))) (* (floor h) (* (floor h) (* dX.v dX.v)))) (+ (* (floor h) (* dY.v (* (floor h) dY.v))) (* dY.u (* dY.u (* (floor w) (floor w)))))))))
139.0ms	w	@	-inf	(* (log (fmax (+ (* (floor w) (* (floor w) (pow dX.u 2))) (pow (* (floor h) dX.v) 2)) (+ (* (floor w) (* (floor w) (pow dY.u 2))) (* (floor h) (* (floor h) (pow dY.v 2)))))) 1/2)
125.0ms	dY.u	@	inf	(log (+ 1 (log2 (sqrt (fmax (pow (* (floor w) dX.u) 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))))))

explain9.6s (1.5%)

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f32`	`#f`	sensitivity	993	68
`-.f32`	`#f`	cancellation	399	30
`sqrt.f32`	`#f`	oflow-rescue	395	0
`tan.f32`	`(tan.f32 (+.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))`	cancellation	182	16
`cos.f32`	`#f`	sensitivity	179	9
`/.f32`	`#f`	o/n	146	0
`exp.f32`	`#f`	sensitivity	39	22
`/.f32`	`#f`	u/n	29	0
`/.f32`	`#f`	o/o	18	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	12	0
↳	`(*.f32 sinTheta_O sinTheta_O)`	underflow	272
↳	`(-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O)))))`	underflow	12
↳	`(/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_O))))`	underflow	136
↳	`(*.f32 eta eta)`	underflow	12
`/.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	8	0
↳	`(/.f32 sin2phi (*.f32 alphay alphay))`	overflow	17
↳	`(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))`	overflow	17
`*.f32`	`#f`	*no**	3	0
`log.f32`	`(log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))`	oflow-rescue	1	0
↳	`(/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))`	overflow	1
`*.f32`	`(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*nu**	1	0
`*.f32`	`(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*uo**	1	0
↳	`(*.f32 u normAngle)`	underflow	2
↳	`(sin.f32 (*.f32 u normAngle))`	underflow	2
↳	`(/.f32 #s(literal 1 binary32) (sin.f32 normAngle))`	overflow	2

Confusion

	Predicted +	Predicted -
+	1669	63
-	398	5550

Precision

0.8074504112239961

Recall

0.9636258660508084

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1669	27	36
-	398	103	5447

Precision?

0.7719617660446063

Recall?

0.9792147806004619

Freqs

test

number	freq
0	5613
1	1747
2	301
3	19

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	23	1	1
-	2	1	2

Precision?

0.8888888888888888

Recall?

0.96

Results

3.9s	15286×	0	valid
39.0ms	74×	1	valid

Compiler

Compiled 18444 to 2196 computations (88.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.1s

ival-mult: 785.0ms (37.4% of total)

ival-div: 215.0ms (10.2% of total)

ival-floor: 205.0ms (9.8% of total)

ival-add: 154.0ms (7.3% of total)

ival-sqrt: 141.0ms (6.7% of total)

ival-log: 106.0ms (5% of total)

ival-sub: 89.0ms (4.2% of total)

ival-sin: 84.0ms (4% of total)

ival-cos: 46.0ms (2.2% of total)

ival-exp: 40.0ms (1.9% of total)

ival-neg: 31.0ms (1.5% of total)

const: 29.0ms (1.4% of total)

...c/correct-round.rkt:121:19: 27.0ms (1.3% of total)

ival-pi: 25.0ms (1.2% of total)

ival-tan: 20.0ms (1% of total)

ival-fmax: 19.0ms (0.9% of total)

ival-if: 18.0ms (0.9% of total)

ival-log2: 15.0ms (0.7% of total)

ival-fabs: 10.0ms (0.5% of total)

backward-pass: 8.0ms (0.4% of total)

ival-atan: 7.0ms (0.3% of total)

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

ival->=: 6.0ms (0.3% of total)

ival->: 5.0ms (0.2% of total)

ival-asin: 5.0ms (0.2% of total)

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

preprocess8.6s (1.3%)

Algorithm

30×	egg-herbie

Rules

30630×	`fma-define`
21782×	`fma-neg`
15892×	`unsub-neg`
14706×	`distribute-lft-neg-in`
11858×	`distribute-rgt-neg-in`

Stop Event

11×	saturated
19×	node limit

Compiler

Compiled 51400 to 15380 computations (70.1% saved)

bsearch38.0ms (0%)

Algorithm

70×	binary-search
12×	left-value

Stop Event

70×	narrow-enough

Compiler

Compiled 3881 to 1847 computations (52.4% saved)

simplify2.4min (22.1%)

soundness1.5min (14.3%)

sample1.5min (14.2%)

prune58.4s (9.1%)

end44.7s (6.9%)

localize44.0s (6.8%)

eval33.7s (5.2%)

rewrite32.4s (5%)

analyze32.0s (5%)

regimes29.6s (4.6%)

series26.1s (4%)

explain9.6s (1.5%)

preprocess8.6s (1.3%)

bsearch38.0ms (0%)

Profiling