Details

analyze134.0ms (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)

sample1.9s (28.4%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 108 to 70 computations (35.2% saved)

simplify48.0ms (0.7%)

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)

localize53.0ms (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)))

series113.0ms (1.7%)

Counts

4 → 84

Calls

4 calls:

61.0ms	(/.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)))
16.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
8.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite90.0ms (1.3%)

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 → 111

Calls

4 calls:

87.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
87.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
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))))
87.0ms	(.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 (1.1%)

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

195 → 169

Iterations

Useful iterations: 2 (0.0ms)

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

prune251.0ms (3.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	157	12	169
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	12	171

Error

0.0b

Counts

171 → 12

Alt Table

Status	Error	Program
	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))))
	0.9b	(.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 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	(/.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))))
	0.5b	(log1p.f32 (expm1.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)))))
▶	0.4b	(/.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	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.8b	(.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))
	0.7b	(.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))))
	0.9b	(.f32 (/.f32 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 (fma.f32 alpha 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	(pow.f32 (/.f32 (.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)) -1)
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Compiler

Compiled 6870 to 3840 computations (44.1% saved)

localize47.0ms (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))))
✓	3.1b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series112.0ms (1.7%)

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))))

24.0ms

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

rewrite115.0ms (1.7%)

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 → 85

Calls

2 calls:

112.0ms

(/.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))))

112.0ms

(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

simplify79.0ms (1.2%)

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

121 → 131

Iterations

Useful iterations: 2 (0.0ms)

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

prune254.0ms (3.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	178	5	183
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	184	11	195

Error

0.0b

Counts

195 → 11

Alt Table

Status	Error	Program
	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))))
	0.9b	(.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))
	0.8b	(exp.f32 (log.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)))))
	0.6b	(.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	(/.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))))
▶	0.5b	(log1p.f32 (expm1.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)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (/.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) 1) (/.f32 (cbrt.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))))
	0.7b	(.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))))
	0.5b	(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)))))

Compiler

Compiled 7653 to 4158 computations (45.7% saved)

localize56.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f32 (expm1.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)))))
✓	0.3b	(expm1.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))))
✓	0.3b	(/.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)))
	3.1b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series332.0ms (4.9%)

Counts

3 → 72

Calls

3 calls:

177.0ms

(expm1.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))))

80.0ms

(log1p.f32 (expm1.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)))))

74.0ms

(/.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)))

rewrite97.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

705×	`log-prod_binary32`
245×	`expm1-udef_binary32`
245×	`log1p-udef_binary32`
243×	`log-pow_binary32`
142×	`add-sqr-sqrt_binary32`

Counts

3 → 132

Calls

3 calls:

91.0ms

(log1p.f32 (expm1.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)))))

90.0ms

(expm1.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))))

90.0ms

(/.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	16	95
1	295	95
2	3376	95
3	5978	95
0	0	0
1	0	0

simplify166.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

696×	`associate-/l*_binary32`
486×	`fma-def_binary32`
279×	`associate-*l/_binary32`
248×	`*-commutative_binary32`
159×	`+-commutative_binary32`

Counts

204 → 166

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	652	11267
1	2371	10825
2	4987	10825

prune342.0ms (5.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	189	10	199

Error

0.0b

Counts

199 → 10

Alt Table

Status	Error	Program
	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))))
	0.9b	(.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))
	0.7b	(log1p.f32 (pow.f32 (sqrt.f32 (expm1.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))
	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	(/.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 (+.f32 alpha 1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (/.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) 1) (/.f32 (cbrt.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))))
	0.7b	(.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))))
	0.5b	(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)))))

Compiler

Compiled 14544 to 9271 computations (36.3% saved)

localize59.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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)

series188.0ms (2.8%)

Counts

4 → 48

Calls

4 calls:

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))))
41.0ms	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))
28.0ms	(pow.f32 (log.f32 (*.f32 alpha alpha)) 3)
0.0ms	(pow.f32 (PI.f32) 3)

rewrite131.0ms (1.9%)

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 → 158

Calls

4 calls:

122.0ms	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (log.f32 (.f32 alpha alpha)) 3))
122.0ms	(/.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))))
122.0ms	(pow.f32 (log.f32 (*.f32 alpha alpha)) 3)
122.0ms	(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

simplify72.0ms (1.1%)

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

206 → 208

Iterations

Useful iterations: 1 (0.0ms)

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

prune288.0ms (4.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	205	3	208
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	209	9	218

Error

0.0b

Counts

218 → 9

Alt Table

Status	Error	Program
	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))))
	0.9b	(.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))
	0.7b	(log1p.f32 (pow.f32 (sqrt.f32 (expm1.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))
	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))))
	1.0b	(+.f32 (fma.f32 (/.f32 alpha (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 alpha (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (neg.f32 (.f32 (cbrt.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))) (.f32 (cbrt.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))) (cbrt.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 (neg.f32 (cbrt.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))) (.f32 (cbrt.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))) (cbrt.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))) (.f32 (cbrt.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))) (.f32 (cbrt.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))) (cbrt.f32 (/.f32 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 (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))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.f32 (pow.f32 (.f32 (PI.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) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (+.f32 alpha -1) (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)))))

Compiler

Compiled 14168 to 7112 computations (49.8% saved)

regimes1.5s (22.1%)

Accuracy

Total 0.4b remaining (95.6%)

Threshold costs 0.4b (95.6%)

Counts

262 → 1

Compiler

Compiled 32650 to 21718 computations (33.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	25	39
2	26	39
3	24	39

end216.0ms (3.2%)

Compiler: Compiled 518 to 299 computations (42.3% saved)

Details

analyze134.0ms (2%)

sample1.9s (28.4%)

simplify48.0ms (0.7%)

prune4.0ms (0.1%)

localize53.0ms (0.8%)

series113.0ms (1.7%)

rewrite90.0ms (1.3%)

simplify77.0ms (1.1%)

prune251.0ms (3.7%)

localize47.0ms (0.7%)

series112.0ms (1.7%)

rewrite115.0ms (1.7%)

simplify79.0ms (1.2%)

prune254.0ms (3.8%)

localize56.0ms (0.8%)

series332.0ms (4.9%)

rewrite97.0ms (1.4%)

simplify166.0ms (2.5%)

prune342.0ms (5.1%)

localize59.0ms (0.9%)

series188.0ms (2.8%)

rewrite131.0ms (1.9%)

simplify72.0ms (1.1%)

prune288.0ms (4.3%)

regimes1.5s (22.1%)

simplify2.0ms (0%)

end216.0ms (3.2%)

Profiling