Details

analyze93.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.3%	87.7%	0
0%	12.3%	87.7%	1
6.2%	6.2%	87.7%	2
6.2%	6.2%	87.7%	3
9.2%	3.1%	87.7%	4
9.2%	3.1%	87.7%	5
10.8%	1.5%	87.7%	6
10.8%	1.5%	87.7%	7
11.5%	0.8%	87.7%	8
11.5%	0.8%	87.7%	9
11.9%	0.4%	87.7%	10
11.9%	0.4%	87.7%	11
12.1%	0.2%	87.7%	12
12.1%	0.2%	87.7%	13
12.1%	0.1%	87.8%	14

Compiler

Compiled 42 to 32 computations (23.8% saved)

sample1.9s (21.5%)

Results

1.8s	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 111 to 85 computations (23.4% saved)

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

940×	`fma-neg_binary32`
929×	`fma-def_binary32`
740×	`times-frac_binary32`
329×	`div-sub_binary32`
317×	`associate-l_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	45	35
2	107	35
3	264	33
4	605	33
5	2500	33
6	3754	33
7	5049	33

prune5.0ms (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

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.9b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Error

Program

▶

0.7b

(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))

0.9b

(/.f32 1 (+.f32 (+.f32 1 c) (*.f32 (*.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Compiler

Compiled 148 to 113 computations (23.6% saved)

localize53.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f32 (fma.f32 cosTheta -2 1))
✓	0.3b	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
✓	0.4b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
✓	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))

series123.0ms (1.4%)

Counts

4 → 38

Calls

4 calls:

78.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
24.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
13.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
8.0ms	(sqrt.f32 (fma.f32 cosTheta -2 1))

rewrite98.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

315×	`log1p-udef_binary32`
180×	`add-sqr-sqrt_binary32`
172×	`log1p-expm1-u_binary32`
172×	`expm1-log1p-u_binary32`
169×	`add-log-exp_binary32`

Counts

4 → 103

Calls

4 calls:

96.0ms	(sqrt.f32 (fma.f32 cosTheta -2 1))
96.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
96.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
96.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	79
1	367	75
2	4816	75
3	5237	75
0	0	0
1	0	0

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Rules

582×	`times-frac_binary32`
355×	`cancel-sign-sub-inv_binary32`
325×	`fma-neg_binary32`
246×	`fma-def_binary32`
222×	`associate-r_binary32`

Counts

141 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	2281
1	696	2147
2	2682	2095
3	4678	2095
4	5070	2095

prune222.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	141	9	150
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	143	9	152

Error

0.0b

Counts

152 → 9

Alt Table

Status	Error	Program
	13.3b	(/.f32 1 (+.f32 (+.f32 1 c) (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (.f32 (PI.f32) (pow.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) 2))))))
	1.1b	(.f32 (pow.f32 (pow.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) 2) -1) (pow.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) -1))
	1.0b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) 3))))
	0.8b	(/.f32 1 (+.f32 (+.f32 1 c) (pow.f32 (sqrt.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) 2)))
	1.1b	(/.f32 1 (+.f32 (+.f32 1 c) (pow.f32 (cbrt.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) 3)))
	0.8b	(-.f32 (fma.f32 cosTheta (sqrt.f32 (PI.f32)) (fma.f32 5/2 (.f32 (pow.f32 cosTheta 3) (sqrt.f32 (PI.f32))) (fma.f32 7/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 4)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 3/2) (.f32 c (pow.f32 cosTheta 3))) (fma.f32 3 (.f32 (pow.f32 (PI.f32) 3/2) (pow.f32 cosTheta 4)) (fma.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2) (fma.f32 (.f32 cosTheta cosTheta) (sqrt.f32 (PI.f32)) (fma.f32 (.f32 c c) (.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2)) (.f32 (pow.f32 (PI.f32) 3/2) (+.f32 (.f32 3 (.f32 (.f32 c c) (pow.f32 cosTheta 4))) (.f32 6 (.f32 c (pow.f32 cosTheta 4))))))))))))) (fma.f32 c (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (fma.f32 3 (.f32 (.f32 c c) (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2))) (fma.f32 6 (.f32 (PI.f32) (.f32 c (pow.f32 cosTheta 4))) (+.f32 (+.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (+.f32 1 c) (.f32 2 (.f32 (PI.f32) (pow.f32 cosTheta 3))))) (+.f32 (.f32 (pow.f32 cosTheta 4) (+.f32 (pow.f32 (PI.f32) 2) (.f32 (PI.f32) 6))) (.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2)) (+.f32 (pow.f32 c 3) (*.f32 c 3)))))))))
	0.9b	(pow.f32 (pow.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) -1/2) 2)
▶	0.8b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32))) (/.f32 (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	13.5b	(.f32 (/.f32 1 (-.f32 (pow.f32 (+.f32 1 c) 2) (/.f32 (fma.f32 cosTheta -2 1) (.f32 (PI.f32) (pow.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) 2))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

Compiler

Compiled 5814 to 3667 computations (36.9% saved)

localize67.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)))
✓	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32))) (/.f32 (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
✓	0.6b	(.f32 (/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32))) (/.f32 (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
✓	0.8b	(/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32)))

series118.0ms (1.4%)

Counts

4 → 46

Calls

4 calls:

78.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32))) (/.f32 (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
28.0ms	(.f32 (/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32))) (/.f32 (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
8.0ms	(/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32)))
4.0ms	(cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)))

rewrite85.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

211×	`prod-diff_binary32`
210×	`add-sqr-sqrt_binary32`
201×	`log1p-expm1-u_binary32`
201×	`expm1-log1p-u_binary32`
196×	`add-cbrt-cube_binary32`

Counts

4 → 111

Calls

4 calls:

82.0ms	(cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)))
82.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32))) (/.f32 (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
82.0ms	(.f32 (/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32))) (/.f32 (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
82.0ms	(/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	101
1	431	78
2	4895	78
3	5271	78
0	0	0
1	0	0

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

746×	`times-frac_binary32`
286×	`fma-def_binary32`
254×	`sub-neg_binary32`
243×	`associate-r_binary32`
190×	`associate-l_binary32`

Counts

157 → 187

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	290	3202
1	920	3028
2	3438	2994
3	5056	2994

prune273.0ms (3.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	189	7	196

Error

0.0b

Counts

196 → 7

Alt Table

Status	Error	Program
	1.1b	(.f32 (pow.f32 (pow.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) 2) -1) (pow.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) -1))
▶	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (PI.f32)))))
	13.5b	(.f32 (/.f32 1 (-.f32 (pow.f32 (+.f32 1 c) 2) (/.f32 (fma.f32 cosTheta -2 1) (.f32 (PI.f32) (pow.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) 2))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.8b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (cbrt.f32 (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 2/3) (PI.f32))) (cbrt.f32 (/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32))))) (/.f32 (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.8b	(/.f32 1 (+.f32 (+.f32 1 c) (pow.f32 (sqrt.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) 2)))
	0.8b	(-.f32 (fma.f32 cosTheta (sqrt.f32 (PI.f32)) (fma.f32 5/2 (.f32 (pow.f32 cosTheta 3) (sqrt.f32 (PI.f32))) (fma.f32 7/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 4)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 3/2) (.f32 c (pow.f32 cosTheta 3))) (fma.f32 3 (.f32 (pow.f32 (PI.f32) 3/2) (pow.f32 cosTheta 4)) (fma.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2) (fma.f32 (.f32 cosTheta cosTheta) (sqrt.f32 (PI.f32)) (fma.f32 (.f32 c c) (.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2)) (.f32 (pow.f32 (PI.f32) 3/2) (+.f32 (.f32 3 (.f32 (.f32 c c) (pow.f32 cosTheta 4))) (.f32 6 (.f32 c (pow.f32 cosTheta 4))))))))))))) (fma.f32 c (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (fma.f32 3 (.f32 (.f32 c c) (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2))) (fma.f32 6 (.f32 (PI.f32) (.f32 c (pow.f32 cosTheta 4))) (+.f32 (+.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (+.f32 1 c) (.f32 2 (.f32 (PI.f32) (pow.f32 cosTheta 3))))) (+.f32 (.f32 (pow.f32 cosTheta 4) (+.f32 (pow.f32 (PI.f32) 2) (.f32 (PI.f32) 6))) (.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2)) (+.f32 (pow.f32 c 3) (*.f32 c 3)))))))))
	0.8b	(pow.f32 (pow.f32 (+.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (+.f32 1 c)) -1/2) 2)

Compiler

Compiled 8209 to 5480 computations (33.2% saved)

localize68.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
✓	0.1b	(.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
✓	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (PI.f32)))))
✓	0.5b	(/.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (PI.f32)))

series126.0ms (1.5%)

Counts

4 → 38

Calls

4 calls:

75.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (PI.f32)))))
24.0ms	(/.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (PI.f32)))
17.0ms	(.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
10.0ms	(/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

rewrite91.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

214×	`add-sqr-sqrt_binary32`
207×	`log1p-expm1-u_binary32`
207×	`expm1-log1p-u_binary32`
201×	`add-cbrt-cube_binary32`
201×	`add-log-exp_binary32`

Counts

4 → 101

Calls

4 calls:

89.0ms	(/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
89.0ms	(.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
89.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (PI.f32)))))
89.0ms	(/.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (PI.f32)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	124
1	440	93
2	4748	93
3	4955	93
0	0	0
1	0	0

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

792×	`times-frac_binary32`
414×	`cancel-sign-sub-inv_binary32`
243×	`fma-def_binary32`
215×	`associate-r_binary32`
213×	`sub-neg_binary32`

Counts

139 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	253	2736
1	796	2540
2	2992	2526
3	5352	2526

prune204.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	161	7	168

Error

0.0b

Counts

168 → 7

Alt Table

Status	Error	Program
	1.1b	(.f32 (pow.f32 (pow.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) 2) -1) (pow.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) -1))
✓	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (PI.f32)))))
▶	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (/.f32 1 (cbrt.f32 (PI.f32))) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (cbrt.f32 (sqrt.f32 (PI.f32)))))))
	0.8b	(-.f32 (fma.f32 cosTheta (sqrt.f32 (PI.f32)) (fma.f32 5/2 (.f32 (pow.f32 cosTheta 3) (sqrt.f32 (PI.f32))) (fma.f32 7/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 4)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 3/2) (.f32 c (pow.f32 cosTheta 3))) (fma.f32 3 (.f32 (pow.f32 (PI.f32) 3/2) (pow.f32 cosTheta 4)) (fma.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2) (fma.f32 (.f32 cosTheta cosTheta) (sqrt.f32 (PI.f32)) (fma.f32 (.f32 c c) (.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2)) (.f32 (pow.f32 (PI.f32) 3/2) (+.f32 (.f32 3 (.f32 (.f32 c c) (pow.f32 cosTheta 4))) (.f32 6 (.f32 c (pow.f32 cosTheta 4))))))))))))) (fma.f32 c (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (fma.f32 3 (.f32 (.f32 c c) (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2))) (fma.f32 6 (.f32 (PI.f32) (.f32 c (pow.f32 cosTheta 4))) (+.f32 (+.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (+.f32 1 c) (.f32 2 (.f32 (PI.f32) (pow.f32 cosTheta 3))))) (+.f32 (.f32 (pow.f32 cosTheta 4) (+.f32 (pow.f32 (PI.f32) 2) (.f32 (PI.f32) 6))) (.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2)) (+.f32 (pow.f32 c 3) (*.f32 c 3)))))))))
	13.5b	(.f32 (/.f32 1 (-.f32 (pow.f32 (+.f32 1 c) 2) (/.f32 (fma.f32 cosTheta -2 1) (.f32 (PI.f32) (pow.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) 2))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.8b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (cbrt.f32 (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 2/3) (PI.f32))) (cbrt.f32 (/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32))))) (/.f32 (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.8b	(pow.f32 (pow.f32 (+.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (+.f32 1 c)) -1/2) 2)

Compiler

Compiled 6836 to 4548 computations (33.5% saved)

localize75.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f32 (fma.f32 cosTheta -2 1))
✓	0.4b	(.f32 (/.f32 1 (cbrt.f32 (PI.f32))) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (cbrt.f32 (sqrt.f32 (PI.f32)))))
✓	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (/.f32 1 (cbrt.f32 (PI.f32))) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (cbrt.f32 (sqrt.f32 (PI.f32)))))))
✓	0.5b	(/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (cbrt.f32 (sqrt.f32 (PI.f32))))

series140.0ms (1.6%)

Counts

3 → 26

Calls

3 calls:

78.0ms

(/.f32 1 (+.f32 (+.f32 1 c) (*.f32 (/.f32 1 (cbrt.f32 (PI.f32))) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (cbrt.f32 (sqrt.f32 (PI.f32)))))))

34.0ms

(/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (cbrt.f32 (sqrt.f32 (PI.f32))))

28.0ms

(*.f32 (/.f32 1 (cbrt.f32 (PI.f32))) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (cbrt.f32 (sqrt.f32 (PI.f32)))))

rewrite78.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

221×	`add-sqr-sqrt_binary32`
211×	`log1p-expm1-u_binary32`
211×	`expm1-log1p-u_binary32`
206×	`add-cbrt-cube_binary32`
206×	`add-log-exp_binary32`

Counts

3 → 82

Calls

3 calls:

76.0ms

(*.f32 (/.f32 1 (cbrt.f32 (PI.f32))) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (cbrt.f32 (sqrt.f32 (PI.f32)))))

76.0ms

(/.f32 1 (+.f32 (+.f32 1 c) (*.f32 (/.f32 1 (cbrt.f32 (PI.f32))) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (cbrt.f32 (sqrt.f32 (PI.f32)))))))

76.0ms

(/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (cbrt.f32 (sqrt.f32 (PI.f32))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	99
1	455	82
2	4804	82
3	4956	82
0	0	0
1	0	0

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Rules

586×	`times-frac_binary32`
372×	`fma-neg_binary32`
354×	`cancel-sign-sub-inv_binary32`
223×	`fma-def_binary32`
219×	`associate-r_binary32`

Counts

108 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	2169
1	660	2023
2	2594	1895
3	4901	1891
4	5131	1891

prune230.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	151	7	158

Error

0.0b

Counts

158 → 7

Alt Table

Status	Error	Program
	1.1b	(.f32 (pow.f32 (pow.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) 2) -1) (pow.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) -1))
✓	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 1/6) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (PI.f32)))))
	13.5b	(.f32 (/.f32 1 (-.f32 (pow.f32 (+.f32 1 c) 2) (/.f32 (fma.f32 cosTheta -2 1) (.f32 (PI.f32) (pow.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) 2))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.8b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (cbrt.f32 (/.f32 (pow.f32 (fma.f32 cosTheta -2 1) 2/3) (PI.f32))) (cbrt.f32 (/.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (PI.f32))))) (/.f32 (cbrt.f32 (sqrt.f32 (fma.f32 cosTheta -2 1))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	1.1b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (/.f32 1 (cbrt.f32 (PI.f32))) (-.f32 (/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) cosTheta) (.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) (+.f32 (*.f32 3/2 cosTheta) 1))))))
	0.8b	(-.f32 (fma.f32 cosTheta (sqrt.f32 (PI.f32)) (fma.f32 5/2 (.f32 (pow.f32 cosTheta 3) (sqrt.f32 (PI.f32))) (fma.f32 7/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 4)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 3/2) (.f32 c (pow.f32 cosTheta 3))) (fma.f32 3 (.f32 (pow.f32 (PI.f32) 3/2) (pow.f32 cosTheta 4)) (fma.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2) (fma.f32 (.f32 cosTheta cosTheta) (sqrt.f32 (PI.f32)) (fma.f32 (.f32 c c) (.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2)) (.f32 (pow.f32 (PI.f32) 3/2) (+.f32 (.f32 3 (.f32 (.f32 c c) (pow.f32 cosTheta 4))) (.f32 6 (.f32 c (pow.f32 cosTheta 4))))))))))))) (fma.f32 c (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (fma.f32 3 (.f32 (.f32 c c) (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2))) (fma.f32 6 (.f32 (PI.f32) (.f32 c (pow.f32 cosTheta 4))) (+.f32 (+.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (+.f32 1 c) (.f32 2 (.f32 (PI.f32) (pow.f32 cosTheta 3))))) (+.f32 (.f32 (pow.f32 cosTheta 4) (+.f32 (pow.f32 (PI.f32) 2) (.f32 (PI.f32) 6))) (.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2)) (+.f32 (pow.f32 c 3) (*.f32 c 3)))))))))
	0.8b	(pow.f32 (pow.f32 (+.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (+.f32 1 c)) -1/2) 2)

Compiler

Compiled 5605 to 3570 computations (36.3% saved)

regimes3.9s (45.3%)

Accuracy

Total 0.4b remaining (92.8%)

Threshold costs 0.4b (92.8%)

Counts

396 → 1

Compiler

Compiled 75954 to 59228 computations (22% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	44
1	36	44
2	46	42
3	62	42
4	78	42
5	88	42
6	94	42
7	96	42
8	95	42

end342.0ms (4%)

Compiler: Compiled 437 to 316 computations (27.7% saved)

Details

analyze93.0ms (1.1%)

sample1.9s (21.5%)

simplify44.0ms (0.5%)

prune5.0ms (0.1%)

localize53.0ms (0.6%)

series123.0ms (1.4%)

rewrite98.0ms (1.1%)

simplify90.0ms (1%)

prune222.0ms (2.6%)

localize67.0ms (0.8%)

series118.0ms (1.4%)

rewrite85.0ms (1%)

simplify82.0ms (0.9%)

prune273.0ms (3.2%)

localize68.0ms (0.8%)

series126.0ms (1.5%)

rewrite91.0ms (1.1%)

simplify74.0ms (0.9%)

prune204.0ms (2.4%)

localize75.0ms (0.9%)

series140.0ms (1.6%)

rewrite78.0ms (0.9%)

simplify82.0ms (1%)

prune230.0ms (2.7%)

regimes3.9s (45.3%)

simplify4.0ms (0%)

end342.0ms (4%)

Profiling