Details

analyze175.0ms (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)

sample52.0ms (0.6%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 63 to 41 computations (34.9% saved)

simplify49.0ms (0.5%)

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

prune4.0ms (0%)

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

0.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.4b	(/.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)

localize53.0ms (0.6%)

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))))
0.3b	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))

rewrite223.0ms (2.4%)

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:

11.0ms	(/.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))))
7.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
7.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
6.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 3092 to 1407 computations (54.5% saved)

series237.0ms (2.5%)

Error

0.2b

Counts

4 → 34

Calls

4 calls:

95.0ms	(/.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))))
33.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
29.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
16.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 2964 to 2115 computations (28.6% saved)

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

513×	`times-frac_binary32`
450×	`associate-l_binary32`
385×	`associate-r_binary32`
374×	`associate-/r*_binary32`
293×	`associate-/l*_binary32`

Counts

137 → 122

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	315	4080
1	930	3614
2	4651	3614
3	5086	3614

prune206.0ms (2.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	113	9	122
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	10	123

Error

0.0b

Counts

123 → 10

Alt Table

Status	Error	Program
▶	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) 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 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(/.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 1 (.f32 alpha alpha))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (/.f32 (.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (cbrt.f32 (+.f32 (.f32 alpha alpha) -1))) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.4b	(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 (pow.f32 cosTheta 6) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3))))) (+.f32 (.f32 1 1) (-.f32 (.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta) (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)) (.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.8b	(/.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))))

Compiler

Compiled 3706 to 1763 computations (52.4% saved)

localize54.0ms (0.6%)

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 (log.f32 (pow.f32 (.f32 alpha alpha) PI.f32)) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
3.1b	(pow.f32 (*.f32 alpha alpha) PI.f32)

rewrite206.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 96

Calls

4 calls:

9.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) PI.f32)) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
8.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
6.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
3.0ms	(pow.f32 (*.f32 alpha alpha) PI.f32)

Compiler

Compiled 2875 to 1347 computations (53.1% saved)

series250.0ms (2.6%)

Error

Counts

4 → 34

Calls

4 calls:

104.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) PI.f32)) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
31.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
29.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
16.0ms	(pow.f32 (*.f32 alpha alpha) PI.f32)

Compiler

Compiled 3216 to 2367 computations (26.4% saved)

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

390×	`unswap-sqr_binary32`
355×	`associate-l_binary32`
330×	`times-frac_binary32`
300×	`associate-r_binary32`
221×	`associate-/r*_binary32`

Counts

130 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	3846
1	761	3487
2	3762	3466
3	5130	3466

prune179.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	115	10	125

Error

0.0b

Counts

125 → 10

Alt Table

Status	Error	Program
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) 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 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(/.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 1 (.f32 alpha alpha))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (/.f32 (.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (cbrt.f32 (+.f32 (.f32 alpha alpha) -1))) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
▶	0.4b	(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 (pow.f32 cosTheta 6) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3))))) (+.f32 (.f32 1 1) (-.f32 (.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta) (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)) (.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.8b	(/.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))))

Compiler

Compiled 3481 to 1668 computations (52.1% saved)

localize115.0ms (1.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
0.3b	(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 (pow.f32 cosTheta 6) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3)))))
0.3b	(*.f32 PI.f32 (log.f32 alpha))
0.7b	(pow.f32 (+.f32 (*.f32 alpha alpha) -1) 3)

rewrite350.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

23×	`add-cbrt-cube_binary32`
23×	`add-exp-log_binary32`
20×	`add-sqr-sqrt_binary32`
16×	`*-un-lft-identity_binary32`
15×	`add-cube-cbrt_binary32`

Counts

4 → 106

Calls

4 calls:

11.0ms	(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 (pow.f32 cosTheta 6) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3)))))
6.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
5.0ms	(pow.f32 (+.f32 (*.f32 alpha alpha) -1) 3)
4.0ms	(*.f32 PI.f32 (log.f32 alpha))

Compiler

Compiled 6792 to 3994 computations (41.2% saved)

series566.0ms (6%)

Error

0.0b

Counts

4 → 30

Calls

4 calls:

367.0ms	(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 (pow.f32 cosTheta 6) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3)))))
50.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
25.0ms	(pow.f32 (+.f32 (*.f32 alpha alpha) -1) 3)
22.0ms	(*.f32 PI.f32 (log.f32 alpha))

Compiler

Compiled 6216 to 4107 computations (33.9% saved)

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

828×	`times-frac_binary32`
459×	`associate-/r*_binary32`
459×	`associate-/l*_binary32`
158×	`distribute-rgt-in_binary32`
153×	`distribute-lft-in_binary32`

Counts

136 → 111

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	474	4605
1	1349	4162
2	5130	4162

prune335.0ms (3.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	111	10	121

Error

0.0b

Counts

121 → 10

Alt Table

Status	Error	Program
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) 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 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(/.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 1 (.f32 alpha alpha))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (/.f32 (.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (cbrt.f32 (+.f32 (.f32 alpha alpha) -1))) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
✓	0.4b	(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 (pow.f32 cosTheta 6) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3))))) (+.f32 (.f32 1 1) (-.f32 (.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta) (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)) (.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
▶	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.8b	(/.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))))

Compiler

Compiled 7240 to 4284 computations (40.8% saved)

localize80.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

rewrite783.0ms (8.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

511×	`times-frac_binary32`
249×	`add-sqr-sqrt_binary32`
235×	`*-un-lft-identity_binary32`
233×	`add-cube-cbrt_binary32`
162×	`cancel-sign-sub-inv_binary32`

Counts

4 → 319

Calls

4 calls:

69.0ms	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
10.0ms	(/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))
5.0ms	(/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32)
4.0ms	(*.f32 PI.f32 (log.f32 alpha))

Compiler

Compiled 17200 to 6220 computations (63.8% saved)

series387.0ms (4.1%)

Error

0.0b

Counts

4 → 32

Calls

4 calls:

143.0ms	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
114.0ms	(/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))
21.0ms	(/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32)
18.0ms	(*.f32 PI.f32 (log.f32 alpha))

Compiler

Compiled 4900 to 3143 computations (35.9% saved)

simplify463.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

690×	`times-frac_binary32`
275×	`neg-mul-1_binary32`
273×	`neg-sub0_binary32`
259×	`associate-/l/_binary32`
223×	`*-commutative_binary32`

Counts

351 → 290

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	992	19049
1	3198	18607
2	4954	18607
3	5000	18607
4	4967	18607

prune527.0ms (5.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	288	2	290
Fresh	1	5	6
Picked	1	0	1
Done	0	3	3
Total	290	10	300

Error

Counts

300 → 10

Alt Table

Status	Error	Program
	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) 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 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (cbrt.f32 (/.f32 (/.f32 1/8 (pow.f32 (log.f32 alpha) 3)) (pow.f32 PI.f32 3))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.6b	(.f32 (/.f32 (.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (cbrt.f32 (+.f32 (.f32 alpha alpha) -1))) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.5b	(/.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 1 (.f32 alpha alpha))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.4b	(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 (pow.f32 cosTheta 6) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3))))) (+.f32 (.f32 1 1) (-.f32 (.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta) (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)) (.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.5b	(-.f32 (.f32 (/.f32 alpha (.f32 (.f32 PI.f32 (log.f32 alpha)) 2)) (/.f32 alpha (+.f32 1 (.f32 cosTheta (-.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))
	0.8b	(/.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))))

Compiler

Compiled 13869 to 5127 computations (63% saved)

regimes1.6s (16.9%)

Accuracy

Total 0.4b remaining (94.5%)

Threshold costs 0.4b (94.5%)

Compiler

Compiled 23828 to 14522 computations (39.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary32`
2×	`*-commutative_binary32`
1×	`sub-neg_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	37
1	22	37
2	23	37
3	21	37

end1.0ms (0%)

Compiler: Compiled 26 to 16 computations (38.5% saved)

sample2.2s (23.7%)

Algorithm

1×

intervals

Results

918.0ms	8000×	body	128	valid
194.0ms	8000×	pre	128	true

Compiler

Compiled 453 to 285 computations (37.1% saved)

Details

analyze175.0ms (1.9%)

sample52.0ms (0.6%)

simplify49.0ms (0.5%)

prune4.0ms (0%)

localize53.0ms (0.6%)

rewrite223.0ms (2.4%)

series237.0ms (2.5%)

simplify114.0ms (1.2%)

prune206.0ms (2.2%)

localize54.0ms (0.6%)

rewrite206.0ms (2.2%)

series250.0ms (2.6%)

simplify114.0ms (1.2%)

prune179.0ms (1.9%)

localize115.0ms (1.2%)

rewrite350.0ms (3.7%)

series566.0ms (6%)

simplify89.0ms (0.9%)

prune335.0ms (3.5%)

localize80.0ms (0.8%)

rewrite783.0ms (8.3%)

series387.0ms (4.1%)

simplify463.0ms (4.9%)

prune527.0ms (5.6%)

regimes1.6s (16.9%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample2.2s (23.7%)

Profiling