Details

analyze120.0ms (0.7%)

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)

sample1.8s (9.7%)

Results

1.7s

8256×

body

128

valid

Compiler

Compiled 108 to 70 computations (35.2% saved)

simplify152.0ms (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%)

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

0.4b

Counts

3 → 2

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))))
	0.4b	(/.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)))

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))))

0.4b

(/.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)))

Compiler

Compiled 145 to 87 computations (40% saved)

localize171.0ms (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 (.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)))

series104.0ms (0.6%)

Counts

4 → 84

Calls

4 calls:

57.0ms	(/.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))))
28.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
10.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
9.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite95.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

266×	`log1p-udef_binary32`
265×	`expm1-udef_binary32`
154×	`add-sqr-sqrt_binary32`
146×	`log1p-expm1-u_binary32`
146×	`expm1-log1p-u_binary32`

Counts

4 → 107

Calls

4 calls:

93.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
93.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
93.0ms	(/.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))))
93.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	310	60
2	4242	60
3	4972	60
0	0	0
1	0	0

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

335×	`associate-/r*_binary32`
303×	`cancel-sign-sub-inv_binary32`
267×	`associate-r_binary32`
258×	`fma-neg_binary32`
223×	`sub-neg_binary32`

Counts

191 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	264	3015
1	865	2707
2	3733	2705
3	4989	2705

prune289.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	156	9	165
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	9	167

Error

0.0b

Counts

167 → 9

Alt Table

Status	Error	Program
	0.6b	(pow.f32 (sqrt.f32 (/.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)))) 2)
	0.5b	(.f32 (/.f32 1 (PI.f32)) (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.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 -2 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (+.f32 (fma.f32 4 (/.f32 (.f32 (pow.f32 alpha 6) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 4 (/.f32 (.f32 (.f32 alpha alpha) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))) (fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha))) (-.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (fma.f32 (/.f32 (pow.f32 cosTheta 6) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 8) (PI.f32)) (fma.f32 6 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (+.f32 (/.f32 (pow.f32 cosTheta 6) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 3 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 4)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))))))) (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (pow.f32 cosTheta 4) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))))))
▶	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))))
	0.9b	(.f32 (/.f32 (+.f32 alpha 1) (pow.f32 (cbrt.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) 2)) (/.f32 (+.f32 alpha -1) (cbrt.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	0.7b	(.f32 (/.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))

Compiler

Compiled 6883 to 3845 computations (44.1% saved)

localize45.0ms (0.2%)

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))

series94.0ms (0.5%)

Counts

2 → 36

Calls

2 calls:

71.0ms

(/.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))))

24.0ms

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

rewrite118.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

379×	`fma-neg_binary32`
266×	`log1p-udef_binary32`
265×	`expm1-udef_binary32`
156×	`add-sqr-sqrt_binary32`
149×	`log1p-expm1-u_binary32`

Counts

2 → 83

Calls

2 calls:

116.0ms

(/.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))))

116.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	314	39
2	4188	39
3	4991	39
4	5302	39
0	0	0
1	0	0

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

335×	`associate-/r*_binary32`
300×	`cancel-sign-sub-inv_binary32`
265×	`associate-r_binary32`
246×	`fma-neg_binary32`
220×	`sub-neg_binary32`

Counts

119 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	2450
1	856	2289
2	3741	2243
3	5049	2243

prune358.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	175	4	179
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	179	9	188

Error

0.0b

Counts

188 → 9

Alt Table

Status	Error	Program
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	0.6b	(.f32 (/.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
	0.6b	(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
	0.5b	(.f32 (fma.f32 alpha alpha -1) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.6b	(fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (+.f32 (fma.f32 4 (/.f32 (.f32 (pow.f32 alpha 6) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 4 (/.f32 (.f32 (.f32 alpha alpha) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))) (fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha))) (-.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (fma.f32 (/.f32 (pow.f32 cosTheta 6) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 8) (PI.f32)) (fma.f32 6 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (+.f32 (/.f32 (pow.f32 cosTheta 6) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 3 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 4)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))))))) (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (pow.f32 cosTheta 4) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))))))
	0.6b	(pow.f32 (sqrt.f32 (/.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)))) 2)
▶	0.4b	(pow.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) 1)
	0.9b	(.f32 (/.f32 (+.f32 alpha 1) (pow.f32 (cbrt.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) 2)) (/.f32 (+.f32 alpha -1) (cbrt.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))

Compiler

Compiled 7722 to 4205 computations (45.5% saved)

localize47.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
✓	0.0b	(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
✓	0.3b	(/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
	3.0b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series734.0ms (4%)

Counts

3 → 60

Calls

3 calls:

358.0ms

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

310.0ms

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

66.0ms

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

rewrite72.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

667×	`log-prod_binary32`
230×	`expm1-udef_binary32`
230×	`log1p-udef_binary32`
228×	`log-pow_binary32`
134×	`add-sqr-sqrt_binary32`

Counts

3 → 105

Calls

3 calls:

70.0ms

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

70.0ms

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

70.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	65
1	276	65
2	3186	65
3	5618	65
0	0	0
1	0	0

simplify85.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

424×	`fma-neg_binary32`
366×	`associate-r_binary32`
335×	`associate-/r*_binary32`
272×	`associate-l_binary32`
249×	`sub-neg_binary32`

Counts

165 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	3481
1	967	3094
2	4210	3085
3	5134	3085

prune296.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	186	9	195

Error

0.0b

Counts

195 → 9

Alt Table

Status	Error	Program
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	0.6b	(.f32 (/.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
▶	0.5b	(pow.f32 (/.f32 (fma.f32 alpha alpha -1) (+.f32 (log.f32 (.f32 (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))) (log.f32 (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))) 1)
	0.6b	(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
	0.5b	(.f32 (fma.f32 alpha alpha -1) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.6b	(fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (+.f32 (fma.f32 4 (/.f32 (.f32 (pow.f32 alpha 6) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 4 (/.f32 (.f32 (.f32 alpha alpha) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))) (fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha))) (-.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (fma.f32 (/.f32 (pow.f32 cosTheta 6) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 8) (PI.f32)) (fma.f32 6 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (+.f32 (/.f32 (pow.f32 cosTheta 6) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 3 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 4)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))))))) (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (pow.f32 cosTheta 4) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))))))
	0.6b	(pow.f32 (sqrt.f32 (/.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)))) 2)
	0.9b	(.f32 (/.f32 (+.f32 alpha 1) (pow.f32 (cbrt.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) 2)) (/.f32 (+.f32 alpha -1) (cbrt.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))

Compiler

Compiled 7778 to 4484 computations (42.4% saved)

localize94.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (fma.f32 alpha alpha -1) (+.f32 (log.f32 (.f32 (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))) (log.f32 (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))))
✓	0.3b	(+.f32 (log.f32 (.f32 (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))) (log.f32 (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
✓	0.5b	(.f32 (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))
	3.0b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series10.0s (54.3%)

Counts

3 → 72

Calls

3 calls:

5.9s

(+.f32 (log.f32 (*.f32 (cbrt.f32 (pow.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) (cbrt.f32 (pow.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))) (log.f32 (cbrt.f32 (pow.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))

2.9s

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

1.1s

(*.f32 (cbrt.f32 (pow.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) (cbrt.f32 (pow.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))

rewrite93.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

628×	`prod-diff_binary32`
174×	`add-sqr-sqrt_binary32`
165×	`log1p-expm1-u_binary32`
165×	`expm1-log1p-u_binary32`
164×	`add-log-exp_binary32`

Counts

3 → 92

Calls

3 calls:

89.0ms

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

89.0ms

(+.f32 (log.f32 (*.f32 (cbrt.f32 (pow.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) (cbrt.f32 (pow.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))) (log.f32 (cbrt.f32 (pow.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))

89.0ms

(*.f32 (cbrt.f32 (pow.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) (cbrt.f32 (pow.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	82
1	362	79
2	4154	79
3	5273	79
0	0	0
1	0	0

simplify172.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

595×	`unswap-sqr_binary32`
462×	`associate-r_binary32`
369×	`associate-l_binary32`
214×	`*-commutative_binary32`
209×	`times-frac_binary32`

Counts

164 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	6816
1	825	6407
2	4026	6194
3	5779	6194

prune442.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	204	9	213

Error

0.0b

Counts

213 → 9

Alt Table

Status	Error	Program
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	0.6b	(pow.f32 (.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (/.f32 1 (log.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))) 1)
✓	0.5b	(pow.f32 (/.f32 (fma.f32 alpha alpha -1) (+.f32 (log.f32 (.f32 (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))) (log.f32 (cbrt.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))) 1)
	0.6b	(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
	0.5b	(.f32 (fma.f32 alpha alpha -1) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.6b	(fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (+.f32 (fma.f32 4 (/.f32 (.f32 (pow.f32 alpha 6) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 4 (/.f32 (.f32 (.f32 alpha alpha) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))) (fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha))) (-.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (fma.f32 (/.f32 (pow.f32 cosTheta 6) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 8) (PI.f32)) (fma.f32 6 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (+.f32 (/.f32 (pow.f32 cosTheta 6) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 3 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 4)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))))))) (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (pow.f32 cosTheta 4) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))))))
	0.6b	(pow.f32 (sqrt.f32 (/.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)))) 2)
	0.5b	(pow.f32 (pow.f32 (/.f32 (log.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (fma.f32 alpha alpha -1)) -1) 1)
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))

Compiler

Compiled 14602 to 8424 computations (42.3% saved)

regimes2.6s (14.1%)

Accuracy

Total 0.4b remaining (90.1%)

Threshold costs 0.4b (90.1%)

Counts

357 → 1

Compiler

Compiled 56483 to 37043 computations (34.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary32`
1×	`+-commutative_binary32`
1×	`distribute-neg-frac_binary32`
1×	`sub-neg_binary32`
1×	`neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	60
1	25	60
2	27	60
3	28	60
4	26	60

end298.0ms (1.6%)

Compiler: Compiled 529 to 321 computations (39.3% saved)

Details

analyze120.0ms (0.7%)

sample1.8s (9.7%)

simplify152.0ms (0.8%)

prune4.0ms (0%)

localize171.0ms (0.9%)

series104.0ms (0.6%)

rewrite95.0ms (0.5%)

simplify77.0ms (0.4%)

prune289.0ms (1.6%)

localize45.0ms (0.2%)

series94.0ms (0.5%)

rewrite118.0ms (0.6%)

simplify71.0ms (0.4%)

prune358.0ms (2%)

localize47.0ms (0.3%)

series734.0ms (4%)

rewrite72.0ms (0.4%)

simplify85.0ms (0.5%)

prune296.0ms (1.6%)

localize94.0ms (0.5%)

series10.0s (54.3%)

rewrite93.0ms (0.5%)

simplify172.0ms (0.9%)

prune442.0ms (2.4%)

regimes2.6s (14.1%)

simplify3.0ms (0%)

end298.0ms (1.6%)

Profiling