Details

analyze797.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0%	0.1%	99.9%	1
0%	0.1%	99.9%	2
0%	0.1%	99.9%	3
0%	0%	99.9%	4
0%	0%	99.9%	5
0%	0%	99.9%	6
0.1%	0%	99.9%	7
0.1%	0%	99.9%	8
0.1%	0%	99.9%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample75.0ms (0.2%)

Algorithm

1×

intervals

Results

35.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 72 to 53 computations (26.4% saved)

simplify67.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-+l-_binary32`
416×	`associate-+r-_binary32`
386×	`associate--l-_binary32`
320×	`neg-mul-1_binary32`
316×	`distribute-rgt-in_binary32`

Counts

1 → 1

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	39
1	41	39
2	113	39
3	402	39
4	1502	36
5	4687	36
6	4944	36
7	5024	36

prune9.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.5b

Counts

2 → 2

Alt Table

Status	Error	Program
	13.5b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
▶	0.5b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))

Status

Error

Program

13.5b

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 1 (*.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))

▶

0.5b

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) PI.f32)) (sqrt.f32 (*.f32 (-.f32 ux (*.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))))

Compiler

Compiled 134 to 94 computations (29.9% saved)

localize62.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
0.2b	(.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))
0.3b	(.f32 (.f32 uy 2) PI.f32)
0.3b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))

rewrite265.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

13×	`*-un-lft-identity_binary32`
13×	`add-sqr-sqrt_binary32`
13×	`add-cbrt-cube_binary32`
13×	`add-log-exp_binary32`
13×	`add-exp-log_binary32`

Counts

4 → 90

Calls

4 calls:

15.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
12.0ms	(.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))
8.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
4.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 3166 to 1687 computations (46.7% saved)

series413.0ms (1.1%)

Error

0.3b

Counts

4 → 41

Calls

4 calls:

166.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
38.0ms	(.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))
27.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
10.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 3451 to 2407 computations (30.3% saved)

simplify154.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

484×	`associate-l_binary32`
418×	`associate-r_binary32`
400×	`cancel-sign-sub-inv_binary32`
294×	`times-frac_binary32`
275×	`*-commutative_binary32`

Counts

131 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	352	4993
1	928	4417
2	3619	4408
3	4754	4378
4	5251	4378

prune207.0ms (0.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	104	12	116
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Error

0.0b

Counts

118 → 12

Alt Table

Status	Error	Program
	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (.f32 (cbrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (cbrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))) (cbrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))
	0.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (.f32 (cbrt.f32 (-.f32 ux (.f32 ux maxCos))) (cbrt.f32 (-.f32 ux (.f32 ux maxCos)))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (cbrt.f32 (-.f32 ux (.f32 maxCos ux)))))))
	3.3b	(-.f32 (.f32 2 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 uy PI.f32))) (.f32 4/3 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (pow.f32 (.f32 uy PI.f32) 3))))
	1.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (exp.f32 (log.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.8b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)))) (.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
▶	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 maxCos ux) 3))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	1.4b	(.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32)))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))) (.f32 (sqrt.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32)))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (*.f32 maxCos ux))))))))
	1.1b	(.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))) (sqrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (*.f32 maxCos ux))))))))
	18.9b	(log.f32 (exp.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.8b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (.f32 (cbrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (cbrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (cbrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))

Compiler

Compiled 4182 to 2181 computations (47.8% saved)

localize89.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (*.f32 maxCos ux)))))
0.3b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
0.3b	(*.f32 uy PI.f32)
0.3b	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))))))

rewrite323.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

40×	`associate-*r/_binary32`
19×	`add-sqr-sqrt_binary32`
18×	`flip--_binary32`
18×	`sqrt-div_binary32`
18×	`flip3--_binary32`

Counts

4 → 119

Calls

4 calls:

17.0ms	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
13.0ms	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))))))
12.0ms	(.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (*.f32 maxCos ux)))))
3.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 5473 to 1702 computations (68.9% saved)

series712.0ms (1.8%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

254.0ms	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
229.0ms	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))))))
62.0ms	(.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (*.f32 maxCos ux)))))
14.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 8442 to 5954 computations (29.5% saved)

simplify172.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

574×	`*-commutative_binary32`
208×	`associate-+r+_binary32`
180×	`associate-/l*_binary32`
158×	`associate-+l+_binary32`
132×	`associate-*l/_binary32`

Counts

167 → 146

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	640	10448
1	1763	9558
2	5017	9558

prune334.0ms (0.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	145	13	158

Error

0.0b

Counts

158 → 13

Alt Table

Status	Error	Program
	1.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (exp.f32 (log.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (fabs.f32 (cbrt.f32 (+.f32 ux (.f32 maxCos ux))))) (/.f32 (sqrt.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (+.f32 (-.f32 2 ux) (.f32 maxCos ux)))) (sqrt.f32 (cbrt.f32 (+.f32 ux (.f32 maxCos ux))))))
	0.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (.f32 (cbrt.f32 (-.f32 ux (.f32 ux maxCos))) (cbrt.f32 (-.f32 ux (.f32 ux maxCos)))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (cbrt.f32 (-.f32 ux (.f32 maxCos ux)))))))
	3.3b	(-.f32 (.f32 2 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 uy PI.f32))) (.f32 4/3 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (pow.f32 (.f32 uy PI.f32) 3))))
	0.9b	(/.f32 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 (sqrt.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (+.f32 (-.f32 2 ux) (.f32 maxCos ux))))) (cbrt.f32 (sqrt.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (+.f32 (-.f32 2 ux) (.f32 maxCos ux))))))) (cbrt.f32 (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))
▶	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (/.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))) (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux)))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
	0.8b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)))) (.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
	1.9b	(/.f32 (.f32 (.f32 ux (sin.f32 (.f32 2 (.f32 uy PI.f32)))) (sqrt.f32 (-.f32 2 ux))) (sqrt.f32 (+.f32 ux (*.f32 maxCos ux))))
	1.7b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (exp.f32 (log.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (+.f32 (-.f32 2 ux) (.f32 maxCos ux))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
	0.7b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 (sqrt.f32 uy) (.f32 PI.f32 (sqrt.f32 uy))))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (+.f32 ux (.f32 ux maxCos))))
	18.9b	(log.f32 (exp.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.8b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (.f32 (cbrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (cbrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (cbrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))

Compiler

Compiled 7642 to 3458 computations (54.8% saved)

localize136.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))) (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (*.f32 maxCos ux))))))
0.3b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (/.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))) (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux)))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
0.3b	(*.f32 uy PI.f32)
0.3b	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (/.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))) (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux))))))))

rewrite374.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

22×	`add-sqr-sqrt_binary32`
22×	`add-cbrt-cube_binary32`
22×	`add-exp-log_binary32`
16×	`sqrt-prod_binary32`
16×	`*-un-lft-identity_binary32`

Counts

4 → 111

Calls

4 calls:

24.0ms	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (/.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))) (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux)))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
23.0ms	(/.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))) (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (*.f32 maxCos ux))))))
23.0ms	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (/.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))) (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
3.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 8759 to 3045 computations (65.2% saved)

series6.6s (16.9%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

2.4s	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (/.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))) (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux)))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
2.1s	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (/.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))) (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
596.0ms	(/.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))) (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (*.f32 maxCos ux))))))
15.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 41039 to 31715 computations (22.7% saved)

simplify432.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

405×	`associate-+r+_binary32`
349×	`associate-r_binary32`
309×	`associate-l_binary32`
133×	`associate-/r*_binary32`
99×	`associate-/l*_binary32`

Counts

159 → 136

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1994	35717
1	4969	35717

prune1.2s (3.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	137	12	149

Error

0.0b

Counts

149 → 12

Alt Table

Status	Error	Program
	1.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (exp.f32 (log.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (fabs.f32 (cbrt.f32 (+.f32 ux (.f32 maxCos ux))))) (/.f32 (sqrt.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (+.f32 (-.f32 2 ux) (.f32 maxCos ux)))) (sqrt.f32 (cbrt.f32 (+.f32 ux (.f32 maxCos ux))))))
	1.7b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (exp.f32 (log.f32 (/.f32 (.f32 (.f32 ux (-.f32 ux (.f32 (.f32 maxCos maxCos) ux))) (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))) (+.f32 4 (.f32 (-.f32 ux (.f32 maxCos ux)) (+.f32 (-.f32 ux (.f32 maxCos ux)) 2)))))))) (sqrt.f32 (+.f32 ux (.f32 ux maxCos))))
	1.9b	(/.f32 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) ux) (sqrt.f32 (/.f32 (-.f32 8 (pow.f32 ux 3)) (+.f32 (.f32 ux ux) (+.f32 4 (.f32 2 ux)))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
	0.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (.f32 (cbrt.f32 (-.f32 ux (.f32 ux maxCos))) (cbrt.f32 (-.f32 ux (.f32 ux maxCos)))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (cbrt.f32 (-.f32 ux (.f32 maxCos ux)))))))
	3.3b	(-.f32 (.f32 2 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 uy PI.f32))) (.f32 4/3 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (pow.f32 (.f32 uy PI.f32) 3))))
	0.9b	(/.f32 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 (sqrt.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (+.f32 (-.f32 2 ux) (.f32 maxCos ux))))) (cbrt.f32 (sqrt.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (+.f32 (-.f32 2 ux) (.f32 maxCos ux))))))) (cbrt.f32 (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
▶	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))
	0.8b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)))) (.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
	0.7b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 (sqrt.f32 uy) (.f32 PI.f32 (sqrt.f32 uy))))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (+.f32 ux (.f32 ux maxCos))))
	18.9b	(log.f32 (exp.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.8b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (.f32 (cbrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (cbrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (cbrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))

Compiler

Compiled 24413 to 14561 computations (40.4% saved)

localize228.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (*.f32 maxCos ux))))
0.3b	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))))
0.3b	(*.f32 uy PI.f32)
0.4b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))

rewrite1.4s (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

304×	`sqrt-div_binary32`
144×	`frac-times_binary32`
128×	`associate-*r/_binary32`
93×	`flip--_binary32`
93×	`flip3--_binary32`

Counts

4 → 193

Calls

4 calls:

74.0ms	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))))
65.0ms	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))
24.0ms	(.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (*.f32 maxCos ux))))
7.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 13734 to 5991 computations (56.4% saved)

series1.3s (3.3%)

Error

0.0b

Counts

4 → 47

Calls

4 calls:

537.0ms	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))))
286.0ms	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))
112.0ms	(.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (*.f32 maxCos ux))))
30.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 8718 to 6107 computations (29.9% saved)

simplify802.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

433×	`*-commutative_binary32`
243×	`distribute-rgt-in_binary32`
236×	`distribute-lft-in_binary32`
200×	`times-frac_binary32`
150×	`associate-l_binary32`

Counts

240 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	876	20667
1	2381	19865
2	4967	19775
3	4978	19775

prune1.3s (3.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	213	2	215
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	216	11	227

Error

0.0b

Counts

227 → 11

Alt Table

Status	Error	Program
	1.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (exp.f32 (log.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (fabs.f32 (cbrt.f32 (+.f32 ux (.f32 maxCos ux))))) (/.f32 (sqrt.f32 (.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux)))) (+.f32 (-.f32 2 ux) (.f32 maxCos ux)))) (sqrt.f32 (cbrt.f32 (+.f32 ux (.f32 maxCos ux))))))
	0.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (.f32 (cbrt.f32 (-.f32 ux (.f32 ux maxCos))) (cbrt.f32 (-.f32 ux (.f32 ux maxCos)))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (cbrt.f32 (-.f32 ux (.f32 maxCos ux)))))))
	3.3b	(-.f32 (.f32 2 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 uy PI.f32))) (.f32 4/3 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (pow.f32 (.f32 uy PI.f32) 3))))
✓	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))) (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))
	0.8b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)))) (.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
	0.7b	(/.f32 (.f32 (sqrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (+.f32 1 (+.f32 (.f32 maxCos ux) (-.f32 1 ux)))))) (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (.f32 (+.f32 (-.f32 2 ux) (.f32 maxCos ux)) (.f32 ux (-.f32 ux (.f32 (.f32 maxCos ux) maxCos)))))))) (sqrt.f32 (sqrt.f32 (+.f32 ux (*.f32 maxCos ux)))))
	1.7b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (exp.f32 (log.f32 (/.f32 (.f32 (.f32 ux (-.f32 ux (.f32 (.f32 maxCos maxCos) ux))) (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))) (+.f32 4 (.f32 (-.f32 ux (.f32 maxCos ux)) (+.f32 (-.f32 ux (.f32 maxCos ux)) 2)))))))) (sqrt.f32 (+.f32 ux (.f32 ux maxCos))))
	0.7b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 (sqrt.f32 uy) (.f32 PI.f32 (sqrt.f32 uy))))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (+.f32 ux (.f32 ux maxCos))))
	18.9b	(log.f32 (exp.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.7b	(/.f32 (.f32 (sqrt.f32 (sqrt.f32 (.f32 (+.f32 1 (+.f32 (.f32 maxCos ux) (-.f32 1 ux))) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 maxCos ux) 3))))) (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (.f32 (+.f32 (-.f32 2 ux) (.f32 maxCos ux)) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 maxCos ux) 3))))))) (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 (.f32 maxCos ux) (+.f32 ux (.f32 maxCos ux))))))

Compiler

Compiled 14443 to 7140 computations (50.6% saved)

regimes18.8s (48.2%)

Accuracy

Total 0.4b remaining (82.7%)

Threshold costs 0.4b (82.7%)

Compiler

Compiled 173800 to 108527 computations (37.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary32`
6×	`+-commutative_binary32`
5×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	41
1	37	41
2	47	41
3	53	41
4	57	41
5	58	41
6	57	41

end1.0ms (0%)

Compiler: Compiled 28 to 20 computations (28.6% saved)

sample2.7s (6.9%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
267.0ms	8000×	pre	128	true

Compiler

Compiled 552 to 344 computations (37.7% saved)

Details

analyze797.0ms (2%)

sample75.0ms (0.2%)

simplify67.0ms (0.2%)

prune9.0ms (0%)

localize62.0ms (0.2%)

rewrite265.0ms (0.7%)

series413.0ms (1.1%)

simplify154.0ms (0.4%)

prune207.0ms (0.5%)

localize89.0ms (0.2%)

rewrite323.0ms (0.8%)

series712.0ms (1.8%)

simplify172.0ms (0.4%)

prune334.0ms (0.9%)

localize136.0ms (0.4%)

rewrite374.0ms (1%)

series6.6s (16.9%)

simplify432.0ms (1.1%)

prune1.2s (3.1%)

localize228.0ms (0.6%)

rewrite1.4s (3.7%)

series1.3s (3.3%)

simplify802.0ms (2.1%)

prune1.3s (3.4%)

regimes18.8s (48.2%)

simplify5.0ms (0%)

end1.0ms (0%)

sample2.7s (6.9%)

Profiling