Details

analyze120.0ms (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)

sample1.9s (24.7%)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 108 to 70 computations (35.2% saved)

simplify46.0ms (0.6%)

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

0.4b

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)

localize45.0ms (0.6%)

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)))

series120.0ms (1.5%)

Counts

4 → 84

Calls

4 calls:

71.0ms	(/.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))))
27.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
12.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
10.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite95.0ms (1.2%)

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

simplify75.0ms (1%)

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

prune402.0ms (5.2%)

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
	0.8b	(.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))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	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 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))))
	0.5b	(expm1.f32 (log1p.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)))))
	0.9b	(.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)))))
	0.9b	(.f32 (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)))) (pow.f32 (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)))) 2))
▶	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	(exp.f32 (log.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)))))
	0.6b	(.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))))
	0.8b	(-.f32 (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (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))))) (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))))))))

Compiler

Compiled 6889 to 3847 computations (44.2% saved)

localize48.0ms (0.6%)

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))))
✓	3.0b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series113.0ms (1.5%)

Counts

2 → 36

Calls

2 calls:

87.0ms

(/.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))))

26.0ms

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

rewrite120.0ms (1.5%)

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:

117.0ms

(/.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))))

117.0ms

(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

simplify75.0ms (1%)

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

prune276.0ms (3.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	180	10	190

Error

0.0b

Counts

190 → 10

Alt Table

Status	Error	Program
	0.8b	(.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))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	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 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))))
	0.9b	(.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)))))
	0.9b	(.f32 (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)))) (pow.f32 (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)))) 2))
	0.5b	(expm1.f32 (log1p.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)))))
	0.8b	(-.f32 (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (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))))) (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))))))))
▶	0.5b	(fma.f32 (.f32 alpha alpha) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (neg.f32 (/.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))))

Compiler

Compiled 7714 to 4185 computations (45.7% saved)

localize57.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
✓	0.2b	(/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
✓	0.3b	(fma.f32 (.f32 alpha alpha) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (neg.f32 (/.f32 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))

series652.0ms (8.4%)

Counts

3 → 60

Calls

3 calls:

413.0ms

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

158.0ms

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

81.0ms

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

rewrite139.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

247×	`log-pow_binary32`
246×	`expm1-udef_binary32`
246×	`log1p-udef_binary32`
229×	`prod-diff_binary32`
210×	`fma-neg_binary32`

Counts

3 → 117

Calls

3 calls:

136.0ms

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

136.0ms

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

136.0ms

(fma.f32 (*.f32 alpha alpha) (/.f32 1 (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) (neg.f32 (/.f32 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	16	97
1	318	71
2	3301	71
3	4845	71
4	4941	71
5	4954	71
0	0	0
1	0	0

simplify89.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

571×	`associate-/r*_binary32`
456×	`associate-r_binary32`
345×	`associate-l_binary32`
280×	`fma-def_binary32`
235×	`times-frac_binary32`

Counts

177 → 200

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	436	5573
1	1405	5248
2	5004	5248

prune545.0ms (7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	357	1	358
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	358	10	368

Error

0.0b

Counts

368 → 10

Alt Table

Status	Error	Program
	0.8b	(.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))))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	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 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))))
	0.5b	(expm1.f32 (log1p.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)))))
	0.8b	(-.f32 (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (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))))) (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))))))))
✓	0.5b	(fma.f32 (.f32 alpha alpha) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (neg.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
	0.8b	(fma.f32 (.f32 alpha alpha) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (neg.f32 (/.f32 1 (.f32 (.f32 (cbrt.f32 (PI.f32)) (log.f32 (pow.f32 (.f32 alpha alpha) (pow.f32 (cbrt.f32 (PI.f32)) 2)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))
	0.9b	(.f32 (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)))) (pow.f32 (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)))) 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))))

Compiler

Compiled 22433 to 11655 computations (48% saved)

localize86.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.7b	(pow.f32 (log.f32 (*.f32 alpha alpha)) 3)
✓	1.0b	(pow.f32 (PI.f32) 3)

series186.0ms (2.4%)

Counts

4 → 48

Calls

4 calls:

75.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
67.0ms	(pow.f32 (log.f32 (*.f32 alpha alpha)) 3)
44.0ms	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))
0.0ms	(pow.f32 (PI.f32) 3)

rewrite128.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

743×	`prod-diff_binary32`
186×	`add-sqr-sqrt_binary32`
177×	`log1p-expm1-u_binary32`
177×	`expm1-log1p-u_binary32`
174×	`add-cbrt-cube_binary32`

Counts

4 → 155

Calls

4 calls:

120.0ms	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))
120.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
120.0ms	(pow.f32 (log.f32 (*.f32 alpha alpha)) 3)
120.0ms	(pow.f32 (PI.f32) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	60
1	391	58
2	4702	58
3	6160	58
0	0	0
1	0	0

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Rules

335×	`associate-/r*_binary32`
306×	`associate-r_binary32`
300×	`cancel-sign-sub-inv_binary32`
246×	`fma-neg_binary32`
226×	`associate-l_binary32`

Counts

203 → 205

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	264	2626
1	882	2465
2	3902	2465
3	5026	2465

prune372.0ms (4.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	203	2	205
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	206	9	215

Error

Counts

215 → 9

Alt Table

Status	Error	Program
	0.8b	(.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))))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) (fma.f32 alpha alpha -1))
	0.6b	(.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))))
✓	0.5b	(fma.f32 (.f32 alpha alpha) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (neg.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
	0.9b	(.f32 (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)))) (pow.f32 (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)))) 2))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	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))))
	0.8b	(-.f32 (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (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))))) (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))))))))

Compiler

Compiled 14009 to 7044 computations (49.7% saved)

regimes1.8s (22.5%)

Accuracy

Total 0.4b remaining (95.2%)

Threshold costs 0.4b (95.2%)

Counts

257 → 1

Compiler

Compiled 33966 to 21978 computations (35.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	60
1	35	60
2	36	60
3	34	60

end232.0ms (3%)

Compiler: Compiled 462 to 287 computations (37.9% saved)

Details

analyze120.0ms (1.5%)

sample1.9s (24.7%)

simplify46.0ms (0.6%)

prune4.0ms (0.1%)

localize45.0ms (0.6%)

series120.0ms (1.5%)

rewrite95.0ms (1.2%)

simplify75.0ms (1%)

prune402.0ms (5.2%)

localize48.0ms (0.6%)

series113.0ms (1.5%)

rewrite120.0ms (1.5%)

simplify75.0ms (1%)

prune276.0ms (3.5%)

localize57.0ms (0.7%)

series652.0ms (8.4%)

rewrite139.0ms (1.8%)

simplify89.0ms (1.1%)

prune545.0ms (7%)

localize86.0ms (1.1%)

series186.0ms (2.4%)

rewrite128.0ms (1.6%)

simplify78.0ms (1%)

prune372.0ms (4.8%)

regimes1.8s (22.5%)

simplify3.0ms (0%)

end232.0ms (3%)

Profiling