Details

analyze2.4s (10.3%)

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 (12.3%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.7s	8256×	body	128	valid
38.0ms	129×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify61.0ms (0.3%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(*.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)))))
▶	0.2b	(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

0.2b

(*.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)))))

▶

0.2b

(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)

localize69.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))))
✓	0.1b	(log.f32 (/.f32 1 (*.f32 2 v)))
✓	6.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	6.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series118.0ms (0.5%)

Counts

4 → 72

Calls

4 calls:

64.0ms	(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)))))
28.0ms	(log.f32 (/.f32 1 (*.f32 2 v)))
13.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
12.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite178.0ms (0.8%)

Algorithm

4×	egg-rewrite

Rules

61×	`egg`
61×	`egg`
53×	`egg`
22×	`egg`

Counts

4 → 197

Calls

4 calls:

47.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
47.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
42.0ms	(log.f32 (/.f32 1 (*.f32 2 v)))
38.0ms	(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)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	125	7
2	1688	7
3	5384	7
0	6	7
1	125	7
2	1688	7
3	5384	7
0	7	6
1	140	6
2	1450	6
3	5189	6
0	22	30
1	505	30
2	5026	30

simplify131.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

468×	`times-frac_binary32`
309×	`associate-r_binary32`
267×	`associate-/l*_binary32`
241×	`associate-+r+_binary32`
240×	`associate-/r*_binary32`

Counts

269 → 230

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	4691
1	865	4599
2	4329	4301
3	5092	4301

prune284.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	226	4	230
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	228	4	232

Error

0.1b

Counts

232 → 4

Alt Table

Status	Error	Program
	0.2b	(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) 2) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))))
	0.3b	(pow.f32 (E.f32) (+.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1/2 v))))
	0.2b	(.f32 (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 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) (-.f32 (log.f32 (/.f32 1/2 (pow.f32 (cbrt.f32 v) 2))) (log.f32 (cbrt.f32 v)))))

Compiler

Compiled 9397 to 5582 computations (40.6% saved)

localize80.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f32 (log.f32 (/.f32 1/2 (pow.f32 (cbrt.f32 v) 2))) (log.f32 (cbrt.f32 v)))
✓	0.5b	(pow.f32 (cbrt.f32 v) 2)
	6.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	6.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series1.8s (7.7%)

Counts

2 → 24

Calls

2 calls:

1.7s	(-.f32 (log.f32 (/.f32 1/2 (pow.f32 (cbrt.f32 v) 2))) (log.f32 (cbrt.f32 v)))
42.0ms	(pow.f32 (cbrt.f32 v) 2)

rewrite147.0ms (0.6%)

Algorithm

2×	egg-rewrite

Rules

138×	`egg`
43×	`egg`

Counts

2 → 181

Calls

2 calls:

71.0ms	(pow.f32 (cbrt.f32 v) 2)
69.0ms	(-.f32 (log.f32 (/.f32 1/2 (pow.f32 (cbrt.f32 v) 2))) (log.f32 (cbrt.f32 v)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	99	4
2	936	4
3	4427	4
4	5288	4
0	10	16
1	214	6
2	2469	6
3	5098	6

simplify56.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-neg_binary32`
529×	`log-prod_binary32`
464×	`unswap-sqr_binary32`
294×	`associate-l_binary32`
268×	`sub-neg_binary32`

Counts

205 → 187

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	428
1	88	416
2	207	408
3	656	376
4	2669	372
5	4935	372

prune441.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	309	0	309
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	309	4	313

Error

0.1b

Counts

313 → 4

Alt Table

Status	Error	Program
▶	0.2b	(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) 2) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))))
	0.3b	(pow.f32 (E.f32) (+.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1/2 v))))
	0.2b	(.f32 (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 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) (-.f32 (log.f32 (/.f32 1/2 (pow.f32 (cbrt.f32 v) 2))) (log.f32 (cbrt.f32 v)))))

Compiler

Compiled 11445 to 5723 computations (50% saved)

localize66.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))
✓	0.1b	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
✓	0.2b	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
✓	2.6b	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

series3.1s (13.7%)

Counts

4 → 232

Calls

4 calls:

2.9s	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
152.0ms	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
60.0ms	(exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))
25.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

rewrite297.0ms (1.3%)

Algorithm

4×	egg-rewrite

Rules

72×	`egg`
26×	`egg`
24×	`egg`
23×	`egg`

Counts

4 → 145

Calls

4 calls:

77.0ms	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
77.0ms	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
74.0ms	(exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))
65.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	223	13
2	3112	13
3	4973	13
0	20	29
1	453	29
2	4976	29
3	5884	29
0	19	27
1	435	27
2	4899	27
3	5821	27
0	16	21
1	367	21
2	4789	21
3	5276	21

simplify198.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

521×	`associate-/l*_binary32`
502×	`fma-def_binary32`
481×	`associate-/r*_binary32`
405×	`associate-l_binary32`
239×	`*-commutative_binary32`

Counts

377 → 239

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	585	12847
1	1963	12736
2	5412	12736

prune1.4s (6.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	474	4	478
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	476	6	482

Error

0.0b

Counts

482 → 6

Alt Table

Status	Error	Program
	0.2b	(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) -1) v) 6931/10000)))) 2) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))))
	0.3b	(pow.f32 (E.f32) (+.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1/2 v))))
	0.2b	(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) 2) (.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) v) 1/3) (cbrt.f32 1/2)))
	0.2b	(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) 2) (cbrt.f32 (.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) -1) v) 6931/10000)))))
✓	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) (-.f32 (log.f32 (/.f32 1/2 (pow.f32 (cbrt.f32 v) 2))) (log.f32 (cbrt.f32 v)))))
▶	0.2b	(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) 2) (.f32 (pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))) 2/3) 1/3) (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000)))))))

Compiler

Compiled 36632 to 22270 computations (39.2% saved)

localize117.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))))
	0.2b	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
✓	0.3b	(pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))) 2/3)
	2.6b	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

series6.2s (27.2%)

Counts

2 → 120

Calls

2 calls:

3.3s

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

2.9s

(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))) 2/3)

rewrite147.0ms (0.6%)

Algorithm

2×	egg-rewrite

Rules

24×	`egg`
23×	`egg`

Counts

2 → 47

Calls

2 calls:

76.0ms

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

69.0ms

(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))) 2/3)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	30
1	455	28
2	4796	28
3	4935	28
0	19	29
1	423	27
2	4835	27
3	5634	27

simplify216.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

553×	`fma-def_binary32`
507×	`associate-/l*_binary32`
498×	`associate-/r*_binary32`
266×	`*-commutative_binary32`
157×	`associate-*l/_binary32`

Counts

167 → 120

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	626	10620
1	2123	10316
2	5007	10316

prune995.0ms (4.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	256	5	261

Error

0.0b

Counts

261 → 5

Alt Table

Status	Error	Program
	0.2b	(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) -1) v) 6931/10000)))) 2) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))))
	0.3b	(pow.f32 (E.f32) (+.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1/2 v))))
	0.2b	(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) 2) (cbrt.f32 (.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) -1) v) 6931/10000)))))
	0.2b	(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) 2) (.f32 (pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))) 2/3) 1/3) (cbrt.f32 (/.f32 (cbrt.f32 (.f32 1/2 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v) 6931/10000)))) (cbrt.f32 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) (-.f32 (log.f32 (/.f32 1/2 (pow.f32 (cbrt.f32 v) 2))) (log.f32 (cbrt.f32 v)))))

Compiler

Compiled 28783 to 18800 computations (34.7% saved)

regimes1.4s (6.2%)

Accuracy

Total 0.0b remaining (46.9%)

Threshold costs 0.0b (46.9%)

Counts

105 → 1

Compiler

Compiled 41511 to 29284 computations (29.5% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	47
1	38	47
2	52	47
3	66	47
4	75	47
5	80	47
6	82	47
7	80	47

end167.0ms (0.7%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 442 to 310 computations (29.9% saved)

Details

analyze2.4s (10.3%)

sample2.8s (12.3%)

simplify61.0ms (0.3%)

prune5.0ms (0%)

localize69.0ms (0.3%)

series118.0ms (0.5%)

rewrite178.0ms (0.8%)

simplify131.0ms (0.6%)

prune284.0ms (1.2%)

localize80.0ms (0.4%)

series1.8s (7.7%)

rewrite147.0ms (0.6%)

simplify56.0ms (0.2%)

prune441.0ms (1.9%)

localize66.0ms (0.3%)

series3.1s (13.7%)

rewrite297.0ms (1.3%)

simplify198.0ms (0.9%)

prune1.4s (6.1%)

localize117.0ms (0.5%)

series6.2s (27.2%)

rewrite147.0ms (0.6%)

simplify216.0ms (0.9%)

prune995.0ms (4.3%)

regimes1.4s (6.2%)

simplify5.0ms (0%)

end167.0ms (0.7%)

Profiling