Details

analyze123.0ms (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)

sample1.8s (26.6%)

Results

1.7s

8256×

body

128

valid

Compiler

Compiled 108 to 70 computations (35.2% saved)

simplify25.0ms (0.4%)

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)

localize49.0ms (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 (.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)))

series105.0ms (1.6%)

Counts

4 → 84

Calls

4 calls:

58.0ms	(/.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)))
10.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
9.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite73.0ms (1.1%)

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:

68.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
68.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
68.0ms	(/.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))))
68.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

simplify62.0ms (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

prune249.0ms (3.7%)

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

0.0b

Counts

169 → 10

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 (pow.f32 (.f32 (fma.f32 alpha alpha -1) cosTheta) 1) cosTheta))))
	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))))
	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)
	3.0b	(-.f32 (exp.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)))))) 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))))
	0.7b	(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))))))
	0.9b	(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 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
	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))))))
	0.9b	(pow.f32 (cbrt.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)

Compiler

Compiled 6866 to 3908 computations (43.1% saved)

localize58.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (pow.f32 (.f32 (fma.f32 alpha alpha -1) cosTheta) 1) cosTheta)
✓	0.2b	(*.f32 (fma.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 (pow.f32 (.f32 (fma.f32 alpha alpha -1) cosTheta) 1) cosTheta))))
	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

series81.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

62.0ms

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

11.0ms

(*.f32 (pow.f32 (*.f32 (fma.f32 alpha alpha -1) cosTheta) 1) cosTheta)

8.0ms

(*.f32 (fma.f32 alpha alpha -1) cosTheta)

rewrite66.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

275×	`log1p-udef_binary32`
160×	`add-sqr-sqrt_binary32`
155×	`log1p-expm1-u_binary32`
155×	`expm1-log1p-u_binary32`
150×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	342	50
2	4735	50

Stop Event

1×	node limit

Counts

3 → 88

Calls

3 calls:

64.0ms

(*.f32 (pow.f32 (*.f32 (fma.f32 alpha alpha -1) cosTheta) 1) cosTheta)

64.0ms

(*.f32 (fma.f32 alpha alpha -1) cosTheta)

64.0ms

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

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	258	2875
1	945	2567
2	3969	2567

Stop Event

1×	node limit

Counts

160 → 142

prune236.0ms (3.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	165	10	175

Error

0.0b

Counts

175 → 10

Alt Table

Status	Error	Program
	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))))
	0.5b	(.f32 (/.f32 1 (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 cosTheta (.f32 (fma.f32 alpha alpha -1) cosTheta) 1)))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (pow.f32 (.f32 (fma.f32 alpha alpha -1) cosTheta) 1) cosTheta))))
	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))))
▶	0.5b	(.f32 (/.f32 1 (PI.f32)) (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 cosTheta (.f32 (fma.f32 alpha alpha -1) cosTheta) 1))))
	0.7b	(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))))))
	0.6b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
	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))))))
	3.0b	(-.f32 (exp.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)))))) 1)
	0.9b	(pow.f32 (cbrt.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)

Compiler

Compiled 6798 to 4182 computations (38.5% saved)

localize52.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f32 (.f32 2 (log.f32 alpha)) (fma.f32 cosTheta (*.f32 (fma.f32 alpha alpha -1) cosTheta) 1))
	0.2b	(*.f32 (fma.f32 alpha alpha -1) cosTheta)
✓	0.3b	(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 cosTheta (*.f32 (fma.f32 alpha alpha -1) cosTheta) 1)))
✓	0.5b	(.f32 (/.f32 1 (PI.f32)) (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 cosTheta (.f32 (fma.f32 alpha alpha -1) cosTheta) 1))))

series304.0ms (4.6%)

Counts

3 → 72

Calls

3 calls:

126.0ms

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

101.0ms

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

76.0ms

(*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta (*.f32 (fma.f32 alpha alpha -1) cosTheta) 1))

rewrite73.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

276×	`expm1-udef_binary32`
276×	`log1p-udef_binary32`
156×	`add-sqr-sqrt_binary32`
144×	`add-log-exp_binary32`
144×	`log1p-expm1-u_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	78
1	325	78
2	4251	78

Stop Event

1×	node limit

Counts

3 → 120

Calls

3 calls:

67.0ms

(*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta (*.f32 (fma.f32 alpha alpha -1) cosTheta) 1))

67.0ms

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

67.0ms

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

simplify114.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

830×	`fma-def_binary32`
552×	`associate-/l*_binary32`
283×	`*-commutative_binary32`
209×	`+-commutative_binary32`
165×	`associate-/r*_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	764	9727
1	2966	9463

Stop Event

1×	node limit

Counts

192 → 216

prune482.0ms (7.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	242	2	244
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	246	8	254

Error

Counts

254 → 8

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 (pow.f32 (.f32 (fma.f32 alpha alpha -1) cosTheta) 1) cosTheta))))
▶	0.4b	(/.f32 (.f32 -1 (/.f32 (.f32 1/2 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) (fma.f32 cosTheta (*.f32 (fma.f32 alpha alpha -1) cosTheta) 1))) (neg.f32 (PI.f32)))
	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))))
	0.7b	(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))))))
	0.7b	(/.f32 (/.f32 (/.f32 (.f32 1/2 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) (fma.f32 cosTheta (.f32 (fma.f32 alpha alpha -1) cosTheta) 1)) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32)))
	0.6b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
	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))))))
	3.0b	(-.f32 (exp.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)))))) 1)

Compiler

Compiled 16164 to 11449 computations (29.2% saved)

localize65.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 (.f32 1/2 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) (fma.f32 cosTheta (.f32 (fma.f32 alpha alpha -1) cosTheta) 1))
	0.2b	(*.f32 (fma.f32 alpha alpha -1) cosTheta)
✓	0.3b	(/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))
✓	0.4b	(/.f32 (.f32 -1 (/.f32 (.f32 1/2 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) (fma.f32 cosTheta (*.f32 (fma.f32 alpha alpha -1) cosTheta) 1))) (neg.f32 (PI.f32)))

series254.0ms (3.8%)

Counts

3 → 60

Calls

3 calls:

123.0ms

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

113.0ms

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

18.0ms

(/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))

rewrite48.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

174×	`add-sqr-sqrt_binary32`
160×	`add-cbrt-cube_binary32`
160×	`add-log-exp_binary32`
159×	`add-exp-log_binary32`
159×	`log1p-expm1-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	72
1	352	68

Stop Event

1×	node limit

Counts

3 → 134

Calls

3 calls:

43.0ms

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

43.0ms

(/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))

43.0ms

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

simplify103.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-def_binary32`
555×	`associate-/l*_binary32`
256×	`*-commutative_binary32`
202×	`+-commutative_binary32`
165×	`associate-/r*_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	733	9036
1	2828	8881

Stop Event

1×	node limit

Counts

194 → 225

prune437.0ms (6.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	250	3	253
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	253	8	261

Error

Counts

261 → 8

Alt Table

Status	Error	Program
	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))))
	0.5b	(/.f32 (.f32 -1 (/.f32 (.f32 1/2 (-.f32 (/.f32 (pow.f32 alpha 2) (log.f32 alpha)) (/.f32 1 (log.f32 alpha)))) (fma.f32 cosTheta (*.f32 (fma.f32 alpha alpha -1) cosTheta) 1))) (neg.f32 (PI.f32)))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (pow.f32 (.f32 (fma.f32 alpha alpha -1) cosTheta) 1) cosTheta))))
✓	0.4b	(/.f32 (.f32 -1 (/.f32 (.f32 1/2 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) (fma.f32 cosTheta (*.f32 (fma.f32 alpha alpha -1) cosTheta) 1))) (neg.f32 (PI.f32)))
	0.7b	(exp.f32 (log.f32 (/.f32 (/.f32 1/2 (.f32 (fma.f32 cosTheta (.f32 (fma.f32 alpha alpha -1) cosTheta) 1) (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)))) (PI.f32))))
	0.7b	(.f32 (/.f32 1 (pow.f32 (cbrt.f32 (PI.f32)) 2)) (/.f32 (/.f32 1/2 (.f32 (fma.f32 cosTheta (*.f32 (fma.f32 alpha alpha -1) cosTheta) 1) (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)))) (cbrt.f32 (PI.f32))))
	0.6b	(.f32 (/.f32 (cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
	3.0b	(-.f32 (exp.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)))))) 1)

Compiler

Compiled 16712 to 11723 computations (29.9% saved)

regimes1.6s (24.1%)

Accuracy

Total 0.4b remaining (92.8%)

Threshold costs 0.4b (92.8%)

Counts

290 → 1

Compiler

Compiled 37037 to 25339 computations (31.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary32`
8×	`+-commutative_binary32`
8×	`sub-neg_binary32`
8×	`neg-sub0_binary32`
8×	`neg-mul-1_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	31	35
2	43	35
3	58	33
4	73	33
5	80	33
6	84	33
7	85	33

Stop Event

1×

saturated

end159.0ms (2.4%)

Compiler: Compiled 272 to 193 computations (29% saved)

Details

analyze123.0ms (1.8%)

sample1.8s (26.6%)

simplify25.0ms (0.4%)

prune4.0ms (0.1%)

localize49.0ms (0.7%)

series105.0ms (1.6%)

rewrite73.0ms (1.1%)

simplify62.0ms (0.9%)

prune249.0ms (3.7%)

localize58.0ms (0.9%)

series81.0ms (1.2%)

rewrite66.0ms (1%)

simplify59.0ms (0.9%)

prune236.0ms (3.5%)

localize52.0ms (0.8%)

series304.0ms (4.6%)

rewrite73.0ms (1.1%)

simplify114.0ms (1.7%)

prune482.0ms (7.2%)

localize65.0ms (1%)

series254.0ms (3.8%)

rewrite48.0ms (0.7%)

simplify103.0ms (1.6%)

prune437.0ms (6.5%)

regimes1.6s (24.1%)

simplify3.0ms (0%)

end159.0ms (2.4%)

Profiling