Details

analyze115.0ms (0.6%)

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)

sample1.6s (8.3%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 82 to 54 computations (34.1% saved)

preprocess24.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

712×	`distribute-rgt-in_binary32`
694×	`distribute-lft-in_binary32`
348×	`fma-def_binary32`
322×	`times-frac_binary32`
140×	`associate-/l/_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	66
1	79	62
2	317	62
3	1615	62
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 26 to 16 computations (38.5% saved)

simplify24.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

435×	`associate-l_binary32`
360×	`distribute-rgt-in_binary32`
359×	`distribute-lft-in_binary32`
342×	`associate-r_binary32`
242×	`associate-/r*_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	45	31
2	166	31
3	823	31
4	4240	31

Stop Event

1×	node limit

Counts

1 → 2

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

0.5b

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)

localize41.0ms (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 (.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)))

series100.0ms (0.5%)

Counts

4 → 84

Calls

21 calls:

12.0ms	(/.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))))	cosTheta	0
11.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))	alpha	0
10.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))	alpha	0
9.0ms	(/.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))))	cosTheta	-inf
8.0ms	(/.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))))	alpha	-inf

rewrite72.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

266×	`log1p-udef_binary32`
159×	`add-sqr-sqrt_binary32`
155×	`*-un-lft-identity_binary32`
155×	`pow1_binary32`
147×	`add-exp-log_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	311	60
2	4649	60

Stop Event

1×	node limit

Counts

4 → 107

simplify65.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	264	3015
1	961	2707
2	3995	2707

Stop Event

1×	node limit

Counts

191 → 167

prune216.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	156	11	167
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	11	169

Error

0.0b

Counts

169 → 11

Alt Table

Status	Error	Program
	0.6b	(pow.f32 (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))) -1)
	0.8b	(-.f32 (fma.f32 3 (.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 2 (.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha)))) (.f32 cosTheta cosTheta)) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (.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 (/.f32 cosTheta 2) (/.f32 cosTheta (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (/.f32 (pow.f32 cosTheta 4) (PI.f32)) (.f32 2 (log.f32 alpha)))) (fma.f32 3 (.f32 (/.f32 (/.f32 (pow.f32 cosTheta 4) (PI.f32)) (.f32 2 (log.f32 alpha))) (pow.f32 alpha 4)) (/.f32 cosTheta (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) cosTheta))))))
	0.7b	(pow.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) 2)
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
▶	0.4b	(cbrt.f32 (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3))
	0.7b	(.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (cbrt.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	(.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)))
	0.6b	(fma.f32 1/2 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2)) (.f32 (/.f32 alpha (log.f32 alpha)) (/.f32 alpha (PI.f32))) (.f32 (/.f32 alpha (.f32 (PI.f32) (log.f32 alpha))) (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))))) (/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 alpha))))
	10.0b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))
	0.8b	(exp.f32 (log.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.6b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (PI.f32)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))

Compiler

Compiled 6890 to 3924 computations (43% saved)

localize50.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f32 (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3))
✓	0.3b	(/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))
✓	0.8b	(pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3)
✓	3.1b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series378.0ms (2%)

Counts

4 → 72

Calls

18 calls:

81.0ms	(/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))	alpha	inf
41.0ms	(pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3)	cosTheta	0
40.0ms	(/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))	alpha	-inf
30.0ms	(/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))	alpha	0
30.0ms	(pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3)	alpha	0

rewrite80.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

267×	`expm1-udef_binary32`
267×	`log1p-udef_binary32`
162×	`add-sqr-sqrt_binary32`
157×	`pow1_binary32`
155×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	90
1	353	90
2	4203	90

Stop Event

1×	node limit

Counts

4 → 156

simplify85.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

926×	`associate-/r*_binary32`
618×	`times-frac_binary32`
419×	`fma-def_binary32`
378×	`associate-/l*_binary32`
226×	`*-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	576	6332
1	2216	6154

Stop Event

1×	node limit

Counts

228 → 254

prune473.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	250	4	254
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	255	10	265

Error

0.0b

Counts

265 → 10

Alt Table

Status	Error	Program
	0.5b	(/.f32 (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha -1) (.f32 2 (log.f32 alpha)))))
	0.8b	(-.f32 (fma.f32 3 (.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 2 (.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha)))) (.f32 cosTheta cosTheta)) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (.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 (/.f32 cosTheta 2) (/.f32 cosTheta (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (/.f32 (pow.f32 cosTheta 4) (PI.f32)) (.f32 2 (log.f32 alpha)))) (fma.f32 3 (.f32 (/.f32 (/.f32 (pow.f32 cosTheta 4) (PI.f32)) (.f32 2 (log.f32 alpha))) (pow.f32 alpha 4)) (/.f32 cosTheta (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) cosTheta))))))
	0.7b	(pow.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) 2)
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
▶	0.5b	(cbrt.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 2))))
	10.0b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))
	0.7b	(cbrt.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (/.f32 (/.f32 1 (PI.f32)) (.f32 2 (log.f32 alpha))))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3))
✓	0.4b	(cbrt.f32 (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3))
	0.5b	(cbrt.f32 (pow.f32 (/.f32 (-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 alpha)))) (.f32 1/2 (/.f32 1 (.f32 (PI.f32) (log.f32 alpha))))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 3))
	0.6b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (PI.f32)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))

Compiler

Compiled 13178 to 8830 computations (33% saved)

localize62.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 2))
✓	0.4b	(.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 2)))
✓	0.4b	(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
✓	0.5b	(pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 2)

series8.7s (45.4%)

Counts

4 → 84

Calls

21 calls:

5.8s	(.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 2))	alpha	-inf
890.0ms	(.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 2))	alpha	0
728.0ms	(.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 2)))	alpha	-inf
300.0ms	(.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 2))	cosTheta	0
188.0ms	(.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 2))	cosTheta	inf

rewrite78.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

186×	`add-sqr-sqrt_binary32`
182×	`pow1_binary32`
181×	`*-un-lft-identity_binary32`
171×	`add-log-exp_binary32`
170×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	180
1	386	112
2	4909	112

Stop Event

1×	node limit

Counts

4 → 102

simplify529.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

731×	`times-frac_binary32`
11×	`unpow2_binary32`
10×	`cube-mult_binary32`
10×	`unpow3_binary32`
4×	`fma-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4356	75703

Stop Event

1×	node limit

Counts

186 → 227

prune2.5s (13.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	264	1	265
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	265	10	275

Error

Counts

275 → 10

Alt Table

Status	Error	Program
▶	0.5b	(/.f32 (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha -1) (.f32 2 (log.f32 alpha)))))
	0.8b	(-.f32 (fma.f32 3 (.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 2 (.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha)))) (.f32 cosTheta cosTheta)) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (.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 (/.f32 cosTheta 2) (/.f32 cosTheta (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (/.f32 (pow.f32 cosTheta 4) (PI.f32)) (.f32 2 (log.f32 alpha)))) (fma.f32 3 (.f32 (/.f32 (/.f32 (pow.f32 cosTheta 4) (PI.f32)) (.f32 2 (log.f32 alpha))) (pow.f32 alpha 4)) (/.f32 cosTheta (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) cosTheta))))))
	0.7b	(pow.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) 2)
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.5b	(cbrt.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 2))))
	0.6b	(cbrt.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (cbrt.f32 (pow.f32 (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (PI.f32)) (.f32 2 (log.f32 alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 5/2)) 3)))
	10.0b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))
	0.7b	(cbrt.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (/.f32 (/.f32 1 (PI.f32)) (.f32 2 (log.f32 alpha))))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3))
✓	0.4b	(cbrt.f32 (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3))
	0.6b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (PI.f32)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))

Compiler

Compiled 106094 to 83905 computations (20.9% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series166.0ms (0.9%)

Counts

4 → 72

Calls

18 calls:

66.0ms	(/.f32 (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha -1) (.f32 2 (log.f32 alpha)))))	alpha	-inf
13.0ms	(/.f32 (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha -1) (.f32 2 (log.f32 alpha)))))	cosTheta	0
12.0ms	(/.f32 (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha -1) (.f32 2 (log.f32 alpha)))))	alpha	0
9.0ms	(/.f32 (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha -1) (.f32 2 (log.f32 alpha)))))	alpha	inf
7.0ms	(/.f32 (fma.f32 alpha alpha -1) (*.f32 2 (log.f32 alpha)))	alpha	-inf

rewrite83.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

280×	`log1p-udef_binary32`
165×	`add-sqr-sqrt_binary32`
161×	`*-un-lft-identity_binary32`
161×	`pow1_binary32`
152×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	79
1	334	76
2	4573	76

Stop Event

1×	node limit

Counts

4 → 156

simplify102.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

580×	`times-frac_binary32`
564×	`fma-def_binary32`
386×	`associate-/l*_binary32`
203×	`*-commutative_binary32`
154×	`+-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	588	6949
1	2215	6744

Stop Event

1×	node limit

Counts

228 → 261

prune394.0ms (2.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	261	0	261
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	261	10	271

Error

Counts

271 → 10

Alt Table

Status	Error	Program
✓	0.5b	(/.f32 (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha -1) (.f32 2 (log.f32 alpha)))))
	0.8b	(-.f32 (fma.f32 3 (.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 2 (.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha)))) (.f32 cosTheta cosTheta)) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (.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 (/.f32 cosTheta 2) (/.f32 cosTheta (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (/.f32 (pow.f32 cosTheta 4) (PI.f32)) (.f32 2 (log.f32 alpha)))) (fma.f32 3 (.f32 (/.f32 (/.f32 (pow.f32 cosTheta 4) (PI.f32)) (.f32 2 (log.f32 alpha))) (pow.f32 alpha 4)) (/.f32 cosTheta (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) cosTheta))))))
	0.7b	(pow.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) 2)
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.5b	(cbrt.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 2))))
	0.6b	(cbrt.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (cbrt.f32 (pow.f32 (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (PI.f32)) (.f32 2 (log.f32 alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 5/2)) 3)))
	10.0b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))
	0.7b	(cbrt.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (/.f32 (/.f32 1 (PI.f32)) (.f32 2 (log.f32 alpha))))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3))
✓	0.4b	(cbrt.f32 (pow.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3))
	0.6b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (PI.f32)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))

Compiler

Compiled 13579 to 9070 computations (33.2% saved)

regimes2.9s (15.3%)

Accuracy

Total 0.4b remaining (91.1%)

Threshold costs 0.4b (91.1%)

Counts

424 → 1

Compiler

Compiled 60583 to 42070 computations (30.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	19	40

Stop Event

1×

saturated

end232.0ms (1.2%)

Stop Event

1×

fuel

Compiler

Compiled 486 to 323 computations (33.5% saved)

Details

analyze115.0ms (0.6%)

sample1.6s (8.3%)

preprocess24.0ms (0.1%)

simplify24.0ms (0.1%)

prune4.0ms (0%)

localize41.0ms (0.2%)

series100.0ms (0.5%)

rewrite72.0ms (0.4%)

simplify65.0ms (0.3%)

prune216.0ms (1.1%)

localize50.0ms (0.3%)

series378.0ms (2%)

rewrite80.0ms (0.4%)

simplify85.0ms (0.4%)

prune473.0ms (2.5%)

localize62.0ms (0.3%)

series8.7s (45.4%)

rewrite78.0ms (0.4%)

simplify529.0ms (2.8%)

prune2.5s (13.2%)

localize45.0ms (0.2%)

series166.0ms (0.9%)

rewrite83.0ms (0.4%)

simplify102.0ms (0.5%)

prune394.0ms (2.1%)

regimes2.9s (15.3%)

simplify2.0ms (0%)

end232.0ms (1.2%)

Profiling