Details

analyze150.0ms (2.3%)

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)

sample2.0s (31.5%)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 108 to 70 computations (35.2% saved)

simplify50.0ms (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 (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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)))

series155.0ms (2.4%)

Counts

4 → 84

Calls

4 calls:

87.0ms	(/.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))))
44.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
13.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
11.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite37.0ms (0.6%)

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:

10.0ms	(/.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)
6.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
6.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)

simplify142.0ms (2.2%)

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

prune336.0ms (5.2%)

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

Counts

233 → 8

Alt Table

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

Compiler

Compiled 9151 to 4907 computations (46.4% saved)

localize77.0ms (1.2%)

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

series83.0ms (1.3%)

Counts

4 → 36

Calls

4 calls:

49.0ms	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3))
31.0ms	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
3.0ms	(pow.f32 (fma.f32 alpha alpha -1) 3)
0.0ms	(pow.f32 (PI.f32) 3)

rewrite23.0ms (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)

simplify130.0ms (2%)

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 → 166

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

prune230.0ms (3.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	168	6	174

Error

Counts

174 → 6

Alt Table

Status	Error	Program
	0.5b	(/.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))))
▶	0.3b	(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))))
✓	0.4b	(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))))
	0.7b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (.f32 (pow.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) 3) (pow.f32 (cbrt.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))))
	0.6b	(-.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 6259 to 4443 computations (29% saved)

localize95.0ms (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 (*.f32 2 (log.f32 alpha)) 3)
	0.7b	(pow.f32 (fma.f32 alpha alpha -1) 3)
✓	1.0b	(pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3))

series630.0ms (9.8%)

Counts

2 → 12

Calls

2 calls:

630.0ms	(.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))

rewrite20.0ms (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:

10.0ms	(.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))

simplify104.0ms (1.6%)

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

prune276.0ms (4.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	186	6	192

Error

Counts

192 → 6

Alt Table

Status	Error	Program
▶	0.5b	(/.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))))
✓	0.3b	(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))))
✓	0.4b	(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))))
	0.6b	(-.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)))
	0.7b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (expm1.f32 (log1p.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))))

Compiler

Compiled 7857 to 5849 computations (25.6% saved)

localize50.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.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))))
✓	3.3b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series124.0ms (1.9%)

Counts

2 → 36

Calls

2 calls:

98.0ms

(/.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))))

25.0ms

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

rewrite15.0ms (0.2%)

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:

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))))

3.0ms

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

simplify77.0ms (1.2%)

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

prune246.0ms (3.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	209	6	215

Error

Counts

215 → 6

Alt Table

Status	Error	Program
✓	0.5b	(/.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))))
✓	0.3b	(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))))
✓	0.4b	(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))))
	0.5b	(/.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (+.f32 (*.f32 alpha alpha) 1)))
	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)))
	0.7b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (expm1.f32 (log1p.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))))

Compiler

Compiled 8006 to 4351 computations (45.7% saved)

regimes1.1s (17.8%)

Accuracy

Total 0.4b remaining (96.8%)

Threshold costs 0.4b (96.8%)

Counts

187 → 1

Compiler

Compiled 27370 to 18186 computations (33.6% saved)

simplify2.0ms (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

end157.0ms (2.4%)

Compiler: Compiled 281 to 206 computations (26.7% saved)

Details

analyze150.0ms (2.3%)

sample2.0s (31.5%)

simplify50.0ms (0.8%)

prune4.0ms (0.1%)

localize47.0ms (0.7%)

series155.0ms (2.4%)

rewrite37.0ms (0.6%)

simplify142.0ms (2.2%)

prune336.0ms (5.2%)

localize77.0ms (1.2%)

series83.0ms (1.3%)

rewrite23.0ms (0.4%)

simplify130.0ms (2%)

prune230.0ms (3.6%)

localize95.0ms (1.5%)

series630.0ms (9.8%)

rewrite20.0ms (0.3%)

simplify104.0ms (1.6%)

prune276.0ms (4.3%)

localize50.0ms (0.8%)

series124.0ms (1.9%)

rewrite15.0ms (0.2%)

simplify77.0ms (1.2%)

prune246.0ms (3.8%)

regimes1.1s (17.8%)

simplify2.0ms (0%)

end157.0ms (2.4%)

Profiling