Details

analyze162.0ms (2.2%)

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)

sample1.8s (25.2%)

Results

1.8s

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

prune7.0ms (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
▶	0.4b	(/.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

▶

0.4b

(/.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)

localize59.0ms (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)))

series112.0ms (1.5%)

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))))
29.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
11.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
11.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)

rewrite71.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

266×	`log1p-udef_binary32`
154×	`add-sqr-sqrt_binary32`
146×	`log1p-expm1-u_binary32`
146×	`expm1-log1p-u_binary32`
144×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	312	60
2	4616	60

Stop Event

1×	node limit

Counts

4 → 107

Calls

4 calls:

69.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
69.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
69.0ms	(/.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))))
69.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

simplify66.0ms (0.9%)

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

prune242.0ms (3.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	157	10	167
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	10	169

Error

Counts

169 → 10

Alt Table

Status	Error	Program
▶	0.4b	(log1p.f32 (expm1.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))))
	0.5b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (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 (/.f32 1 alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(.f32 (/.f32 (cbrt.f32 (pow.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))))
	0.5b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.7b	(-.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))))))
	0.8b	(fma.f32 2 (.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 2 (log.f32 alpha)))) (.f32 cosTheta cosTheta)) (-.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (PI.f32)) (.f32 2 (log.f32 alpha))) (fma.f32 (.f32 (/.f32 cosTheta 2) (/.f32 cosTheta (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 cosTheta (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) cosTheta)))))
	0.6b	(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 (/.f32 1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.8b	(.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) 2)) (/.f32 (fma.f32 alpha alpha -1) (cbrt.f32 (.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)))

Compiler

Compiled 6914 to 3934 computations (43.1% saved)

localize59.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(log1p.f32 (expm1.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))))
✓	0.3b	(expm1.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))
✓	0.3b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))
✓	3.1b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series349.0ms (4.8%)

Counts

4 → 84

Calls

4 calls:

165.0ms	(expm1.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))
88.0ms	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))
68.0ms	(log1p.f32 (expm1.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))))
26.0ms	(pow.f32 (*.f32 alpha alpha) (PI.f32))

rewrite76.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

253×	`expm1-udef_binary32`
253×	`log1p-udef_binary32`
148×	`egg-rr`
146×	`add-sqr-sqrt_binary32`
142×	`fma-def_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	103
1	305	103
2	3867	103

Stop Event

1×	node limit

Counts

4 → 148

Calls

4 calls:

72.0ms	(log1p.f32 (expm1.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))))
72.0ms	(expm1.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))
72.0ms	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))
72.0ms	(pow.f32 (*.f32 alpha alpha) (PI.f32))

simplify162.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	661	11431
1	2595	10989

Stop Event

1×	node limit

Counts

232 → 190

prune392.0ms (5.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	186	4	190
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	190	10	200

Error

Counts

200 → 10

Alt Table

Status	Error	Program
	0.8b	(log1p.f32 (expm1.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) 2)) (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (cbrt.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))))))
▶	0.5b	(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (PI.f32)) (.f32 2 (log.f32 alpha)))
✓	0.4b	(log1p.f32 (expm1.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))))
	0.5b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (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 (/.f32 1 alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(.f32 (/.f32 (cbrt.f32 (pow.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))))
	0.5b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.5b	(/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (fma.f32 alpha alpha -1)))
	0.6b	(log1p.f32 (expm1.f32 (-.f32 (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2)) (.f32 (pow.f32 (-.f32 1 (pow.f32 cosTheta 2)) 2) (.f32 (PI.f32) (log.f32 alpha))))) (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha)))))) (.f32 1/2 (/.f32 1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))))))
	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)))

Compiler

Compiled 14364 to 9630 computations (33% saved)

localize45.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series193.0ms (2.7%)

Counts

4 → 84

Calls

4 calls:

131.0ms	(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (PI.f32)) (.f32 2 (log.f32 alpha)))
34.0ms	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (PI.f32))
26.0ms	(/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
2.0ms	(*.f32 cosTheta cosTheta)

rewrite74.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

264×	`expm1-udef_binary32`
264×	`log1p-udef_binary32`
149×	`add-sqr-sqrt_binary32`
139×	`add-log-exp_binary32`
139×	`log1p-expm1-u_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	77
1	307	77
2	4150	77

Stop Event

1×	node limit

Counts

4 → 137

Calls

4 calls:

71.0ms	(*.f32 cosTheta cosTheta)
71.0ms	(/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
71.0ms	(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (PI.f32)) (.f32 2 (log.f32 alpha)))
71.0ms	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (PI.f32))

simplify87.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

840×	`associate-/r*_binary32`
568×	`times-frac_binary32`
532×	`fma-def_binary32`
387×	`associate-/l*_binary32`
185×	`*-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	607	7547
1	2253	7353

Stop Event

1×	node limit

Counts

221 → 238

prune388.0ms (5.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	239	9	248

Error

Counts

248 → 9

Alt Table

Status	Error	Program
	0.8b	(log1p.f32 (expm1.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) 2)) (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (cbrt.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))))))
	0.6b	(fma.f32 1/2 (fma.f32 (/.f32 alpha (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2) alpha)) (.f32 (/.f32 cosTheta (PI.f32)) (/.f32 cosTheta (log.f32 alpha))) (.f32 (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 alpha (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 -1/2 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))))
✓	0.5b	(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (PI.f32)) (.f32 2 (log.f32 alpha)))
✓	0.4b	(log1p.f32 (expm1.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))))
▶	0.5b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (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 (/.f32 1 alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(.f32 (/.f32 (cbrt.f32 (pow.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))))
	0.5b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (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)))

Compiler

Compiled 13232 to 8823 computations (33.3% saved)

localize66.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
✓	0.3b	(/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))
✓	0.5b	(pow.f32 (fma.f32 alpha alpha -1) 2)
	3.1b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series96.0ms (1.3%)

Counts

3 → 48

Calls

3 calls:

73.0ms

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

20.0ms

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

3.0ms

(pow.f32 (fma.f32 alpha alpha -1) 2)

rewrite69.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

305×	`log1p-udef_binary32`
179×	`add-sqr-sqrt_binary32`
170×	`log1p-expm1-u_binary32`
170×	`expm1-log1p-u_binary32`
168×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	75
1	385	61
2	4783	61

Stop Event

1×	node limit

Counts

3 → 113

Calls

3 calls:

66.0ms

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

66.0ms

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

66.0ms

(pow.f32 (fma.f32 alpha alpha -1) 2)

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Rules

362×	`associate-/r*_binary32`
312×	`fma-neg_binary32`
307×	`associate-r_binary32`
226×	`associate-l_binary32`
225×	`times-frac_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	3087
1	1152	2858
2	4758	2842

Stop Event

1×	node limit

Counts

161 → 184

prune284.0ms (3.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	205	9	214

Error

Counts

214 → 9

Alt Table

Status	Error	Program
	0.8b	(log1p.f32 (expm1.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) 2)) (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (cbrt.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))))))
	0.6b	(fma.f32 1/2 (fma.f32 (/.f32 alpha (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2) alpha)) (.f32 (/.f32 cosTheta (PI.f32)) (/.f32 cosTheta (log.f32 alpha))) (.f32 (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 alpha (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 -1/2 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))))
✓	0.5b	(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (PI.f32)) (.f32 2 (log.f32 alpha)))
✓	0.4b	(log1p.f32 (expm1.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))))
✓	0.5b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (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 (/.f32 1 alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(.f32 (/.f32 (cbrt.f32 (pow.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))))
	0.5b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (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)))

Compiler

Compiled 8627 to 5415 computations (37.2% saved)

regimes2.1s (28.8%)

Accuracy

Total 0.4b remaining (89.1%)

Threshold costs 0.4b (89.1%)

Counts

367 → 1

Compiler

Compiled 46430 to 32582 computations (29.8% saved)

simplify2.0ms (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	14	37
1	23	37
2	24	37

Stop Event

1×

saturated

end191.0ms (2.6%)

Compiler: Compiled 334 to 224 computations (32.9% saved)

Details

analyze162.0ms (2.2%)

sample1.8s (25.2%)

simplify23.0ms (0.3%)

prune7.0ms (0.1%)

localize59.0ms (0.8%)

series112.0ms (1.5%)

rewrite71.0ms (1%)

simplify66.0ms (0.9%)

prune242.0ms (3.3%)

localize59.0ms (0.8%)

series349.0ms (4.8%)

rewrite76.0ms (1%)

simplify162.0ms (2.2%)

prune392.0ms (5.4%)

localize45.0ms (0.6%)

series193.0ms (2.7%)

rewrite74.0ms (1%)

simplify87.0ms (1.2%)

prune388.0ms (5.3%)

localize66.0ms (0.9%)

series96.0ms (1.3%)

rewrite69.0ms (0.9%)

simplify70.0ms (1%)

prune284.0ms (3.9%)

regimes2.1s (28.8%)

simplify2.0ms (0%)

end191.0ms (2.6%)

Profiling