Details

analyze97.0ms (1.4%)

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 (27.5%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 111 to 85 computations (23.4% saved)

simplify24.0ms (0.3%)

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	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)))))
▶	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)))))))

Status

Error

Program

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)))))

▶

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)))))))

Compiler

Compiled 148 to 113 computations (23.6% saved)

localize57.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.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))))
✓	0.3b	(/.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)))))))
✓	0.4b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

series96.0ms (1.4%)

Counts

4 → 46

Calls

4 calls:

61.0ms	(/.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)))))))
21.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
9.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
5.0ms	(*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))

rewrite74.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

317×	`log1p-udef_binary32`
180×	`add-sqr-sqrt_binary32`
172×	`log1p-expm1-u_binary32`
172×	`expm1-log1p-u_binary32`
170×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	81
1	372	77
2	5000	77

Stop Event

1×	node limit

Counts

4 → 97

Calls

4 calls:

72.0ms	(*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))
72.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
72.0ms	(/.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)))))))
72.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

582×	`times-frac_binary32`
316×	`cancel-sign-sub-inv_binary32`
254×	`fma-def_binary32`
220×	`associate-r_binary32`
183×	`associate-+r+_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	2362
1	703	2228
2	2767	2103

Stop Event

1×	node limit

Counts

143 → 146

prune209.0ms (3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	134	12	146
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	136	12	148

Error

0.0b

Counts

148 → 12

Alt Table

Status	Error	Program
	0.7b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (sqrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 2))))))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (/.f32 1 (sqrt.f32 (.f32 cosTheta (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (.f32 cosTheta (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32))))))))))
	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))))
	13.7b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (+.f32 c (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) 2))) (-.f32 1 (+.f32 c (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta))))
▶	0.6b	(+.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 5/2 (pow.f32 cosTheta 3)))) (-.f32 (fma.f32 7/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 4)) (+.f32 (fma.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2) (fma.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta) (fma.f32 (.f32 (pow.f32 cosTheta 3) (.f32 c c)) (pow.f32 (PI.f32) 3/2) (.f32 (pow.f32 (PI.f32) 3/2) (.f32 (pow.f32 cosTheta 4) (+.f32 (.f32 3 (.f32 c c)) (.f32 c 6))))))) (.f32 (pow.f32 (PI.f32) 3/2) (+.f32 (.f32 2 (.f32 (pow.f32 cosTheta 3) c)) (.f32 3 (pow.f32 cosTheta 4)))))) (fma.f32 c (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (+.f32 (+.f32 (+.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (.f32 (pow.f32 cosTheta 3) (.f32 (+.f32 1 c) (PI.f32))))) (+.f32 (.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2)) (+.f32 (pow.f32 c 3) (+.f32 (.f32 3 c) 1))) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) 6)))) (.f32 (pow.f32 cosTheta 4) (+.f32 (.f32 3 (.f32 (.f32 c c) (pow.f32 (PI.f32) 2))) (.f32 6 (*.f32 (PI.f32) c))))))))
	0.8b	(*.f32 (pow.f32 (sqrt.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c))) -1) (pow.f32 (sqrt.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c))) -1))
	0.9b	(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c))) 2) -1) (pow.f32 (cbrt.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c))) -1))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (cbrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 3))))))
	0.7b	(pow.f32 (pow.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c)) -1/2) 2)
	1.0b	(pow.f32 (/.f32 1 (cbrt.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c)))) 3)
	18.3b	(pow.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) (+.f32 1 c))) 3) 1/3)
	12.2b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (.f32 (PI.f32) (pow.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) 2)))))))

Compiler

Compiled 5864 to 3831 computations (34.7% saved)

localize289.0ms (4.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f32 (PI.f32) c)
✓	0.4b	(.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 5/2 (pow.f32 cosTheta 3))))
✓	1.0b	(pow.f32 (PI.f32) 2)
✓	1.0b	(pow.f32 (PI.f32) 3/2)

series9.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

6.0ms	(.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 5/2 (pow.f32 cosTheta 3))))
3.0ms	(*.f32 (PI.f32) c)
0.0ms	(pow.f32 (PI.f32) 3/2)
0.0ms	(pow.f32 (PI.f32) 2)

rewrite54.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

265×	`expm1-udef_binary32`
265×	`log1p-udef_binary32`
174×	`fma-neg_binary32`
157×	`log1p-expm1-u_binary32`
157×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	345	29
2	4069	29

Stop Event

1×	node limit

Counts

4 → 79

Calls

4 calls:

52.0ms	(*.f32 (PI.f32) c)
52.0ms	(.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 5/2 (pow.f32 cosTheta 3))))
52.0ms	(pow.f32 (PI.f32) 2)
52.0ms	(pow.f32 (PI.f32) 3/2)

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

818×	`unswap-sqr_binary32`
372×	`sqr-pow_binary32`
301×	`*-commutative_binary32`
296×	`fma-def_binary32`
283×	`cube-prod_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	273
1	29	273
2	61	237
3	156	219
4	355	219
5	878	219
6	1176	219
7	1687	219
8	2974	219
9	3075	219
10	3234	219
11	3443	219
12	3746	219
13	4174	219
14	4738	219

Stop Event

1×	node limit

Counts

103 → 86

prune658.0ms (9.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	164	12	176

Error

0.0b

Counts

176 → 12

Alt Table

Status	Error	Program
▶	0.7b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (sqrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 2))))))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (/.f32 1 (sqrt.f32 (.f32 cosTheta (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (.f32 cosTheta (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32))))))))))
	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))))
	13.7b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (+.f32 c (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) 2))) (-.f32 1 (+.f32 c (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta))))
✓	0.6b	(+.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 5/2 (pow.f32 cosTheta 3)))) (-.f32 (fma.f32 7/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 4)) (+.f32 (fma.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2) (fma.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta) (fma.f32 (.f32 (pow.f32 cosTheta 3) (.f32 c c)) (pow.f32 (PI.f32) 3/2) (.f32 (pow.f32 (PI.f32) 3/2) (.f32 (pow.f32 cosTheta 4) (+.f32 (.f32 3 (.f32 c c)) (.f32 c 6))))))) (.f32 (pow.f32 (PI.f32) 3/2) (+.f32 (.f32 2 (.f32 (pow.f32 cosTheta 3) c)) (.f32 3 (pow.f32 cosTheta 4)))))) (fma.f32 c (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (+.f32 (+.f32 (+.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (.f32 (pow.f32 cosTheta 3) (.f32 (+.f32 1 c) (PI.f32))))) (+.f32 (.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2)) (+.f32 (pow.f32 c 3) (+.f32 (.f32 3 c) 1))) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) 6)))) (.f32 (pow.f32 cosTheta 4) (+.f32 (.f32 3 (.f32 (.f32 c c) (pow.f32 (PI.f32) 2))) (.f32 6 (*.f32 (PI.f32) c))))))))
	0.8b	(*.f32 (pow.f32 (sqrt.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c))) -1) (pow.f32 (sqrt.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c))) -1))
	0.9b	(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c))) 2) -1) (pow.f32 (cbrt.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c))) -1))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (cbrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 3))))))
	0.7b	(pow.f32 (pow.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c)) -1/2) 2)
	1.0b	(pow.f32 (/.f32 1 (cbrt.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c)))) 3)
	18.3b	(pow.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) (+.f32 1 c))) 3) 1/3)
	12.2b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (.f32 (PI.f32) (pow.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) 2)))))))

Compiler

Compiled 25912 to 16120 computations (37.8% saved)

localize65.0ms (0.9%)

Local error

Found 4 expressions with local error:

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

series180.0ms (2.6%)

Counts

4 → 29

Calls

4 calls:

126.0ms	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (sqrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 2))))))
29.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (sqrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 2)))
14.0ms	(pow.f32 (sqrt.f32 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 2)
12.0ms	(.f32 (sqrt.f32 (PI.f32)) (pow.f32 (sqrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 2))

rewrite42.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

193×	`add-sqr-sqrt_binary32`
187×	`log1p-expm1-u_binary32`
187×	`expm1-log1p-u_binary32`
183×	`add-cbrt-cube_binary32`
181×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	81
1	432	77

Stop Event

1×	node limit

Counts

4 → 112

Calls

4 calls:

38.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (sqrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 2)))
38.0ms	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (sqrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 2))))))
38.0ms	(.f32 (sqrt.f32 (PI.f32)) (pow.f32 (sqrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 2))
38.0ms	(pow.f32 (sqrt.f32 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 2)

simplify48.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

582×	`times-frac_binary32`
316×	`cancel-sign-sub-inv_binary32`
240×	`fma-def_binary32`
218×	`associate-r_binary32`
174×	`associate-+r+_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	205	2180
1	682	2046
2	2708	1927

Stop Event

1×	node limit

Counts

141 → 152

prune173.0ms (2.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	153	11	164

Error

0.0b

Counts

164 → 11

Alt Table

Status	Error	Program
✓	0.7b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (sqrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 2))))))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (/.f32 1 (sqrt.f32 (.f32 cosTheta (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (.f32 cosTheta (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32))))))))))
	13.7b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (+.f32 c (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) 2))) (-.f32 1 (+.f32 c (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta))))
✓	0.6b	(+.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 5/2 (pow.f32 cosTheta 3)))) (-.f32 (fma.f32 7/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 4)) (+.f32 (fma.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2) (fma.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta) (fma.f32 (.f32 (pow.f32 cosTheta 3) (.f32 c c)) (pow.f32 (PI.f32) 3/2) (.f32 (pow.f32 (PI.f32) 3/2) (.f32 (pow.f32 cosTheta 4) (+.f32 (.f32 3 (.f32 c c)) (.f32 c 6))))))) (.f32 (pow.f32 (PI.f32) 3/2) (+.f32 (.f32 2 (.f32 (pow.f32 cosTheta 3) c)) (.f32 3 (pow.f32 cosTheta 4)))))) (fma.f32 c (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (+.f32 (+.f32 (+.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (.f32 (pow.f32 cosTheta 3) (.f32 (+.f32 1 c) (PI.f32))))) (+.f32 (.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2)) (+.f32 (pow.f32 c 3) (+.f32 (.f32 3 c) 1))) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) 6)))) (.f32 (pow.f32 cosTheta 4) (+.f32 (.f32 3 (.f32 (.f32 c c) (pow.f32 (PI.f32) 2))) (.f32 6 (*.f32 (PI.f32) c))))))))
	0.8b	(*.f32 (pow.f32 (sqrt.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c))) -1) (pow.f32 (sqrt.f32 (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 1 c))) -1))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (cbrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 3))))))
▶	0.7b	(pow.f32 (pow.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) -1/2) 2)
	1.0b	(pow.f32 (/.f32 1 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))) 3)
	18.3b	(pow.f32 (pow.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) 3) 1/3)
	0.9b	(/.f32 1 (+.f32 1 (+.f32 c (pow.f32 (cbrt.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) 3))))
	12.2b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (.f32 (PI.f32) (pow.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) 2)))))))

Compiler

Compiled 5866 to 3716 computations (36.7% saved)

localize60.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) -1/2)
✓	0.5b	(pow.f32 (pow.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) -1/2) 2)
✓	0.6b	(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta)
✓	0.8b	(sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))

series247.0ms (3.6%)

Counts

4 → 44

Calls

4 calls:

131.0ms	(pow.f32 (pow.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) -1/2) 2)
88.0ms	(pow.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) -1/2)
16.0ms	(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta)
11.0ms	(sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))

rewrite39.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

203×	`add-sqr-sqrt_binary32`
198×	`log1p-expm1-u_binary32`
198×	`expm1-log1p-u_binary32`
193×	`add-cbrt-cube_binary32`
191×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	87
1	428	87

Stop Event

1×	node limit

Counts

4 → 90

Calls

4 calls:

37.0ms	(pow.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) -1/2)
37.0ms	(pow.f32 (pow.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) -1/2) 2)
37.0ms	(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta)
37.0ms	(sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32)))

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-def_binary32`
582×	`associate-r_binary32`
405×	`associate-l_binary32`
357×	`associate-/r*_binary32`
191×	`*-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	500	6606
1	1710	6090

Stop Event

1×	node limit

Counts

134 → 170

prune286.0ms (4.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	170	11	181

Error

0.0b

Counts

181 → 11

Alt Table

Status	Error	Program
✓	0.7b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (sqrt.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) 2))))))
	0.8b	(/.f32 1 (+.f32 1 (+.f32 c (.f32 (/.f32 1 (sqrt.f32 (.f32 cosTheta (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (.f32 cosTheta (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32))))))))))
	1.0b	(pow.f32 (/.f32 1 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))) 3)
	0.7b	(pow.f32 (fabs.f32 (pow.f32 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)))) -1/2)) 2)
	13.7b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (+.f32 c (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) 2))) (-.f32 1 (+.f32 c (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta))))
✓	0.6b	(+.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 5/2 (pow.f32 cosTheta 3)))) (-.f32 (fma.f32 7/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 4)) (+.f32 (fma.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2) (fma.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta) (fma.f32 (.f32 (pow.f32 cosTheta 3) (.f32 c c)) (pow.f32 (PI.f32) 3/2) (.f32 (pow.f32 (PI.f32) 3/2) (.f32 (pow.f32 cosTheta 4) (+.f32 (.f32 3 (.f32 c c)) (.f32 c 6))))))) (.f32 (pow.f32 (PI.f32) 3/2) (+.f32 (.f32 2 (.f32 (pow.f32 cosTheta 3) c)) (.f32 3 (pow.f32 cosTheta 4)))))) (fma.f32 c (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (+.f32 (+.f32 (+.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (.f32 (pow.f32 cosTheta 3) (.f32 (+.f32 1 c) (PI.f32))))) (+.f32 (.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2)) (+.f32 (pow.f32 c 3) (+.f32 (.f32 3 c) 1))) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) 6)))) (.f32 (pow.f32 cosTheta 4) (+.f32 (.f32 3 (.f32 (.f32 c c) (pow.f32 (PI.f32) 2))) (.f32 6 (*.f32 (PI.f32) c))))))))
	12.2b	(.f32 (cbrt.f32 (pow.f32 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)))) -2)) (cbrt.f32 (/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)))))))
	0.7b	(pow.f32 (pow.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (*.f32 (cbrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (cbrt.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) -1/2) 2)
	18.3b	(pow.f32 (pow.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) 3) 1/3)
	0.9b	(/.f32 1 (+.f32 1 (+.f32 c (pow.f32 (cbrt.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) 3))))
	12.2b	(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (sqrt.f32 (.f32 (PI.f32) (pow.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) 2)))))))

Compiler

Compiled 11160 to 7991 computations (28.4% saved)

regimes1.8s (25.8%)

Accuracy

Total 0.4b remaining (89.2%)

Threshold costs 0.4b (89.2%)

Counts

224 → 1

Compiler

Compiled 44554 to 34338 computations (22.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	24	36

Stop Event

1×

saturated

end329.0ms (4.7%)

Compiler: Compiled 511 to 371 computations (27.4% saved)

Details

analyze97.0ms (1.4%)

sample1.9s (27.5%)

simplify24.0ms (0.3%)

prune6.0ms (0.1%)

localize57.0ms (0.8%)

series96.0ms (1.4%)

rewrite74.0ms (1.1%)

simplify52.0ms (0.8%)

prune209.0ms (3%)

localize289.0ms (4.2%)

series9.0ms (0.1%)

rewrite54.0ms (0.8%)

simplify62.0ms (0.9%)

prune658.0ms (9.5%)

localize65.0ms (0.9%)

series180.0ms (2.6%)

rewrite42.0ms (0.6%)

simplify48.0ms (0.7%)

prune173.0ms (2.5%)

localize60.0ms (0.9%)

series247.0ms (3.6%)

rewrite39.0ms (0.6%)

simplify80.0ms (1.2%)

prune286.0ms (4.1%)

regimes1.8s (25.8%)

simplify2.0ms (0%)

end329.0ms (4.7%)

Profiling