Details

analyze98.0ms (1.5%)

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)

sample1.8s (27.5%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 84 to 64 computations (23.8% saved)

preprocess38.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

602×	`div-sub_binary32`
562×	`associate-/l*_binary32`
544×	`fma-def_binary32`
329×	`associate-/r*_binary32`
268×	`fma-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	80
1	80	70
2	215	70
3	590	66
4	1534	66
5	4062	66
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 27 to 21 computations (22.2% saved)

simplify24.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

929×	`fma-def_binary32`
742×	`times-frac_binary32`
323×	`fma-neg_binary32`
318×	`associate-l_binary32`
303×	`div-sub_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	45	35
2	114	35
3	306	33
4	786	33
5	3763	33

Stop Event

1×	node limit

Counts

1 → 2

prune6.0ms (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 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	0.7b	(/.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

▶

0.5b

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

0.7b

(/.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 (0.8%)

Local error

Found 4 expressions with local error:

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

series92.0ms (1.4%)

Counts

4 → 38

Calls

15 calls:

11.0ms	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))	cosTheta	-inf
10.0ms	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))	cosTheta	inf
10.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))	cosTheta	-inf
9.0ms	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))	c	-inf
9.0ms	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))	c	inf

rewrite42.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

180×	`add-sqr-sqrt_binary32`
172×	`log1p-expm1-u_binary32`
172×	`expm1-log1p-u_binary32`
170×	`add-cbrt-cube_binary32`
168×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	79
1	372	75

Stop Event

1×	node limit

Counts

4 → 105

simplify54.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

582×	`times-frac_binary32`
355×	`cancel-sign-sub-inv_binary32`
246×	`fma-def_binary32`
222×	`associate-r_binary32`
177×	`associate-l_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	2281
1	707	2147
2	2794	2133

Stop Event

1×	node limit

Counts

143 → 151

prune221.0ms (3.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	137	14	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	139	14	153

Error

0.0b

Counts

153 → 14

Alt Table

Status	Error	Program
	19.0b	(pow.f32 (pow.f32 (/.f32 1 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c))) 3) 1/3)
	13.7b	(/.f32 1 (+.f32 1 (+.f32 c (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (.f32 (PI.f32) (pow.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) 2)))))))
	13.8b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c) 2))) (-.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (pow.f32 (sqrt.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) 2)))))
	21.5b	(*.f32 (/.f32 1 (+.f32 1 (pow.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c) 3))) (-.f32 (+.f32 1 (pow.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c) 2)) (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (pow.f32 (sqrt.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) 2))))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (pow.f32 (cbrt.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) 3)))))
	0.8b	(*.f32 (pow.f32 (sqrt.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c))) -1) (pow.f32 (sqrt.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c))) -1))
	0.9b	(/.f32 1 (+.f32 1 (+.f32 c (pow.f32 (cbrt.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) 3))))
	12.1b	(*.f32 (/.f32 1 (cbrt.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)))) (cbrt.f32 (pow.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)) -2)))
▶	0.7b	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (/.f32 1 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	12.0b	(sqrt.f32 (pow.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)) -2))
	1.2b	(-.f32 (fma.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 3)) 5/2 (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 2 (.f32 (pow.f32 cosTheta 3) c)) (pow.f32 cosTheta 3)))))) (+.f32 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 3)) (+.f32 2 (.f32 2 c))) (.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (+.f32 1 c))))
	1.0b	(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c))) 2) -1) (pow.f32 (cbrt.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c))) -1))

Compiler

Compiled 6078 to 3922 computations (35.5% saved)

localize56.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f32 (fma.f32 cosTheta -2 1) (PI.f32))
✓	0.3b	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (/.f32 1 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
✓	0.6b	(.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (/.f32 1 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
✓	0.8b	(sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))

series94.0ms (1.4%)

Counts

4 → 38

Calls

15 calls:

13.0ms	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (/.f32 1 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))	cosTheta	inf
11.0ms	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (/.f32 1 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))	cosTheta	-inf
10.0ms	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (/.f32 1 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))	c	inf
9.0ms	(.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (/.f32 1 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))	cosTheta	-inf
9.0ms	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (/.f32 1 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))	c	-inf

rewrite44.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

185×	`add-sqr-sqrt_binary32`
176×	`log1p-expm1-u_binary32`
176×	`expm1-log1p-u_binary32`
174×	`add-cbrt-cube_binary32`
172×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	73
1	379	73

Stop Event

1×	node limit

Counts

4 → 131

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

589×	`times-frac_binary32`
363×	`cancel-sign-sub-inv_binary32`
227×	`fma-def_binary32`
216×	`associate-r_binary32`
170×	`associate-l_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	2266
1	670	2128
2	2695	2114

Stop Event

1×	node limit

Counts

169 → 175

prune219.0ms (3.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	171	4	175
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	180	9	189

Error

0.0b

Counts

189 → 9

Alt Table

Status	Error	Program
	0.7b	(pow.f32 (pow.f32 (+.f32 1 (+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) c)) -1/2) 2)
	0.5b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (pow.f32 cosTheta -1)) (.f32 (sqrt.f32 (PI.f32)) (exp.f32 (*.f32 cosTheta cosTheta)))))))
▶	0.5b	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (cbrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (/.f32 1 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	1.2b	(-.f32 (fma.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 3)) 5/2 (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 2 (.f32 (pow.f32 cosTheta 3) c)) (pow.f32 cosTheta 3)))))) (+.f32 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 3)) (+.f32 2 (.f32 2 c))) (.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (+.f32 1 c))))
	18.9b	(pow.f32 (pow.f32 (exp.f32 (neg.f32 (log1p.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) c)))) 3) 1/3)
	13.8b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c) 2))) (-.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (pow.f32 (sqrt.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) 2))))
	0.8b	(*.f32 (pow.f32 (sqrt.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c))) -1) (pow.f32 (sqrt.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c))) -1))
	12.1b	(*.f32 (/.f32 1 (cbrt.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)))) (cbrt.f32 (pow.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)) -2)))

Compiler

Compiled 6365 to 4160 computations (34.6% saved)

localize67.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (cbrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (/.f32 1 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
✓	0.6b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (cbrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (/.f32 1 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
✓	0.8b	(cbrt.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))))
	0.8b	(sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))

series84.0ms (1.3%)

Counts

3 → 34

Calls

12 calls:

11.0ms	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (cbrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (/.f32 1 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))	cosTheta	inf
11.0ms	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (cbrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (/.f32 1 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))	cosTheta	-inf
10.0ms	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (cbrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (/.f32 1 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))	c	-inf
10.0ms	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (cbrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (/.f32 1 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))	cosTheta	-inf
9.0ms	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (cbrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (/.f32 1 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))	c	inf

rewrite35.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

204×	`add-sqr-sqrt_binary32`
200×	`log1p-expm1-u_binary32`
200×	`expm1-log1p-u_binary32`
195×	`add-cbrt-cube_binary32`
192×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	92
1	439	65

Stop Event

1×	node limit

Counts

3 → 62

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

642×	`times-frac_binary32`
440×	`cancel-sign-sub-inv_binary32`
248×	`fma-def_binary32`
230×	`associate-r_binary32`
211×	`sub-neg_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	247	2657
1	799	2507
2	3116	2493

Stop Event

1×	node limit

Counts

96 → 118

prune200.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	158	9	167

Error

0.0b

Counts

167 → 9

Alt Table

Status	Error	Program
	0.7b	(pow.f32 (pow.f32 (+.f32 1 (+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) c)) -1/2) 2)
▶	0.5b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (pow.f32 cosTheta -1)) (.f32 (sqrt.f32 (PI.f32)) (exp.f32 (*.f32 cosTheta cosTheta)))))))
✓	0.5b	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (cbrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (/.f32 1 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	1.2b	(-.f32 (fma.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 3)) 5/2 (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 2 (.f32 (pow.f32 cosTheta 3) c)) (pow.f32 cosTheta 3)))))) (+.f32 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 3)) (+.f32 2 (.f32 2 c))) (.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (+.f32 1 c))))
	18.9b	(pow.f32 (pow.f32 (exp.f32 (neg.f32 (log1p.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) c)))) 3) 1/3)
	13.8b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c) 2))) (-.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (pow.f32 (sqrt.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) 2))))
	0.8b	(*.f32 (pow.f32 (sqrt.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c))) -1) (pow.f32 (sqrt.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c))) -1))
	12.1b	(*.f32 (/.f32 1 (cbrt.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)))) (cbrt.f32 (pow.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)) -2)))

Compiler

Compiled 7065 to 4823 computations (31.7% saved)

localize53.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series89.0ms (1.3%)

Counts

4 → 38

Calls

15 calls:

11.0ms	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (pow.f32 cosTheta -1)) (.f32 (sqrt.f32 (PI.f32)) (exp.f32 (*.f32 cosTheta cosTheta)))))))	cosTheta	-inf
11.0ms	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (pow.f32 cosTheta -1)) (.f32 (sqrt.f32 (PI.f32)) (exp.f32 (*.f32 cosTheta cosTheta)))))))	c	-inf
10.0ms	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (pow.f32 cosTheta -1)) (.f32 (sqrt.f32 (PI.f32)) (exp.f32 (*.f32 cosTheta cosTheta)))))))	cosTheta	inf
9.0ms	(/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (pow.f32 cosTheta -1)) (.f32 (sqrt.f32 (PI.f32)) (exp.f32 (*.f32 cosTheta cosTheta))))	cosTheta	-inf
9.0ms	(/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (pow.f32 cosTheta -1)) (.f32 (sqrt.f32 (PI.f32)) (exp.f32 (*.f32 cosTheta cosTheta))))	cosTheta	inf

rewrite42.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

195×	`add-sqr-sqrt_binary32`
187×	`log1p-expm1-u_binary32`
187×	`expm1-log1p-u_binary32`
185×	`add-cbrt-cube_binary32`
182×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	88
1	410	78

Stop Event

1×	node limit

Counts

4 → 102

simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

582×	`times-frac_binary32`
340×	`cancel-sign-sub-inv_binary32`
240×	`fma-def_binary32`
219×	`associate-r_binary32`
175×	`associate-+r+_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	2264
1	690	2115
2	2756	2101

Stop Event

1×	node limit

Counts

140 → 151

prune183.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	151	9	160

Error

0.0b

Counts

160 → 9

Alt Table

Status	Error	Program
	0.7b	(pow.f32 (pow.f32 (+.f32 1 (+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) c)) -1/2) 2)
✓	0.5b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (pow.f32 cosTheta -1)) (.f32 (sqrt.f32 (PI.f32)) (exp.f32 (*.f32 cosTheta cosTheta)))))))
	1.2b	(-.f32 (fma.f32 (sqrt.f32 (PI.f32)) (fma.f32 cosTheta cosTheta cosTheta) (fma.f32 5/2 (.f32 (pow.f32 cosTheta 3) (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 2 (.f32 c (pow.f32 cosTheta 3))) (pow.f32 cosTheta 3)))))) (+.f32 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 3)) (+.f32 2 (.f32 2 c))) (.f32 (.f32 cosTheta (.f32 cosTheta (PI.f32))) (+.f32 1 c))))
✓	0.5b	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (cbrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))) (/.f32 1 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	18.9b	(pow.f32 (pow.f32 (exp.f32 (neg.f32 (log1p.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) c)))) 3) 1/3)
	13.8b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (/.f32 (/.f32 1 cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) c) 2))) (-.f32 1 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (/.f32 (/.f32 1 cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) c)))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (pow.f32 (sqrt.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) 2))))
	0.5b	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (/.f32 1 (cbrt.f32 (.f32 (PI.f32) (pow.f32 (exp.f32 cosTheta) (+.f32 cosTheta cosTheta))))) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) cosTheta) (cbrt.f32 (*.f32 (sqrt.f32 (PI.f32)) (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	12.1b	(*.f32 (/.f32 1 (cbrt.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)))) (cbrt.f32 (pow.f32 (+.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) c)) -2)))

Compiler

Compiled 5415 to 3466 computations (36% saved)

regimes2.6s (39.3%)

Accuracy

Total 0.4b remaining (91.4%)

Threshold costs 0.4b (91.4%)

Counts

288 → 1

Compiler

Compiled 49102 to 38149 computations (22.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary32`
1×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	46
1	24	46

Stop Event

1×

saturated

end252.0ms (3.8%)

Stop Event

1×

fuel

Compiler

Compiled 385 to 287 computations (25.5% saved)

Details

analyze98.0ms (1.5%)

sample1.8s (27.5%)

preprocess38.0ms (0.6%)

simplify24.0ms (0.4%)

prune6.0ms (0.1%)

localize53.0ms (0.8%)

series92.0ms (1.4%)

rewrite42.0ms (0.6%)

simplify54.0ms (0.8%)

prune221.0ms (3.3%)

localize56.0ms (0.8%)

series94.0ms (1.4%)

rewrite44.0ms (0.7%)

simplify52.0ms (0.8%)

prune219.0ms (3.3%)

localize67.0ms (1%)

series84.0ms (1.3%)

rewrite35.0ms (0.5%)

simplify62.0ms (0.9%)

prune200.0ms (3%)

localize53.0ms (0.8%)

series89.0ms (1.3%)

rewrite42.0ms (0.6%)

simplify50.0ms (0.8%)

prune183.0ms (2.7%)

regimes2.6s (39.3%)

simplify2.0ms (0%)

end252.0ms (3.8%)

Profiling