Details

analyze121.0ms (1.6%)

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)

sample1.7s (22.5%)

Results

1.7s

8256×

body

128

valid

Compiler

Compiled 82 to 54 computations (34.1% saved)

preprocess28.0ms (0.4%)

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)

simplify25.0ms (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

prune8.0ms (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)

localize48.0ms (0.6%)

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)))

series109.0ms (1.5%)

Counts

4 → 84

Calls

21 calls:

13.0ms	(/.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	-inf
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 (PI.f32) (log.f32 (.f32 alpha alpha)))	alpha	inf

rewrite72.0ms (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

simplify64.0ms (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

prune241.0ms (3.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	158	9	167
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	160	9	169

Error

0.0b

Counts

169 → 9

Alt Table

Status	Error	Program
	0.7b	(pow.f32 (sqrt.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))))) 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))))
	10.0b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))
	0.6b	(.f32 (/.f32 1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (fma.f32 alpha alpha -1) (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 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 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))))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
▶	0.5b	(expm1.f32 (log1p.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))))))
	0.8b	(exp.f32 (log.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))))))

Compiler

Compiled 6708 to 3808 computations (43.2% saved)

localize50.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series383.0ms (5.1%)

Counts

4 → 84

Calls

21 calls:

75.0ms	(log1p.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)))))	cosTheta	0
43.0ms	(log1p.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)))))	alpha	0
29.0ms	(log1p.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)))))	cosTheta	-inf
23.0ms	(log1p.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)))))	alpha	-inf
22.0ms	(log1p.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)))))	cosTheta	inf

rewrite81.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

316×	`prod-diff_binary32`
253×	`log1p-udef_binary32`
147×	`egg-rr`
146×	`add-sqr-sqrt_binary32`
137×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	103
1	302	103
2	3863	103

Stop Event

1×	node limit

Counts

4 → 147

simplify140.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

817×	`times-frac_binary32`
464×	`fma-def_binary32`
284×	`*-commutative_binary32`
150×	`+-commutative_binary32`
136×	`associate-/r*_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	691	12316
1	2673	12015

Stop Event

1×	node limit

Counts

231 → 187

prune376.0ms (5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	187	9	196

Error

0.0b

Counts

196 → 9

Alt Table

Status	Error	Program
	0.7b	(pow.f32 (sqrt.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))))) 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))))
	10.0b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))
▶	0.6b	(.f32 (/.f32 1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (fma.f32 alpha alpha -1) (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 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 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))))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
✓	0.5b	(expm1.f32 (log1p.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))))))
	0.8b	(exp.f32 (log.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))))))

Compiler

Compiled 15426 to 10447 computations (32.3% saved)

localize49.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
✓	0.3b	(/.f32 1 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))
✓	0.3b	(.f32 (/.f32 1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
	3.1b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series381.0ms (5.1%)

Counts

3 → 60

Calls

15 calls:

96.0ms	(/.f32 1 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))	alpha	inf
94.0ms	(/.f32 1 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))	alpha	-inf
92.0ms	(/.f32 1 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))	alpha	0
15.0ms	(.f32 (/.f32 1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))	cosTheta	0
13.0ms	(.f32 (/.f32 1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))	alpha	-inf

rewrite61.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

252×	`expm1-udef_binary32`
252×	`log1p-udef_binary32`
147×	`add-sqr-sqrt_binary32`
141×	`fma-def_binary32`
136×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	63
1	306	63
2	3911	63

Stop Event

1×	node limit

Counts

3 → 109

simplify49.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

385×	`associate-/r*_binary32`
274×	`associate-r_binary32`
241×	`fma-def_binary32`
234×	`times-frac_binary32`
224×	`+-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	334	3635
1	1219	3426

Stop Event

1×	node limit

Counts

169 → 184

prune249.0ms (3.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	204	10	214

Error

Counts

214 → 10

Alt Table

Status	Error	Program
▶	0.5b	(/.f32 1 (/.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (*.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) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))) 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))))
	10.0b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))
✓	0.6b	(.f32 (/.f32 1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (fma.f32 alpha alpha -1) (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 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
✓	0.5b	(expm1.f32 (log1p.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))))))
	0.8b	(exp.f32 (log.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))))))

Compiler

Compiled 8270 to 5132 computations (37.9% saved)

localize45.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series307.0ms (4.1%)

Counts

4 → 72

Calls

18 calls:

72.0ms	(/.f32 1 (/.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (*.f32 2 (log.f32 alpha))))))	alpha	-inf
60.0ms	(/.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))))	cosTheta	0
31.0ms	(/.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))))	cosTheta	-inf
23.0ms	(/.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))))	cosTheta	inf
14.0ms	(/.f32 1 (/.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (*.f32 2 (log.f32 alpha))))))	cosTheta	0

rewrite82.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

274×	`expm1-udef_binary32`
274×	`log1p-udef_binary32`
158×	`add-sqr-sqrt_binary32`
149×	`egg-rr`
147×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	92
1	328	89
2	4305	89

Stop Event

1×	node limit

Counts

4 → 149

simplify95.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

772×	`associate-/r*_binary32`
591×	`times-frac_binary32`
576×	`fma-def_binary32`
401×	`associate-/l*_binary32`
207×	`*-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	541	6662
1	2103	6459

Stop Event

1×	node limit

Counts

221 → 238

prune450.0ms (6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	239	9	248

Error

Counts

248 → 9

Alt Table

Status	Error	Program
	0.8b	(/.f32 1 (/.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (/.f32 (fma.f32 alpha alpha -1) (pow.f32 (cbrt.f32 (.f32 2 (*.f32 (log.f32 alpha) (PI.f32)))) 3))))
	10.0b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))
✓	0.6b	(.f32 (/.f32 1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (fma.f32 alpha alpha -1) (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 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 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) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))) 2)
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
✓	0.5b	(expm1.f32 (log1p.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))))))
	0.8b	(exp.f32 (log.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))))))

Compiler

Compiled 12489 to 8166 computations (34.6% saved)

regimes2.0s (27%)

Accuracy

Total 0.4b remaining (90.1%)

Threshold costs 0.4b (90.1%)

Counts

322 → 1

Compiler

Compiled 41154 to 28734 computations (30.2% saved)

simplify3.0ms (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

end238.0ms (3.2%)

Stop Event

1×

fuel

Compiler

Compiled 364 to 242 computations (33.5% saved)

Details

analyze121.0ms (1.6%)

sample1.7s (22.5%)

preprocess28.0ms (0.4%)

simplify25.0ms (0.3%)

prune8.0ms (0.1%)

localize48.0ms (0.6%)

series109.0ms (1.5%)

rewrite72.0ms (1%)

simplify64.0ms (0.9%)

prune241.0ms (3.2%)

localize50.0ms (0.7%)

series383.0ms (5.1%)

rewrite81.0ms (1.1%)

simplify140.0ms (1.9%)

prune376.0ms (5%)

localize49.0ms (0.7%)

series381.0ms (5.1%)

rewrite61.0ms (0.8%)

simplify49.0ms (0.7%)

prune249.0ms (3.3%)

localize45.0ms (0.6%)

series307.0ms (4.1%)

rewrite82.0ms (1.1%)

simplify95.0ms (1.3%)

prune450.0ms (6%)

regimes2.0s (27%)

simplify3.0ms (0%)

end238.0ms (3.2%)

Profiling