Details

analyze122.0ms (2.2%)

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 41 to 27 computations (34.1% saved)

sample94.0ms (1.7%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify47.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/l*_binary32`
462×	`associate-l_binary32`
382×	`associate-*l/_binary32`
363×	`associate-r_binary32`
360×	`distribute-lft-in_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	45	31
2	160	31
3	661	31
4	2791	31
5	4866	31
6	4978	31

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.5b

Counts

3 → 2

Alt Table

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

Status

Error

Program

0.5b

(/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))

▶

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 145 to 87 computations (40% saved)

localize47.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))

series151.0ms (2.7%)

Counts

4 → 84

Calls

4 calls:

96.0ms	(/.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))))
29.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
14.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
11.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

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 → 111

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))))
8.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
6.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
5.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

simplify104.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

633×	`associate-l_binary32`
535×	`times-frac_binary32`
508×	`associate-/r*_binary32`
299×	`associate-/l*_binary32`
183×	`fma-def_binary32`

Counts

195 → 231

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	419	5485
1	1280	4813
2	5382	4813

prune299.0ms (5.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	223	8	231
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	225	8	233

Error

0.0b

Counts

233 → 8

Alt Table

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

Compiler

Compiled 8997 to 4837 computations (46.2% saved)

localize50.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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))))
✓	3.0b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series119.0ms (2.1%)

Counts

2 → 36

Calls

2 calls:

92.0ms

(/.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))))

27.0ms

(pow.f32 (*.f32 alpha alpha) (PI.f32))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary32`
10×	`pow1_binary32`
7×	`add-cbrt-cube_binary32`
7×	`*-un-lft-identity_binary32`
7×	`add-sqr-sqrt_binary32`

Counts

2 → 57

Calls

2 calls:

8.0ms

(/.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))))

3.0ms

(pow.f32 (*.f32 alpha alpha) (PI.f32))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

467×	`associate-r_binary32`
452×	`associate-/r*_binary32`
414×	`times-frac_binary32`
406×	`associate-l_binary32`
265×	`associate-/l*_binary32`

Counts

93 → 121

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	360	4112
1	1120	3692
2	5116	3692

prune260.0ms (4.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	207	2	209
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	209	8	217

Error

Counts

217 → 8

Alt Table

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

Compiler

Compiled 8273 to 4499 computations (45.6% saved)

localize71.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3))
✓	0.7b	(pow.f32 (fma.f32 alpha alpha -1) 3)
✓	0.7b	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
✓	1.0b	(pow.f32 (PI.f32) 3)

series83.0ms (1.5%)

Counts

4 → 36

Calls

4 calls:

49.0ms	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3))
30.0ms	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
4.0ms	(pow.f32 (fma.f32 alpha alpha -1) 3)
0.0ms	(pow.f32 (PI.f32) 3)

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary32`
25×	`add-sqr-sqrt_binary32`
16×	`prod-exp_binary32`
15×	`*-un-lft-identity_binary32`
15×	`add-cube-cbrt_binary32`

Counts

4 → 126

Calls

4 calls:

7.0ms	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3))
3.0ms	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
2.0ms	(pow.f32 (PI.f32) 3)
2.0ms	(pow.f32 (fma.f32 alpha alpha -1) 3)

simplify118.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-def_binary32`
478×	`log-prod_binary32`
459×	`exp-prod_binary32`
268×	`associate-r_binary32`
264×	`associate-l_binary32`

Counts

162 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	2300
1	345	2209
2	1554	2043
3	3476	2037
4	4960	2037
5	5127	2037

prune222.0ms (4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	172	8	180

Error

Counts

180 → 8

Alt Table

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

Compiler

Compiled 6517 to 4613 computations (29.2% saved)

localize84.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3))
	0.7b	(pow.f32 (fma.f32 alpha alpha -1) 3)
	0.7b	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
✓	1.0b	(pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3))

series600.0ms (10.8%)

Counts

2 → 12

Calls

2 calls:

599.0ms	(.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3))
0.0ms	(pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-exp-log_binary32`
30×	`pow-exp_binary32`
29×	`unpow-prod-down_binary32`
25×	`prod-exp_binary32`
21×	`add-sqr-sqrt_binary32`

Counts

2 → 88

Calls

2 calls:

8.0ms	(.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3))
3.0ms	(pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3))

simplify107.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-def_binary32`
459×	`*-commutative_binary32`
407×	`distribute-rgt-in_binary32`
299×	`distribute-rgt-neg-out_binary32`
290×	`unswap-sqr_binary32`

Counts

100 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2317
1	285	1896
2	1018	1848
3	2209	1816
4	4649	1816
5	5107	1816

prune260.0ms (4.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	190	8	198

Error

Counts

198 → 8

Alt Table

Status	Error	Program
✓	0.5b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
✓	0.4b	(/.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	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (.f32 -8 (pow.f32 (log.f32 (/.f32 1 alpha)) 3))) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	0.8b	(exp.f32 (log.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
	0.5b	(.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))) (-.f32 alpha 1)))
✓	0.4b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Compiler

Compiled 7910 to 5900 computations (25.4% saved)

regimes805.0ms (14.5%)

Accuracy

Total 0.4b remaining (95.9%)

Threshold costs 0.4b (95.9%)

Counts

136 → 1

Compiler

Compiled 19450 to 12737 computations (34.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	52
1	29	52
2	28	52

end1.0ms (0%)

Compiler: Compiled 36 to 29 computations (19.4% saved)

sample1.7s (31.3%)

Algorithm

1×

intervals

Results

814.0ms	8000×	body	128	valid
205.0ms	8000×	pre	128	true

Compiler

Compiled 320 to 231 computations (27.8% saved)

Details

analyze122.0ms (2.2%)

sample94.0ms (1.7%)

simplify47.0ms (0.8%)

prune4.0ms (0.1%)

localize47.0ms (0.8%)

series151.0ms (2.7%)

rewrite38.0ms (0.7%)

simplify104.0ms (1.9%)

prune299.0ms (5.4%)

localize50.0ms (0.9%)

series119.0ms (2.1%)

rewrite15.0ms (0.3%)

simplify80.0ms (1.4%)

prune260.0ms (4.7%)

localize71.0ms (1.3%)

series83.0ms (1.5%)

rewrite20.0ms (0.4%)

simplify118.0ms (2.1%)

prune222.0ms (4%)

localize84.0ms (1.5%)

series600.0ms (10.8%)

rewrite17.0ms (0.3%)

simplify107.0ms (1.9%)

prune260.0ms (4.7%)

regimes805.0ms (14.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.7s (31.3%)

Profiling