Details

analyze1.9s (14.1%)

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)

sample2.7s (20%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.6s	8256×	body	128	valid
34.0ms	125×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify50.0ms (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)

localize50.0ms (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)

series113.0ms (0.8%)

Counts

4 → 156

Calls

4 calls:

50.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
39.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
14.0ms	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))
10.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite22.0ms (0.2%)

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))

simplify151.0ms (1.1%)

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

prune236.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	156	4	160
Fresh	1	0	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) (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 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (sqrt.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) (.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))))))
	14.4b	(.f32 (/.f32 1/2 v) (.f32 (exp.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))))))) (exp.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))))))))

Compiler

Compiled 6952 to 3989 computations (42.6% saved)

localize50.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)
✓	0.0b	(+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))
✓	0.1b	(exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
✓	0.3b	(sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))

series215.0ms (1.6%)

Counts

4 → 240

Calls

4 calls:

92.0ms	(sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
52.0ms	(exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
37.0ms	(+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))
34.0ms	(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary32`
17×	`add-sqr-sqrt_binary32`
16×	`add-cube-cbrt_binary32`
9×	`times-frac_binary32`
9×	`add-log-exp_binary32`

Counts

4 → 88

Calls

4 calls:

8.0ms	(exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
7.0ms	(sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
6.0ms	(+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))
5.0ms	(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)

simplify185.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

450×	`times-frac_binary32`
325×	`fma-def_binary32`
288×	`associate-/l*_binary32`
271×	`associate-r_binary32`
256×	`associate-l_binary32`

Counts

328 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	436	9884
1	1301	9259
2	4961	9251
3	5072	9251

prune725.0ms (5.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	332	2	334
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	334	4	338

Error

0.0b

Counts

338 → 4

Alt Table

Status	Error	Program
▶	0.1b	(.f32 (/.f32 1/2 v) (.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (sqrt.f32 (exp.f32 (+.f32 6931/10000 (cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (.f32 (.f32 v v) v))))))))
	14.8b	(.f32 (/.f32 1/2 v) (.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (sqrt.f32 (exp.f32 (/.f32 (+.f32 (pow.f32 6931/10000 3) (pow.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v) 3)) (+.f32 (.f32 6931/10000 6931/10000) (-.f32 (.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v) (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)) (.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) (.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))))))
	14.4b	(.f32 (/.f32 1/2 v) (.f32 (exp.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))))))) (exp.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))))))))

Compiler

Compiled 20705 to 12834 computations (38% saved)

localize92.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f32 (.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (.f32 (*.f32 v v) v))
	0.3b	(sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
✓	0.3b	(sqrt.f32 (exp.f32 (+.f32 6931/10000 (cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (.f32 (*.f32 v v) v))))))
✓	18.6b	(cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (.f32 (*.f32 v v) v)))

series466.0ms (3.5%)

Counts

3 → 180

Calls

3 calls:

209.0ms

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

182.0ms

(/.f32 (*.f32 (*.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (*.f32 (*.f32 v v) v))

75.0ms

(cbrt.f32 (/.f32 (*.f32 (*.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (*.f32 (*.f32 v v) v)))

rewrite60.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-cbrt-cube_binary32`
39×	`add-exp-log_binary32`
28×	`frac-times_binary32`
27×	`flip--_binary32`
27×	`flip3--_binary32`

Counts

3 → 95

Calls

3 calls:

21.0ms

(/.f32 (*.f32 (*.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (*.f32 (*.f32 v v) v))

13.0ms

(cbrt.f32 (/.f32 (*.f32 (*.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) (*.f32 (*.f32 v v) v)))

5.0ms

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

simplify214.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

441×	`fma-def_binary32`
375×	`times-frac_binary32`
224×	`associate-/l*_binary32`
215×	`distribute-rgt-in_binary32`
211×	`distribute-lft-in_binary32`

Counts

275 → 228

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	443	13150
1	1434	12111
2	5059	12111

prune694.0ms (5.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	274	1	275
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	275	4	279

Error

0.0b

Counts

279 → 4

Alt Table

Status	Error	Program
▶	0.0b	(.f32 (/.f32 1/2 v) (.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (.f32 (sqrt.f32 (exp.f32 6931/10000)) (sqrt.f32 (exp.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 3) (pow.f32 v 3))))))))
	14.8b	(.f32 (/.f32 1/2 v) (.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (sqrt.f32 (exp.f32 (/.f32 (+.f32 (pow.f32 6931/10000 3) (pow.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v) 3)) (+.f32 (.f32 6931/10000 6931/10000) (-.f32 (.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v) (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)) (.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) (.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))))))
	14.4b	(.f32 (/.f32 1/2 v) (.f32 (exp.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))))))) (exp.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))))))))

Compiler

Compiled 23252 to 13255 computations (43% saved)

localize95.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 3) (pow.f32 v 3))
✓	0.3b	(sqrt.f32 (exp.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 3) (pow.f32 v 3)))))
	0.3b	(sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
✓	18.6b	(cbrt.f32 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 3) (pow.f32 v 3)))

series404.0ms (3%)

Counts

3 → 180

Calls

3 calls:

178.0ms

(/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 3) (pow.f32 v 3))

143.0ms

(sqrt.f32 (exp.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 3) (pow.f32 v 3)))))

82.0ms

(cbrt.f32 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 3) (pow.f32 v 3)))

rewrite131.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

432×	`times-frac_binary32`
296×	`cbrt-prod_binary32`
230×	`add-sqr-sqrt_binary32`
229×	`*-un-lft-identity_binary32`
229×	`add-cube-cbrt_binary32`

Counts

3 → 517

Calls

3 calls:

24.0ms

(sqrt.f32 (exp.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 3) (pow.f32 v 3)))))

11.0ms

(cbrt.f32 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 3) (pow.f32 v 3)))

9.0ms

(/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 3) (pow.f32 v 3))

simplify452.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

822×	`times-frac_binary32`
498×	`associate-/r*_binary32`
388×	`associate-/l*_binary32`
299×	`fma-def_binary32`
132×	`fma-neg_binary32`

Counts

697 → 516

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	649	26382
1	1338	24803
2	4962	24791
3	5042	24791

prune1.4s (10.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	560	3	563
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	562	5	567

Error

0.0b

Counts

567 → 5

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))))))
	0.0b	(.f32 (/.f32 1/2 v) (.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (.f32 (sqrt.f32 (exp.f32 6931/10000)) (sqrt.f32 (exp.f32 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 v 3/2))) (cbrt.f32 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 3) (pow.f32 v 3/2)))))))))
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (.f32 (sqrt.f32 (exp.f32 6931/10000)) (pow.f32 (exp.f32 (cbrt.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) (pow.f32 (sqrt.f32 v) 3)))) (/.f32 (cbrt.f32 (/.f32 (pow.f32 (cbrt.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1))) 6) (*.f32 v (sqrt.f32 v)))) 2)))))
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (.f32 (sqrt.f32 (exp.f32 6931/10000)) (pow.f32 (exp.f32 (cbrt.f32 (/.f32 1 (.f32 v v)))) (/.f32 (cbrt.f32 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 3) v)) 2)))))
	14.4b	(.f32 (/.f32 1/2 v) (.f32 (exp.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))))))) (exp.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))))))))

Compiler

Compiled 35597 to 23071 computations (35.2% saved)

regimes2.8s (20.7%)

Accuracy

Total 0.0b remaining (30.7%)

Threshold costs 0.0b (30.7%)

Counts

224 → 1

Compiler

Compiled 88663 to 62661 computations (29.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	89
1	45	89
2	49	89
3	51	89
4	52	89
5	51	89

end219.0ms (1.6%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 670 to 440 computations (34.3% saved)

Details

analyze1.9s (14.1%)

sample2.7s (20%)

simplify50.0ms (0.4%)

prune5.0ms (0%)

localize50.0ms (0.4%)

series113.0ms (0.8%)

rewrite22.0ms (0.2%)

simplify151.0ms (1.1%)

prune236.0ms (1.8%)

localize50.0ms (0.4%)

series215.0ms (1.6%)

rewrite30.0ms (0.2%)

simplify185.0ms (1.4%)

prune725.0ms (5.4%)

localize92.0ms (0.7%)

series466.0ms (3.5%)

rewrite60.0ms (0.4%)

simplify214.0ms (1.6%)

prune694.0ms (5.2%)

localize95.0ms (0.7%)

series404.0ms (3%)

rewrite131.0ms (1%)

simplify452.0ms (3.4%)

prune1.4s (10.4%)

regimes2.8s (20.7%)

simplify4.0ms (0%)

end219.0ms (1.6%)

Profiling