Details

analyze794.0ms (5.1%)

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)

sample63.0ms (0.4%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 72 to 53 computations (26.4% saved)

simplify123.0ms (0.8%)

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 (0.1%)

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

0.3b

Counts

2 → 2

Alt Table

Status	Error	Program
	13.2b	(.f32 (cos.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))))))
▶	0.4b	(.f32 (cos.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

13.2b

(*.f32 (cos.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))))))

▶

0.4b

(*.f32 (cos.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)

localize67.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.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))
0.2b	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
0.3b	(.f32 (.f32 uy 2) PI.f32)

rewrite312.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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:

14.0ms	(.f32 (cos.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)

series299.0ms (1.9%)

Error

0.2b

Counts

4 → 41

Calls

4 calls:

144.0ms	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
37.0ms	(.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))
26.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
10.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 3403 to 2378 computations (30.1% saved)

simplify141.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

440×	`cancel-sign-sub-inv_binary32`
429×	`associate-l_binary32`
373×	`associate-r_binary32`
245×	`*-commutative_binary32`
218×	`distribute-rgt-neg-in_binary32`

Counts

131 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	322	4439
1	871	3887
2	3414	3878
3	4928	3878
4	4977	3878

prune252.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	92	9	101
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	9	103

Error

0.1b

Counts

103 → 9

Alt Table

Status	Error	Program
	0.8b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))) (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))))) (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))
	5.8b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	2.6b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	13.0b	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (log.f32 (exp.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
▶	0.4b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))))))
	0.5b	(/.f32 (.f32 (cos.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))))
	2.1b	(-.f32 (+.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 2/3 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 (pow.f32 uy 4) (pow.f32 PI.f32 4))))) (+.f32 (.f32 2 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 (.f32 uy uy) (pow.f32 PI.f32 2)))) (.f32 4/45 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 (pow.f32 uy 6) (pow.f32 PI.f32 6))))))
	0.5b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))

Compiler

Compiled 3847 to 2033 computations (47.2% saved)

localize80.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))
0.2b	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
0.3b	(.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))
0.5b	(.f32 (.f32 2 uy) (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)))

rewrite248.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

36×	`add-exp-log_binary32`
36×	`pow1_binary32`
23×	`add-cbrt-cube_binary32`
22×	`cbrt-unprod_binary32`
22×	`prod-exp_binary32`

Counts

4 → 97

Calls

4 calls:

12.0ms	(.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))
11.0ms	(.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))
10.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
8.0ms	(.f32 (.f32 2 uy) (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)))

Compiler

Compiled 3481 to 1599 computations (54.1% saved)

series127.0ms (0.8%)

Error

0.1b

Counts

4 → 29

Calls

4 calls:

42.0ms	(.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))
30.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
22.0ms	(.f32 (.f32 2 uy) (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)))
10.0ms	(.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))

Compiler

Compiled 1925 to 1272 computations (33.9% saved)

simplify128.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

349×	`associate-l_binary32`
319×	`associate-+l+_binary32`
278×	`associate-+r+_binary32`
272×	`associate-r_binary32`
243×	`+-commutative_binary32`

Counts

126 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	2666
1	536	2201
2	2265	2077
3	4342	2077
4	4962	2077
5	4944	2077

prune199.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	98	10	108

Error

0.1b

Counts

108 → 10

Alt Table

Status	Error	Program
	0.8b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))) (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))))) (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))
	5.8b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	2.6b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	13.0b	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (log.f32 (exp.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	13.1b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (log.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (-.f32 ux (*.f32 maxCos ux))))))
✓	0.4b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
▶	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))))))
	0.5b	(/.f32 (.f32 (cos.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))))
	2.1b	(-.f32 (+.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 2/3 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 (pow.f32 uy 4) (pow.f32 PI.f32 4))))) (+.f32 (.f32 2 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 (.f32 uy uy) (pow.f32 PI.f32 2)))) (.f32 4/45 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 (pow.f32 uy 6) (pow.f32 PI.f32 6))))))
	0.5b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))

Compiler

Compiled 2801 to 1417 computations (49.4% saved)

localize81.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))))))
0.3b	(.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (*.f32 maxCos ux))))
0.3b	(.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (*.f32 maxCos ux)))))
0.3b	(.f32 (.f32 uy 2) PI.f32)

rewrite359.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

104×	`sqrt-div_binary32`
60×	`flip--_binary32`
60×	`frac-times_binary32`
60×	`flip3--_binary32`
56×	`associate-*r/_binary32`

Counts

4 → 143

Calls

4 calls:

20.0ms	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))))))
15.0ms	(.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (*.f32 maxCos ux)))))
10.0ms	(.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (*.f32 maxCos ux))))
4.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 7079 to 2405 computations (66% saved)

series296.0ms (1.9%)

Error

0.1b

Counts

4 → 38

Calls

4 calls:

149.0ms	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))))))
45.0ms	(.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (*.f32 maxCos ux))))
38.0ms	(.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (*.f32 maxCos ux)))))
11.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 3805 to 2667 computations (29.9% saved)

simplify206.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

556×	`cancel-sign-sub-inv_binary32`
527×	`associate-l_binary32`
519×	`associate-r_binary32`
340×	`*-commutative_binary32`
192×	`sub-neg_binary32`

Counts

181 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	469	8388
1	1114	7242
2	3872	6914
3	5087	6914

prune327.0ms (2.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	161	11	172

Error

0.1b

Counts

172 → 11

Alt Table

Status	Error	Program
	13.1b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (log.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (-.f32 ux (*.f32 maxCos ux))))))
	4.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (log.f32 (exp.f32 (.f32 (+.f32 (.f32 maxCos ux) (-.f32 2 ux)) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))))))))
	0.8b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))) (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))))) (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))
	5.8b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	13.0b	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (log.f32 (exp.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
✓	0.4b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
✓	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))))))
	0.5b	(/.f32 (.f32 (cos.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))))
	2.1b	(-.f32 (+.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 2/3 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 (pow.f32 uy 4) (pow.f32 PI.f32 4))))) (+.f32 (.f32 2 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 (.f32 uy uy) (pow.f32 PI.f32 2)))) (.f32 4/45 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 (pow.f32 uy 6) (pow.f32 PI.f32 6))))))
▶	0.5b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
	0.6b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 maxCos ux) 3))) (.f32 (sqrt.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))) (-.f32 4 (pow.f32 (sqrt.f32 (-.f32 ux (.f32 maxCos ux))) 4)))))) (sqrt.f32 (.f32 (sqrt.f32 (+.f32 ux (.f32 ux maxCos))) (.f32 (+.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 maxCos ux) (.f32 maxCos ux)) (.f32 ux (.f32 maxCos ux)))))))))

Compiler

Compiled 6967 to 3002 computations (56.9% saved)

localize78.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(cos.f32 (.f32 2 (.f32 uy PI.f32)))
0.2b	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
0.3b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
0.3b	(*.f32 uy PI.f32)

rewrite188.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`add-log-exp_binary32`
12×	`sqrt-div_binary32`
12×	`*-un-lft-identity_binary32`
11×	`add-cbrt-cube_binary32`
11×	`add-exp-log_binary32`

Counts

4 → 72

Calls

4 calls:

14.0ms	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
7.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
4.0ms	(cos.f32 (.f32 2 (.f32 uy PI.f32)))
3.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 2424 to 1215 computations (49.9% saved)

series208.0ms (1.3%)

Error

0.1b

Counts

4 → 36

Calls

4 calls:

106.0ms	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
27.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
15.0ms	(cos.f32 (.f32 2 (.f32 uy PI.f32)))
10.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 3162 to 2153 computations (31.9% saved)

simplify101.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

695×	`distribute-rgt-in_binary32`
484×	`cancel-sign-sub-inv_binary32`
337×	`associate-l_binary32`
305×	`associate-r_binary32`
240×	`distribute-rgt-neg-in_binary32`

Counts

108 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	291	3667
1	765	3254
2	2624	3058
3	5254	3058

prune200.0ms (1.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	72	11	83

Error

0.1b

Counts

83 → 11

Alt Table

Status	Error	Program
	13.1b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (log.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (-.f32 ux (*.f32 maxCos ux))))))
	4.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (log.f32 (exp.f32 (.f32 (+.f32 (.f32 maxCos ux) (-.f32 2 ux)) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))))))))
	0.8b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))) (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))))) (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))
	5.8b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	13.0b	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (log.f32 (exp.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.4b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))))))
	0.5b	(/.f32 (.f32 (cos.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))))
	2.1b	(-.f32 (+.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 2/3 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 (pow.f32 uy 4) (pow.f32 PI.f32 4))))) (+.f32 (.f32 2 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 (.f32 uy uy) (pow.f32 PI.f32 2)))) (.f32 4/45 (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (.f32 (pow.f32 uy 6) (pow.f32 PI.f32 6))))))
	0.5b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
	0.6b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 maxCos ux) 3))) (.f32 (sqrt.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))) (-.f32 4 (pow.f32 (sqrt.f32 (-.f32 ux (.f32 maxCos ux))) 4)))))) (sqrt.f32 (.f32 (sqrt.f32 (+.f32 ux (.f32 ux maxCos))) (.f32 (+.f32 2 (-.f32 ux (.f32 maxCos ux))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 maxCos ux) (.f32 maxCos ux)) (.f32 ux (.f32 maxCos ux)))))))))

Compiler

Compiled 2615 to 1402 computations (46.4% saved)

regimes8.1s (52%)

Accuracy

Total 0.2b remaining (74.6%)

Threshold costs 0.2b (74.6%)

Compiler

Compiled 144254 to 90553 computations (37.2% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary32`
13×	`+-commutative_binary32`
10×	`sub-neg_binary32`
9×	`neg-sub0_binary32`
9×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	57
1	37	57
2	46	57
3	58	57
4	81	57
5	97	57
6	107	57
7	113	57
8	115	57
9	114	57

end2.0ms (0%)

Compiler: Compiled 40 to 31 computations (22.5% saved)

sample2.6s (16.7%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
256.0ms	8000×	pre	128	true

Compiler

Compiled 559 to 354 computations (36.7% saved)

Details

analyze794.0ms (5.1%)

sample63.0ms (0.4%)

simplify123.0ms (0.8%)

prune9.0ms (0.1%)

localize67.0ms (0.4%)

rewrite312.0ms (2%)

series299.0ms (1.9%)

simplify141.0ms (0.9%)

prune252.0ms (1.6%)

localize80.0ms (0.5%)

rewrite248.0ms (1.6%)

series127.0ms (0.8%)

simplify128.0ms (0.8%)

prune199.0ms (1.3%)

localize81.0ms (0.5%)

rewrite359.0ms (2.3%)

series296.0ms (1.9%)

simplify206.0ms (1.3%)

prune327.0ms (2.1%)

localize78.0ms (0.5%)

rewrite188.0ms (1.2%)

series208.0ms (1.3%)

simplify101.0ms (0.6%)

prune200.0ms (1.3%)

regimes8.1s (52%)

simplify7.0ms (0%)

end2.0ms (0%)

sample2.6s (16.7%)

Profiling