Details

analyze1.9s (14.3%)

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)

sample2.4s (17.8%)

Results

2.4s	8256×	body	128	valid
37.0ms	137×	body	128	invalid

Compiler

Compiled 138 to 102 computations (26.1% saved)

preprocess54.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

880×	`fma-neg_binary32`
278×	`associate-+l-_binary32`
233×	`associate-+l+_binary32`
231×	`associate-+r-_binary32`
214×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	385
1	327	363
2	978	341
3	4387	330
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

696×	`fma-def_binary32`
512×	`exp-sum_binary32`
492×	`fma-neg_binary32`
429×	`exp-diff_binary32`
212×	`times-frac_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	53	33
2	147	31
3	584	29
4	2863	29

Stop Event

1×	node limit

Counts

1 → 2

prune8.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	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)))))

Compiler

Compiled 110 to 78 computations (29.1% saved)

localize65.0ms (0.5%)

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	(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000)
✓	7.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	8.6b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

series104.0ms (0.8%)

Counts

4 → 120

Calls

48 calls:

10.0ms	(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)))))	v	-inf
8.0ms	(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)))))	v	inf
5.0ms	(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)))))	sinTheta_i	0
4.0ms	(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)))))	sinTheta_O	0
4.0ms	(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)))))	cosTheta_i	0

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

253×	`add-sqr-sqrt_binary32`
242×	`log1p-expm1-u_binary32`
242×	`expm1-log1p-u_binary32`
241×	`add-cbrt-cube_binary32`
236×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	66
1	507	66

Stop Event

1×	node limit

Counts

4 → 77

simplify102.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	269	6010
1	906	5850
2	4631	4832

Stop Event

1×	node limit

Counts

197 → 124

prune155.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	123	2	125

Error

0.1b

Counts

125 → 2

Alt Table

Status	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)))))
▶	0.5b	(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))) 3) 1/3)

Status

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)))))

▶

0.5b

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

Compiler

Compiled 5937 to 3786 computations (36.2% saved)

localize60.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f32 (/.f32 1 v) 6931/10000)
✓	0.1b	(exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))
✓	0.5b	(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))) 3) 1/3)
✓	3.8b	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

series1.1s (8.5%)

Counts

4 → 175

Calls

48 calls:

266.0ms	(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))) 3) 1/3)	v	-inf
128.0ms	(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))) 3) 1/3)	v	inf
89.0ms	(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))) 3) 1/3)	sinTheta_i	inf
82.0ms	(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))) 3) 1/3)	cosTheta_i	-inf
70.0ms	(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))) 3) 1/3)	sinTheta_i	-inf

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

244×	`add-sqr-sqrt_binary32`
239×	`log1p-expm1-u_binary32`
239×	`expm1-log1p-u_binary32`
234×	`add-cbrt-cube_binary32`
228×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	74
1	516	74

Stop Event

1×	node limit

Counts

4 → 77

simplify244.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

793×	`associate-/l*_binary32`
739×	`fma-def_binary32`
257×	`*-commutative_binary32`
181×	`+-commutative_binary32`
147×	`associate-+r+_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	705	11163
1	2630	11006

Stop Event

1×	node limit

Counts

252 → 152

prune348.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	151	3	154

Error

0.1b

Counts

154 → 3

Alt Table

Status	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)))))
✓	0.5b	(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))) 3) 1/3)
▶	0.3b	(.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))) 3/2)) (cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))) 3/2)))

Compiler

Compiled 11962 to 8291 computations (30.7% saved)

localize69.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000)
✓	0.1b	(exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))
✓	0.4b	(cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))) 3/2))
	3.8b	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

series352.0ms (2.6%)

Counts

3 → 168

Calls

45 calls:

49.0ms	(cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))) 3/2))	v	inf
48.0ms	(cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))) 3/2))	v	-inf
25.0ms	(+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000)	cosTheta_O	0
17.0ms	(exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))	sinTheta_i	0
13.0ms	(cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))) 3/2))	sinTheta_O	0

rewrite51.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

244×	`add-sqr-sqrt_binary32`
238×	`log1p-expm1-u_binary32`
238×	`expm1-log1p-u_binary32`
235×	`add-cbrt-cube_binary32`
229×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	81
1	503	78

Stop Event

1×	node limit

Counts

3 → 68

simplify137.0ms (1%)

Algorithm

1×	egg-herbie

Rules

331×	`times-frac_binary32`
312×	`cancel-sign-sub-inv_binary32`
230×	`associate-/l*_binary32`
207×	`fma-def_binary32`
204×	`associate-r_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	296	7991
1	975	7969
2	4314	6815

Stop Event

1×	node limit

Counts

236 → 132

prune659.0ms (4.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	312	2	314
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	313	4	317

Error

0.0b

Counts

317 → 4

Alt Table

Status	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)))))
	0.3b	(.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))) 3/2)) (cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))) 3/2)))
✓	0.5b	(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))) 3) 1/3)
▶	0.3b	(.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))) 3/2)) (exp.f32 (log.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))))))))

Compiler

Compiled 21668 to 12798 computations (40.9% saved)

localize103.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))))
	0.4b	(cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))) 3/2))
	3.8b	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
✓	5.7b	(log.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))))))

series3.7s (27.6%)

Counts

2 → 96

Calls

30 calls:

396.0ms	(log.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))))))	cosTheta_i	inf
342.0ms	(log.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))))))	sinTheta_i	0
302.0ms	(log.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))))))	cosTheta_O	-inf
301.0ms	(log.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))))))	cosTheta_i	-inf
282.0ms	(log.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))))))	sinTheta_O	0

rewrite37.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

232×	`add-sqr-sqrt_binary32`
220×	`add-cbrt-cube_binary32`
220×	`log1p-expm1-u_binary32`
220×	`expm1-log1p-u_binary32`
217×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	66
1	472	65

Stop Event

1×	node limit

Counts

2 → 46

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

463×	`fma-def_binary32`
401×	`*-commutative_binary32`
344×	`associate-/l*_binary32`
233×	`times-frac_binary32`
211×	`cancel-sign-sub-inv_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	4548
1	394	4528
2	1244	4124
3	2817	4108

Stop Event

1×	node limit

Counts

142 → 78

prune358.0ms (2.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	173	5	178

Error

0.0b

Counts

178 → 5

Alt Table

Status	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)))))
	0.3b	(.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))) 3/2)) (cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))) 3/2)))
	0.1b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))))))) (exp.f32 (log.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))))))))
✓	0.5b	(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000)))) 3) 1/3)
✓	0.3b	(.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (pow.f32 v -1)) 6931/10000))) 3/2)) (exp.f32 (log.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))))))))

Compiler

Compiled 11187 to 6554 computations (41.4% saved)

regimes1.0s (7.7%)

Accuracy

Total 0.0b remaining (20.7%)

Threshold costs 0.0b (20.7%)

Counts

98 → 1

Compiler

Compiled 30549 to 22507 computations (26.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary32`
7×	`*-commutative_binary32`
6×	`sub-neg_binary32`
4×	`neg-sub0_binary32`
4×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	32
1	37	32
2	50	32
3	58	32
4	63	32
5	64	32

Stop Event

1×

saturated

end146.0ms (1.1%)

Stop Event

1×

fuel

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 373 to 262 computations (29.8% saved)

Details

analyze1.9s (14.3%)

sample2.4s (17.8%)

preprocess54.0ms (0.4%)

simplify22.0ms (0.2%)

prune8.0ms (0.1%)

localize65.0ms (0.5%)

series104.0ms (0.8%)

rewrite40.0ms (0.3%)

simplify102.0ms (0.8%)

prune155.0ms (1.1%)

localize60.0ms (0.4%)

series1.1s (8.5%)

rewrite40.0ms (0.3%)

simplify244.0ms (1.8%)

prune348.0ms (2.6%)

localize69.0ms (0.5%)

series352.0ms (2.6%)

rewrite51.0ms (0.4%)

simplify137.0ms (1%)

prune659.0ms (4.9%)

localize103.0ms (0.8%)

series3.7s (27.6%)

rewrite37.0ms (0.3%)

simplify96.0ms (0.7%)

prune358.0ms (2.6%)

regimes1.0s (7.7%)

simplify3.0ms (0%)

end146.0ms (1.1%)

Profiling