Details

analyze255.0ms (1.5%)

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)

sample3.3s (19.6%)

Results

3.2s

8256×

body

128

valid

Compiler

Compiled 108 to 70 computations (35.2% saved)

simplify59.0ms (0.4%)

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

prune7.0ms (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

0.5b

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)

localize98.0ms (0.6%)

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)))

series245.0ms (1.5%)

Counts

4 → 84

Calls

4 calls:

149.0ms	(/.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))))
54.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
24.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
17.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite143.0ms (0.9%)

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:

138.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
138.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
138.0ms	(/.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))))
137.0ms	(.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

simplify133.0ms (0.8%)

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

prune496.0ms (3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	154	11	165
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	156	11	167

Error

0.0b

Counts

167 → 11

Alt Table

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

Compiler

Compiled 7061 to 3951 computations (44% saved)

localize110.0ms (0.7%)

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))))
✓	3.2b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series202.0ms (1.2%)

Counts

2 → 36

Calls

2 calls:

152.0ms

(/.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))))

49.0ms

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

rewrite160.0ms (1%)

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:

155.0ms

(/.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))))

155.0ms

(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

simplify119.0ms (0.7%)

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

prune541.0ms (3.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	180	10	190

Error

0.0b

Counts

190 → 10

Alt Table

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

Compiler

Compiled 7812 to 4249 computations (45.6% saved)

localize127.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(exp.f32 (fma.f32 alpha alpha -1))
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (log.f32 (pow.f32 (exp.f32 (fma.f32 alpha alpha -1)) (*.f32 cosTheta cosTheta))))))
	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	13.3b	(log.f32 (pow.f32 (exp.f32 (fma.f32 alpha alpha -1)) (*.f32 cosTheta cosTheta)))

series5.4s (32.2%)

Counts

3 → 52

Calls

3 calls:

3.5s

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

1.9s

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

4.0ms

(exp.f32 (fma.f32 alpha alpha -1))

rewrite171.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

304×	`log1p-udef_binary32`
176×	`add-sqr-sqrt_binary32`
168×	`log1p-expm1-u_binary32`
168×	`expm1-log1p-u_binary32`
166×	`add-log-exp_binary32`

Counts

3 → 116

Calls

3 calls:

164.0ms

(exp.f32 (fma.f32 alpha alpha -1))

164.0ms

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

164.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	51
1	361	49
2	4726	49
3	5171	49
0	0	0
1	0	0

simplify181.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

398×	`fma-neg_binary32`
264×	`cancel-sign-sub-inv_binary32`
247×	`associate-/l/_binary32`
222×	`times-frac_binary32`
217×	`associate-/r*_binary32`

Counts

168 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	2258
1	590	2042
2	2684	1939
3	4752	1933
4	5000	1933
5	4975	1933

prune743.0ms (4.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	176	10	186

Error

0.0b

Counts

186 → 10

Alt Table

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

Compiler

Compiled 6801 to 3631 computations (46.6% saved)

localize166.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))
✓	0.0b	(log.f32 alpha)
✓	0.3b	(/.f32 (fma.f32 alpha alpha -1) (.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))))
✓	0.4b	(*.f32 (PI.f32) (log.f32 alpha))

series663.0ms (4%)

Counts

4 → 64

Calls

4 calls:

384.0ms	(/.f32 (fma.f32 alpha alpha -1) (.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))))
191.0ms	(.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))
47.0ms	(*.f32 (PI.f32) (log.f32 alpha))
40.0ms	(log.f32 alpha)

rewrite126.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

751×	`log-prod_binary32`
250×	`expm1-udef_binary32`
250×	`log1p-udef_binary32`
224×	`log-pow_binary32`
142×	`add-sqr-sqrt_binary32`

Counts

4 → 110

Calls

4 calls:

121.0ms	(.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))
121.0ms	(log.f32 alpha)
121.0ms	(/.f32 (fma.f32 alpha alpha -1) (.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))))
121.0ms	(*.f32 (PI.f32) (log.f32 alpha))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
1	294	65
2	3470	65
3	6042	65
0	0	0
1	0	0

simplify174.0ms (1%)

Algorithm

1×	egg-herbie

Rules

728×	`associate-/r*_binary32`
527×	`times-frac_binary32`
463×	`fma-def_binary32`
330×	`associate-/l*_binary32`
196×	`*-commutative_binary32`

Counts

174 → 175

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	473	6077
1	1633	5808
2	5142	5808

prune594.0ms (3.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	175	10	185

Error

Counts

185 → 10

Alt Table

Status	Error	Program
✓	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	(expm1.f32 (log1p.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (.f32 (.f32 (PI.f32) (log.f32 alpha)) 2)))))
	0.8b	(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	(.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)))))
	0.6b	(/.f32 (fma.f32 alpha alpha -1) (.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (.f32 2 (+.f32 (log.f32 (.f32 (cbrt.f32 (pow.f32 alpha (PI.f32))) (cbrt.f32 (pow.f32 alpha (PI.f32))))) (log.f32 (cbrt.f32 (pow.f32 alpha (PI.f32))))))))
	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))))
	0.6b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3)))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (log.f32 (pow.f32 (exp.f32 (fma.f32 alpha alpha -1)) (*.f32 cosTheta cosTheta))))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.7b	(pow.f32 (sqrt.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)))) 2)

Compiler

Compiled 9920 to 6479 computations (34.7% saved)

regimes2.1s (12.4%)

Accuracy

Total 0.4b remaining (89%)

Threshold costs 0.4b (89%)

Counts

212 → 1

Compiler

Compiled 26192 to 17662 computations (32.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	24	35
2	25	35
3	23	35

end465.0ms (2.8%)

Compiler: Compiled 487 to 306 computations (37.2% saved)

Details

analyze255.0ms (1.5%)

sample3.3s (19.6%)

simplify59.0ms (0.4%)

prune7.0ms (0%)

localize98.0ms (0.6%)

series245.0ms (1.5%)

rewrite143.0ms (0.9%)

simplify133.0ms (0.8%)

prune496.0ms (3%)

localize110.0ms (0.7%)

series202.0ms (1.2%)

rewrite160.0ms (1%)

simplify119.0ms (0.7%)

prune541.0ms (3.2%)

localize127.0ms (0.8%)

series5.4s (32.2%)

rewrite171.0ms (1%)

simplify181.0ms (1.1%)

prune743.0ms (4.4%)

localize166.0ms (1%)

series663.0ms (4%)

rewrite126.0ms (0.8%)

simplify174.0ms (1%)

prune594.0ms (3.6%)

regimes2.1s (12.4%)

simplify4.0ms (0%)

end465.0ms (2.8%)

Profiling