Details

analyze155.0ms (1.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.6%	99.4%	0
0%	0.6%	99.4%	1
0%	0.6%	99.4%	2
0.3%	0.3%	99.4%	3
0.3%	0.3%	99.4%	4
0.5%	0.2%	99.4%	5
0.5%	0.2%	99.4%	6
0.6%	0.1%	99.4%	7
0.6%	0.1%	99.4%	8
0.6%	0%	99.4%	9
0.6%	0%	99.4%	10
0.6%	0%	99.4%	11
0.6%	0%	99.4%	12
0.6%	0%	99.4%	13
0.6%	0%	99.4%	14

Compiler

Compiled 35 to 23 computations (34.3% saved)

sample40.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 63 to 41 computations (34.9% saved)

simplify52.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/l*_binary32`
583×	`div-sub_binary32`
462×	`associate-l_binary32`
382×	`associate-*l/_binary32`
363×	`associate-r_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	37
1	44	37
2	154	37
3	628	37
4	2620	37
5	4665	37
6	5735	37

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Compiler

Compiled 78 to 48 computations (38.5% saved)

localize42.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.4b	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))

rewrite238.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

22×	`add-cbrt-cube_binary32`
22×	`add-exp-log_binary32`
21×	`pow1_binary32`
18×	`add-sqr-sqrt_binary32`
15×	`associate-r_binary32`

Counts

4 → 103

Calls

4 calls:

13.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
9.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
7.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
7.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 3092 to 1407 computations (54.5% saved)

series281.0ms (3.4%)

Error

0.3b

Counts

4 → 34

Calls

4 calls:

116.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
37.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
35.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
18.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 2964 to 2131 computations (28.1% saved)

simplify132.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

544×	`times-frac_binary32`
456×	`associate-l_binary32`
398×	`associate-/r*_binary32`
390×	`associate-r_binary32`
289×	`associate-/l*_binary32`

Counts

137 → 123

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	295	4077
1	906	3600
2	4675	3600
3	5004	3600

prune227.0ms (2.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	113	10	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	10	124

Error

0.0b

Counts

124 → 10

Alt Table

Status	Error	Program
	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))
	0.6b	(/.f32 (-.f32 (pow.f32 (.f32 alpha alpha) 3) (pow.f32 1 3)) (.f32 (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 (pow.f32 alpha 4) (+.f32 1 (*.f32 alpha alpha)))))
	0.5b	(/.f32 1 (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
	0.5b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 (log.f32 alpha) PI.f32))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (.f32 (.f32 2 (log.f32 alpha)) (cbrt.f32 PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
▶	0.4b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 PI.f32 (.f32 (cbrt.f32 (.f32 2 (log.f32 alpha))) (cbrt.f32 (.f32 2 (log.f32 alpha))))) (cbrt.f32 (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.8b	(exp.f32 (log.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))

Compiler

Compiled 3752 to 1759 computations (53.1% saved)

localize47.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b	(.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta)
0.2b	(.f32 cosTheta (.f32 alpha alpha))
0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta))))
0.4b	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))

rewrite210.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

22×	`add-cbrt-cube_binary32`
22×	`add-exp-log_binary32`
21×	`pow1_binary32`
18×	`add-sqr-sqrt_binary32`
13×	`associate-r_binary32`

Counts

4 → 99

Calls

4 calls:

13.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta))))
9.0ms	(.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta)
6.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))
6.0ms	(.f32 cosTheta (.f32 alpha alpha))

Compiler

Compiled 2954 to 908 computations (69.3% saved)

series261.0ms (3.2%)

Error

0.0b

Counts

4 → 31

Calls

4 calls:

114.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta))))
41.0ms	(.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta)
27.0ms	(.f32 cosTheta (.f32 alpha alpha))
20.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 2858 to 2051 computations (28.2% saved)

simplify120.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

495×	`times-frac_binary32`
392×	`associate-l_binary32`
390×	`associate-/r*_binary32`
368×	`associate-r_binary32`
264×	`associate-/l*_binary32`

Counts

130 → 108

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	304	3914
1	916	3506
2	4740	3506
3	5003	3506

prune189.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	109	9	118

Error

0.0b

Counts

118 → 9

Alt Table

Status	Error	Program
	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))
	0.6b	(/.f32 (-.f32 (pow.f32 (.f32 alpha alpha) 3) (pow.f32 1 3)) (.f32 (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 (pow.f32 alpha 4) (+.f32 1 (*.f32 alpha alpha)))))
	0.5b	(/.f32 1 (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
	0.5b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 (log.f32 alpha) PI.f32))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
▶	0.4b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) PI.f32)) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta) cosTheta))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (.f32 (.f32 2 (log.f32 alpha)) (cbrt.f32 PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.8b	(exp.f32 (log.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))

Compiler

Compiled 3375 to 1569 computations (53.5% saved)

localize48.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b	(.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta)
0.2b	(.f32 cosTheta (.f32 alpha alpha))
0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) PI.f32)) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta) cosTheta))))
3.0b	(pow.f32 (*.f32 alpha alpha) PI.f32)

rewrite208.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

19×	`add-exp-log_binary32`
19×	`pow1_binary32`
16×	`add-cbrt-cube_binary32`
15×	`add-sqr-sqrt_binary32`
12×	`*-un-lft-identity_binary32`

Counts

4 → 92

Calls

4 calls:

13.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) PI.f32)) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta) cosTheta))))
9.0ms	(.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta)
6.0ms	(.f32 cosTheta (.f32 alpha alpha))
4.0ms	(pow.f32 (*.f32 alpha alpha) PI.f32)

Compiler

Compiled 2737 to 875 computations (68% saved)

series284.0ms (3.5%)

Error

0.0b

Counts

4 → 31

Calls

4 calls:

125.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) PI.f32)) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta) cosTheta))))
38.0ms	(.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta)
27.0ms	(.f32 cosTheta (.f32 alpha alpha))
21.0ms	(pow.f32 (*.f32 alpha alpha) PI.f32)

Compiler

Compiled 3110 to 2287 computations (26.5% saved)

simplify115.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

333×	`unswap-sqr_binary32`
329×	`times-frac_binary32`
316×	`associate-l_binary32`
302×	`associate-r_binary32`
245×	`associate-/r*_binary32`

Counts

123 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	3680
1	756	3363
2	3922	3335
3	5232	3335

prune181.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	100	9	109

Error

0.0b

Counts

109 → 9

Alt Table

Status	Error	Program
▶	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))
	0.6b	(/.f32 (-.f32 (pow.f32 (.f32 alpha alpha) 3) (pow.f32 1 3)) (.f32 (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 (pow.f32 alpha 4) (+.f32 1 (*.f32 alpha alpha)))))
	0.5b	(/.f32 1 (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
	0.5b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 (log.f32 alpha) PI.f32))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
✓	0.4b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) PI.f32)) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta) cosTheta))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (.f32 (.f32 2 (log.f32 alpha)) (cbrt.f32 PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.8b	(exp.f32 (log.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))

Compiler

Compiled 3087 to 1471 computations (52.3% saved)

localize62.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.3b	(/.f32 1/2 (*.f32 (log.f32 alpha) PI.f32))
0.4b	(*.f32 (log.f32 alpha) PI.f32)
0.4b	(*.f32 (log.f32 alpha) PI.f32)
0.4b	(/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))

rewrite222.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

45×	`add-cbrt-cube_binary32`
45×	`add-exp-log_binary32`
19×	`cbrt-unprod_binary32`
19×	`prod-exp_binary32`
14×	`add-sqr-sqrt_binary32`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))
8.0ms	(*.f32 (log.f32 alpha) PI.f32)
4.0ms	(*.f32 (log.f32 alpha) PI.f32)
4.0ms	(/.f32 1/2 (*.f32 (log.f32 alpha) PI.f32))

Compiler

Compiled 4314 to 1334 computations (69.1% saved)

series263.0ms (3.2%)

Error

0.0b

Counts

4 → 22

Calls

4 calls:

136.0ms	(/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))
25.0ms	(/.f32 1/2 (*.f32 (log.f32 alpha) PI.f32))
22.0ms	(*.f32 (log.f32 alpha) PI.f32)
20.0ms	(*.f32 (log.f32 alpha) PI.f32)

Compiler

Compiled 3165 to 1906 computations (39.8% saved)

simplify138.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

445×	`times-frac_binary32`
344×	`associate-/r*_binary32`
298×	`associate-l_binary32`
291×	`associate-/l*_binary32`
288×	`cancel-sign-sub-inv_binary32`

Counts

112 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	3513
1	793	2747
2	3850	2720
3	4812	2720
4	4941	2720

prune134.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	71	10	81

Error

Counts

81 → 10

Alt Table

Status	Error	Program
	0.6b	(/.f32 (-.f32 (pow.f32 (.f32 alpha alpha) 3) (pow.f32 1 3)) (.f32 (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 (pow.f32 alpha 4) (+.f32 1 (*.f32 alpha alpha)))))
	0.5b	(/.f32 1 (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 (.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (/.f32 (log.f32 alpha) (/.f32 (cbrt.f32 1/2) PI.f32))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))
	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 1/2 (log.f32 (pow.f32 alpha PI.f32))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.4b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) PI.f32)) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta) cosTheta))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (.f32 (.f32 2 (log.f32 alpha)) (cbrt.f32 PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 (sqrt.f32 1/2) (/.f32 (log.f32 alpha) (/.f32 (sqrt.f32 1/2) PI.f32))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.8b	(exp.f32 (log.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))

Compiler

Compiled 2708 to 1087 computations (59.9% saved)

regimes2.7s (32.8%)

Accuracy

Total 0.4b remaining (94.5%)

Threshold costs 0.4b (94.5%)

Compiler

Compiled 32322 to 19597 computations (39.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	29	37
2	33	37
3	35	37
4	36	37
5	34	37

end2.0ms (0%)

Compiler: Compiled 26 to 17 computations (34.6% saved)

sample1.9s (22.6%)

Algorithm

1×

intervals

Results

597.0ms	8000×	body	128	valid
165.0ms	8000×	pre	128	true

Compiler

Compiled 490 to 287 computations (41.4% saved)

Details

analyze155.0ms (1.9%)

sample40.0ms (0.5%)

simplify52.0ms (0.6%)

prune6.0ms (0.1%)

localize42.0ms (0.5%)

rewrite238.0ms (2.9%)

series281.0ms (3.4%)

simplify132.0ms (1.6%)

prune227.0ms (2.8%)

localize47.0ms (0.6%)

rewrite210.0ms (2.6%)

series261.0ms (3.2%)

simplify120.0ms (1.5%)

prune189.0ms (2.3%)

localize48.0ms (0.6%)

rewrite208.0ms (2.5%)

series284.0ms (3.5%)

simplify115.0ms (1.4%)

prune181.0ms (2.2%)

localize62.0ms (0.8%)

rewrite222.0ms (2.7%)

series263.0ms (3.2%)

simplify138.0ms (1.7%)

prune134.0ms (1.6%)

regimes2.7s (32.8%)

simplify4.0ms (0%)

end2.0ms (0%)

sample1.9s (22.6%)

Profiling