Details

analyze2.1s (15.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	3%	97%	0
0%	3%	97%	1
0%	3%	97%	2
0%	3%	97%	3
0%	3%	97%	4
0%	3%	97%	5
0%	1.5%	98.5%	6
0%	1.5%	98.5%	7
0%	1.5%	98.5%	8
0%	1.5%	98.5%	9
0%	1.5%	98.5%	10
0.6%	0.9%	98.5%	11
0.6%	0.9%	98.5%	12
0.6%	0.9%	98.5%	13
0.6%	0.9%	98.5%	14

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample2.8s (21%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.7s	8256×	body	128	valid
38.0ms	134×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify48.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-neg_binary32`
718×	`fma-def_binary32`
560×	`exp-diff_binary32`
512×	`exp-sum_binary32`
448×	`sub-neg_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	53	33
2	145	31
3	532	29
4	2119	29
5	4431	29
6	4975	29

prune5.0ms (0%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	0.1b	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))

Status

Error

Program

▶

0.1b

(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

0.1b

(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize57.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))
✓	0.0b	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
✓	0.1b	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
✓	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

series125.0ms (0.9%)

Counts

4 → 156

Calls

4 calls:

52.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
46.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
15.0ms	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))
11.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary32`
24×	`add-sqr-sqrt_binary32`
20×	`add-cube-cbrt_binary32`
18×	`prod-diff_binary32`
14×	`exp-sum_binary32`

Counts

4 → 83

Calls

4 calls:

4.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
3.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
0.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
0.0ms	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))

simplify167.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

373×	`distribute-rgt-in_binary32`
252×	`times-frac_binary32`
214×	`fma-neg_binary32`
180×	`associate-r_binary32`
152×	`associate-+r+_binary32`

Counts

239 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	6496
1	704	5860
2	3071	5155
3	4888	5155
4	4936	5155

prune249.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	158	4	162

Error

0.0b

Counts

162 → 4

Alt Table

Status	Error	Program
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
▶	0.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	0.1b	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
	3.2b	(.f32 (/.f32 1/2 v) (.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (exp.f32 (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

Compiler

Compiled 6832 to 3927 computations (42.5% saved)

localize58.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))
	0.0b	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
✓	0.1b	(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

series61.0ms (0.5%)

Counts

1 → 60

Calls

1 calls:

61.0ms

(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`unpow-prod-up_binary32`
12×	`*-un-lft-identity_binary32`
12×	`add-sqr-sqrt_binary32`
10×	`add-cube-cbrt_binary32`
9×	`prod-diff_binary32`

Counts

1 → 37

Calls

1 calls:

4.0ms

(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

simplify104.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-def_binary32`
252×	`times-frac_binary32`
220×	`associate-/l/_binary32`
167×	`associate-r_binary32`
166×	`associate-/l*_binary32`

Counts

97 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	262	4140
1	685	4037
2	2826	3929
3	4927	3929

prune346.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	164	6	170

Error

0.0b

Counts

170 → 6

Alt Table

Status	Error	Program
	0.1b	(.f32 (/.f32 1/2 v) (pow.f32 (pow.f32 (E.f32) (.f32 (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
✓	0.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
▶	0.1b	(.f32 (/.f32 1/2 v) (.f32 (*.f32 (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
	13.6b	(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (E.f32) (fma.f32 1 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (neg.f32 (.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (pow.f32 (E.f32) (fma.f32 (neg.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))
	3.2b	(.f32 (/.f32 1/2 v) (.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (exp.f32 (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

Compiler

Compiled 7529 to 4179 computations (44.5% saved)

localize72.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
	0.1b	(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
✓	0.5b	(cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

series1.6s (11.9%)

Counts

1 → 60

Calls

1 calls:

1.6s	(cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`cbrt-prod_binary32`
14×	`unpow-prod-up_binary32`
10×	`*-un-lft-identity_binary32`
10×	`add-sqr-sqrt_binary32`
10×	`add-cube-cbrt_binary32`

Counts

1 → 32

Calls

1 calls:

3.0ms

(cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

simplify142.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-def_binary32`
262×	`times-frac_binary32`
197×	`associate-r_binary32`
181×	`associate-+r+_binary32`
173×	`associate-/l*_binary32`

Counts

92 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	305	4456
1	785	4412
2	3135	4241
3	4891	4185
4	4938	4185

prune2.1s (15.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	660	3	663
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	664	5	669

Error

0.0b

Counts

669 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	0.6b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (pow.f32 (E.f32) (/.f32 (-.f32 (.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (pow.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6)) (+.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (.f32 (cbrt.f32 (sqrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (sqrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))))
▶	0.1b	(.f32 (/.f32 1/2 v) (.f32 (*.f32 (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
	3.2b	(.f32 (/.f32 1/2 v) (.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (exp.f32 (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

Compiler

Compiled 58217 to 31041 computations (46.7% saved)

localize85.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
✓	0.5b	(cbrt.f32 (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	0.5b	(cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

series742.0ms (5.5%)

Counts

2 → 52

Calls

2 calls:

723.0ms	(cbrt.f32 (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
19.0ms	(exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`exp-sum_binary32`
20×	`*-un-lft-identity_binary32`
20×	`add-sqr-sqrt_binary32`
18×	`prod-diff_binary32`
18×	`add-cube-cbrt_binary32`

Counts

2 → 57

Calls

2 calls:

6.0ms	(cbrt.f32 (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
4.0ms	(exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

simplify100.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

754×	`associate-/r*_binary32`
580×	`fma-def_binary32`
319×	`associate-/r/_binary32`
187×	`times-frac_binary32`
172×	`cancel-sign-sub-inv_binary32`

Counts

109 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	3971
1	558	3694
2	2237	3210
3	5534	3210

prune1.0s (7.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	269	2	271
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	270	6	276

Error

0.0b

Counts

276 → 6

Alt Table

Status	Error	Program
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (.f32 (neg.f32 (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))))
	11.8b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (.f32 (cbrt.f32 (exp.f32 (fma.f32 1 6931/10000 (neg.f32 (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))) (cbrt.f32 (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (*.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))))))
✓	0.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	0.6b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (pow.f32 (E.f32) (/.f32 (-.f32 (.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (pow.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6)) (+.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (.f32 (cbrt.f32 (sqrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (sqrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))))
✓	0.1b	(.f32 (/.f32 1/2 v) (.f32 (*.f32 (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))

Compiler

Compiled 22731 to 13003 computations (42.8% saved)

regimes1.1s (7.8%)

Accuracy

Total 0.0b remaining (23.8%)

Threshold costs 0.0b (23.8%)

Counts

79 → 1

Compiler

Compiled 31433 to 20241 computations (35.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`
3×	`+-commutative_binary32`
3×	`sub-neg_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	75
1	36	75
2	41	75
3	43	75
4	44	75
5	43	75

end291.0ms (2.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 812 to 492 computations (39.4% saved)

Details

analyze2.1s (15.8%)

sample2.8s (21%)

simplify48.0ms (0.4%)

prune5.0ms (0%)

localize57.0ms (0.4%)

series125.0ms (0.9%)

rewrite16.0ms (0.1%)

simplify167.0ms (1.2%)

prune249.0ms (1.8%)

localize58.0ms (0.4%)

series61.0ms (0.5%)

rewrite8.0ms (0.1%)

simplify104.0ms (0.8%)

prune346.0ms (2.6%)

localize72.0ms (0.5%)

series1.6s (11.9%)

rewrite9.0ms (0.1%)

simplify142.0ms (1.1%)

prune2.1s (15.8%)

localize85.0ms (0.6%)

series742.0ms (5.5%)

rewrite16.0ms (0.1%)

simplify100.0ms (0.7%)

prune1.0s (7.5%)

regimes1.1s (7.8%)

simplify4.0ms (0%)

end291.0ms (2.2%)

Profiling