Metrics for Herbie run

Date:	Saturday, May 25th, 2024
Commit:	445b0ec4 on explanations-trifurcate
Hostname:	nightly with Racket 8.11.1
Seed:	2024146
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

simplify2.3min (21.7%)

Algorithm

269×	egg-herbie

Rules

219120×	`fma-define`
126414×	`distribute-lft-in`
123980×	`times-frac`
111072×	`*-commutative`
110556×	`associate-r`

Stop Event

64×	saturated
205×	node limit

Counts

102349 → 73867

sample1.6min (14.8%)

Results

1.2min	247610×	0	valid
1.5s	8313×	0	invalid
960.0ms	2058×	0	precondition
12.0ms	70×	1	valid

Precisions

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

ival-mult: 12.0s (19.6% of total)

ival-<=: 10.6s (17.4% of total)

...c/correct-round.rkt:121:19: 9.3s (15.3% of total)

ival-div: 4.9s (8.1% of total)

ival-sub: 3.1s (5.1% of total)

ival-add: 2.2s (3.6% of total)

ival-sin: 2.2s (3.5% of total)

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

ival-fabs: 2.0s (3.4% of total)

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

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

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

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

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

ival-pi: 839.0ms (1.4% of total)

ival-floor: 798.0ms (1.3% of total)

ival-fmax: 562.0ms (0.9% of total)

ival-if: 542.0ms (0.9% of total)

const: 446.0ms (0.7% of total)

ival-<: 327.0ms (0.5% of total)

ival-tan: 297.0ms (0.5% of total)

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

ival-log2: 247.0ms (0.4% of total)

ival-asin: 227.0ms (0.4% of total)

ival-atan: 184.0ms (0.3% of total)

ival-==: 157.0ms (0.3% of total)

ival-sinh: 98.0ms (0.2% of total)

ival->=: 82.0ms (0.1% of total)

backward-pass: 70.0ms (0.1% of total)

Bogosity

soundness1.4min (12.9%)

Rules

96496×	`fma-define`
64882×	`times-frac`
63982×	`associate-r`
62260×	`*-commutative`
54036×	`distribute-lft-in`

Stop Event

7×	saturated
161×	node limit
30×	fuel

Compiler

Compiled 51109 to 11530 computations (77.4% saved)

prune1.3min (12.2%)

Counts: 140272 → 4016
Compiler: Compiled 336663 to 130124 computations (61.3% saved)

localize38.6s (6%)

Results

18.3s	26309×	0	valid
1.7s	1986×	0	invalid
1.2s	661×	1	valid
1.1s	238×	5	exit
889.0ms	1524×	0	unsamplable
6.0ms	2×	3	valid

Compiler

Compiled 102610 to 5487 computations (94.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0s

ival-mult: 4.2s (32% of total)

ival-div: 1.9s (14.2% of total)

ival-pow: 1.1s (8.6% of total)

ival-add: 690.0ms (5.3% of total)

ival-sqrt: 611.0ms (4.7% of total)

ival-sub: 440.0ms (3.4% of total)

ival-exp: 392.0ms (3% of total)

ival-log: 371.0ms (2.9% of total)

ival-sin: 341.0ms (2.6% of total)

ival-fma: 326.0ms (2.5% of total)

ival-hypot: 325.0ms (2.5% of total)

...c/correct-round.rkt:121:19: 269.0ms (2.1% of total)

ival-log1p: 268.0ms (2.1% of total)

ival-neg: 222.0ms (1.7% of total)

ival-cbrt: 199.0ms (1.5% of total)

ival-fmax: 197.0ms (1.5% of total)

backward-pass: 159.0ms (1.2% of total)

ival-fabs: 148.0ms (1.1% of total)

ival-if: 145.0ms (1.1% of total)

ival-cos: 121.0ms (0.9% of total)

ival-floor: 98.0ms (0.8% of total)

ival-log2: 98.0ms (0.8% of total)

const: 93.0ms (0.7% of total)

ival-pi: 75.0ms (0.6% of total)

ival-expm1: 60.0ms (0.5% of total)

ival-tan: 60.0ms (0.5% of total)

ival-asin: 44.0ms (0.3% of total)

ival->=: 44.0ms (0.3% of total)

ival->: 36.0ms (0.3% of total)

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

ival-sinh: 12.0ms (0.1% of total)

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

ival-e: 8.0ms (0.1% of total)

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

end36.1s (5.6%)

analyze34.9s (5.4%)

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: 23.1s

ival-mult: 5.7s (24.8% of total)

ival-<=: 4.3s (18.7% of total)

...c/correct-round.rkt:121:19: 2.8s (12% of total)

ival-fabs: 1.9s (8.1% of total)

ival-div: 1.1s (4.7% of total)

ival-floor: 790.0ms (3.4% of total)

ival-if: 786.0ms (3.4% of total)

ival-fmax: 767.0ms (3.3% of total)

ival-add: 751.0ms (3.2% of total)

ival-and: 667.0ms (2.9% of total)

ival-sqrt: 620.0ms (2.7% of total)

ival-sub: 505.0ms (2.2% of total)

ival-log: 411.0ms (1.8% of total)

ival-sin: 375.0ms (1.6% of total)

ival-==: 289.0ms (1.2% of total)

ival-cos: 284.0ms (1.2% of total)

ival-log2: 191.0ms (0.8% of total)

const: 130.0ms (0.6% of total)

ival->: 126.0ms (0.5% of total)

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

ival-pi: 100.0ms (0.4% of total)

ival-neg: 88.0ms (0.4% of total)

ival-exp: 83.0ms (0.4% of total)

ival->=: 81.0ms (0.3% of total)

ival-<: 67.0ms (0.3% of total)

ival-atan: 41.0ms (0.2% of total)

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

backward-pass: 22.0ms (0.1% of total)

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

rewrite33.2s (5.2%)

Algorithm

119×	batch-egg-rewrite

Rules

61948×	`log1p-expm1-u`
50233×	`expm1-log1p-u`
36557×	`pow1`
35362×	`add-exp-log`
35154×	`log-prod`

Stop Event

119×	node limit

Counts

2000 → 46442

series31.8s (5%)

Counts

2000 → 55907

Calls

13725 calls:

Time	Variable		Point	Expression
466.0ms	w	@	inf	(pow (fmax (pow (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v)))) 2) (pow (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) 2)) -1/4)
410.0ms	dX.v	@	inf	(pow (fmax (pow (sqrt (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v)))) 2) (pow (sqrt (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) 2)) -1/4)
389.0ms	h	@	-inf	(if (< (if (> (/ (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)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (/ (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 maxAniso)) (/ (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))) (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))))))) 1) (fmax 1 (* (if (> (/ (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)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (floor maxAniso) (/ (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)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))))) (if (> (/ (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)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (/ (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 maxAniso)) (/ (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))) (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))))))))) (if (> (/ (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)))) (fabs (* (floor h) (* (floor w) (* dX.v (neg dY.u)))))) (floor maxAniso)) (floor maxAniso) (/ (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)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))))))
367.0ms	w	@	inf	(sqrt (+ (* (* dX.u (floor w)) (* dX.u (floor w))) (* (* dX.v (floor h)) (* dX.v (floor h)))))
357.0ms	u1	@	0	(* (log u1) 1/2)

eval28.3s (4.4%)

Compiler: Compiled 14221927 to 580581 computations (95.9% saved)

regimes24.0s (3.7%)

Counts

8574 → 384

Calls

145 calls:

814.0ms	dX.v
798.0ms	cosTheta_i
651.0ms	dY.v
544.0ms	u2
532.0ms	u0

Compiler

Compiled 13566 to 9335 computations (31.2% saved)

explain9.6s (1.5%)

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f32`	`#f`	sensitivity	1031	77
`-.f32`	`#f`	cancellation	394	24
`sqrt.f32`	`#f`	oflow-rescue	333	0
`cos.f32`	`#f`	sensitivity	204	7
`tan.f32`	`(tan.f32 (+.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) u1) (*.f32 #s(literal 1/2 binary32) (PI.f32))))`	cancellation	192	19
`/.f32`	`#f`	o/n	110	0
`exp.f32`	`#f`	sensitivity	32	29
`/.f32`	`#f`	u/n	27	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	20	0
↳	`(*.f32 sinTheta_O sinTheta_O)`	underflow	280
↳	`(-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_O)))))`	underflow	20
↳	`(/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_O))))`	underflow	140
↳	`(*.f32 eta eta)`	underflow	20
`/.f32`	`#f`	o/o	6	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	15
↳	`(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))`	overflow	15
`*.f32`	`(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 #s(literal 1 binary32) (sin.f32 normAngle)))`	*nu**	2	0
`sin.f32`	`(sin.f32 (.f32 (.f32 uy #s(literal 2 binary32)) (PI.f32)))`	cancellation	1	0

Confusion

	Predicted +	Predicted -
+	1665	57
-	387	5571

Precision

0.8114035087719298

Recall

0.9668989547038328

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1665	30	27
-	387	102	5469

Precision?

0.7760989010989011

Recall?

0.9843205574912892

Freqs

test

number	freq
0	5628
1	1752
2	294
3	6

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	20	1	1
-	5	0	3

Precision?

0.8076923076923077

Recall?

0.9545454545454546

Results

3.7s	15318×	0	valid
22.0ms	42×	1	valid

Compiler

Compiled 18444 to 2196 computations (88.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0s

ival-mult: 650.0ms (32.1% of total)

ival-div: 246.0ms (12.2% of total)

ival-floor: 230.0ms (11.4% of total)

ival-sub: 157.0ms (7.8% of total)

ival-sin: 128.0ms (6.3% of total)

ival-add: 123.0ms (6.1% of total)

ival-log: 89.0ms (4.4% of total)

ival-sqrt: 81.0ms (4% of total)

ival-exp: 44.0ms (2.2% of total)

ival-cos: 43.0ms (2.1% of total)

ival-neg: 30.0ms (1.5% of total)

const: 29.0ms (1.4% of total)

...c/correct-round.rkt:121:19: 29.0ms (1.4% of total)

ival-pi: 28.0ms (1.4% of total)

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

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

ival-if: 16.0ms (0.8% of total)

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

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

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

backward-pass: 6.0ms (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)

preprocess9.2s (1.4%)

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 46096 to 17158 computations (62.8% saved)

bsearch38.0ms (0%)

Algorithm

50×	binary-search
33×	left-value

Stop Event

50×	narrow-enough

Compiler

Compiled 4084 to 1846 computations (54.8% saved)

simplify2.3min (21.7%)

sample1.6min (14.8%)

soundness1.4min (12.9%)

prune1.3min (12.2%)

localize38.6s (6%)

end36.1s (5.6%)

analyze34.9s (5.4%)

rewrite33.2s (5.2%)

series31.8s (5%)

eval28.3s (4.4%)

regimes24.0s (3.7%)

explain9.6s (1.5%)

preprocess9.2s (1.4%)

bsearch38.0ms (0%)

Profiling