Details

analyze126.0ms (1.8%)

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)

sample1.7s (23.7%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 108 to 70 computations (35.2% saved)

simplify23.0ms (0.3%)

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 (0.1%)

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 (-.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))))
▶	0.5b	(/.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)))

Status

Error

Program

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))))

▶

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)))

Compiler

Compiled 145 to 87 computations (40% saved)

localize44.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))
✓	0.1b	(log.f32 (*.f32 alpha alpha))
✓	0.3b	(/.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 (PI.f32) (log.f32 (.f32 alpha alpha)))

series217.0ms (3%)

Counts

4 → 72

Calls

4 calls:

107.0ms	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))
58.0ms	(/.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)))
31.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
20.0ms	(log.f32 (*.f32 alpha alpha))

rewrite63.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log-prod_binary32`
230×	`expm1-udef_binary32`
230×	`log1p-udef_binary32`
212×	`log-pow_binary32`
132×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	71
1	273	71
2	3432	71

Stop Event

1×	node limit

Counts

4 → 125

Calls

4 calls:

61.0ms	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))
61.0ms	(log.f32 (*.f32 alpha alpha))
61.0ms	(/.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)))
60.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Rules

424×	`fma-neg_binary32`
371×	`associate-r_binary32`
351×	`associate-/r*_binary32`
282×	`associate-l_binary32`
224×	`times-frac_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	292	3573
1	1079	3186
2	4646	3183

Stop Event

1×	node limit

Counts

197 → 191

prune249.0ms (3.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	181	10	191
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	183	10	193

Error

0.0b

Counts

193 → 10

Alt Table

Status	Error	Program
	0.6b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	10.7b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))
	0.5b	(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 (PI.f32) (+.f32 (log.f32 (.f32 alpha (cbrt.f32 (.f32 alpha alpha)))) (log.f32 (cbrt.f32 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
▶	0.4b	(/.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)))
	0.9b	(-.f32 (fma.f32 3 (.f32 (/.f32 alpha (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) alpha)) (pow.f32 cosTheta 4)) (fma.f32 2 (/.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta))) (.f32 2 (log.f32 alpha))) (PI.f32)) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (/.f32 alpha (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) 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 (/.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 (/.f32 cosTheta (PI.f32)) (/.f32 cosTheta (*.f32 2 (log.f32 alpha))))))))
	0.5b	(/.f32 (fma.f32 alpha alpha -1) (.f32 (+.f32 (log.f32 (.f32 (cbrt.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (cbrt.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))) (log.f32 (cbrt.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.8b	(exp.f32 (log.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))))
	0.5b	(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.7b	(pow.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))) 2)
	0.8b	(.f32 (cbrt.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 (/.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))

Compiler

Compiled 7413 to 4475 computations (39.6% saved)

localize43.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series635.0ms (8.9%)

Counts

4 → 72

Calls

4 calls:

276.0ms	(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
268.0ms	(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
65.0ms	(/.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)))
25.0ms	(pow.f32 (*.f32 alpha alpha) (PI.f32))

rewrite62.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	73
1	277	73
2	3448	73

Stop Event

1×	node limit

Counts

4 → 123

Calls

4 calls:

59.0ms	(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
59.0ms	(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
59.0ms	(/.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)))
59.0ms	(pow.f32 (*.f32 alpha alpha) (PI.f32))

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

424×	`fma-neg_binary32`
364×	`associate-r_binary32`
335×	`associate-/r*_binary32`
272×	`associate-l_binary32`
217×	`*-commutative_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	292	3645
1	1081	3258
2	4594	3211

Stop Event

1×	node limit

Counts

195 → 189

prune227.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	192	7	199

Error

0.0b

Counts

199 → 7

Alt Table

Status	Error	Program
✓	0.4b	(/.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)))
	0.9b	(-.f32 (fma.f32 3 (.f32 (/.f32 alpha (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) alpha)) (pow.f32 cosTheta 4)) (fma.f32 2 (/.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta))) (.f32 2 (log.f32 alpha))) (PI.f32)) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (/.f32 alpha (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) 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 (/.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 (/.f32 cosTheta (PI.f32)) (/.f32 cosTheta (*.f32 2 (log.f32 alpha))))))))
	0.8b	(exp.f32 (log.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))))
▶	0.6b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.7b	(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 (.f32 (.f32 2 (log.f32 alpha)) (cbrt.f32 (pow.f32 (PI.f32) 2))) (cbrt.f32 (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
	0.7b	(pow.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))) 2)
	0.8b	(.f32 (cbrt.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 (/.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))

Compiler

Compiled 7173 to 4414 computations (38.5% saved)

localize66.0ms (0.9%)

Local error

Found 4 expressions with local error:

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

series184.0ms (2.6%)

Counts

4 → 52

Calls

4 calls:

142.0ms	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
25.0ms	(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
14.0ms	(/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))
3.0ms	(pow.f32 (fma.f32 alpha alpha -1) 2)

rewrite80.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

179×	`add-sqr-sqrt_binary32`
169×	`log1p-expm1-u_binary32`
169×	`expm1-log1p-u_binary32`
167×	`add-cbrt-cube_binary32`
166×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	85
1	383	71
2	4907	71

Stop Event

1×	node limit

Counts

4 → 145

Calls

4 calls:

76.0ms	(/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))
76.0ms	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
76.0ms	(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
76.0ms	(pow.f32 (fma.f32 alpha alpha -1) 2)

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

728×	`associate-/r*_binary32`
535×	`times-frac_binary32`
413×	`fma-def_binary32`
321×	`associate-/l*_binary32`
191×	`associate-*l/_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	443	5143
1	1689	5045

Stop Event

1×	node limit

Counts

197 → 206

prune331.0ms (4.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	206	7	213

Error

Counts

213 → 7

Alt Table

Status	Error	Program
✓	0.4b	(/.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)))
	0.9b	(-.f32 (fma.f32 3 (.f32 (/.f32 alpha (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) alpha)) (pow.f32 cosTheta 4)) (fma.f32 2 (/.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta))) (.f32 2 (log.f32 alpha))) (PI.f32)) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (/.f32 alpha (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) 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 (/.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 (/.f32 cosTheta (PI.f32)) (/.f32 cosTheta (*.f32 2 (log.f32 alpha))))))))
▶	0.5b	(.f32 (expm1.f32 (log1p.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.8b	(exp.f32 (log.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))))
	0.7b	(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 (.f32 (.f32 2 (log.f32 alpha)) (cbrt.f32 (pow.f32 (PI.f32) 2))) (cbrt.f32 (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
	0.7b	(pow.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))) 2)
	0.8b	(.f32 (cbrt.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 (/.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))

Compiler

Compiled 11735 to 7495 computations (36.1% saved)

localize70.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
✓	0.3b	(.f32 (expm1.f32 (log1p.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
	0.5b	(pow.f32 (fma.f32 alpha alpha -1) 2)

series72.0ms (1%)

Counts

2 → 28

Calls

2 calls:

62.0ms

(*.f32 (expm1.f32 (log1p.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))

9.0ms

(/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))

rewrite74.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

310×	`prod-diff_binary32`
183×	`add-sqr-sqrt_binary32`
174×	`expm1-log1p-u_binary32`
173×	`log1p-expm1-u_binary32`
171×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	67
1	397	53
2	4862	53

Stop Event

1×	node limit

Counts

2 → 96

Calls

2 calls:

71.0ms

(/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))

71.0ms

(*.f32 (expm1.f32 (log1p.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

366×	`cancel-sign-sub-inv_binary32`
347×	`associate-/r*_binary32`
266×	`fma-neg_binary32`
260×	`associate-r_binary32`
235×	`sub-neg_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	268	2428
1	982	2267
2	4153	2267

Stop Event

1×	node limit

Counts

124 → 143

prune276.0ms (3.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	201	7	208

Error

Counts

208 → 7

Alt Table

Status	Error	Program
✓	0.4b	(/.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)))
	0.9b	(-.f32 (fma.f32 3 (.f32 (/.f32 alpha (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) alpha)) (pow.f32 cosTheta 4)) (fma.f32 2 (/.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta))) (.f32 2 (log.f32 alpha))) (PI.f32)) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (/.f32 alpha (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) 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 (/.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 (/.f32 cosTheta (PI.f32)) (/.f32 cosTheta (*.f32 2 (log.f32 alpha))))))))
✓	0.5b	(.f32 (expm1.f32 (log1p.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.8b	(exp.f32 (log.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))))
	0.7b	(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 (.f32 (.f32 2 (log.f32 alpha)) (cbrt.f32 (pow.f32 (PI.f32) 2))) (cbrt.f32 (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
	0.7b	(pow.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))) 2)
	0.8b	(.f32 (cbrt.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 (/.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))

Compiler

Compiled 8421 to 5276 computations (37.3% saved)

regimes2.1s (30%)

Accuracy

Total 0.4b remaining (90.6%)

Threshold costs 0.4b (90.6%)

Counts

375 → 1

Compiler

Compiled 51158 to 35486 computations (30.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	18	31

Stop Event

1×

saturated

end167.0ms (2.3%)

Compiler: Compiled 349 to 232 computations (33.5% saved)

Details

analyze126.0ms (1.8%)

sample1.7s (23.7%)

simplify23.0ms (0.3%)

prune4.0ms (0.1%)

localize44.0ms (0.6%)

series217.0ms (3%)

rewrite63.0ms (0.9%)

simplify69.0ms (1%)

prune249.0ms (3.5%)

localize43.0ms (0.6%)

series635.0ms (8.9%)

rewrite62.0ms (0.9%)

simplify79.0ms (1.1%)

prune227.0ms (3.2%)

localize66.0ms (0.9%)

series184.0ms (2.6%)

rewrite80.0ms (1.1%)

simplify79.0ms (1.1%)

prune331.0ms (4.7%)

localize70.0ms (1%)

series72.0ms (1%)

rewrite74.0ms (1%)

simplify57.0ms (0.8%)

prune276.0ms (3.9%)

regimes2.1s (30%)

simplify2.0ms (0%)

end167.0ms (2.3%)

Profiling