Details

analyze1.9s (20.4%)

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 (26.6%)

Results

2.4s	8256×	body	128	valid
33.0ms	121×	body	128	invalid

Compiler

Compiled 138 to 102 computations (26.1% saved)

preprocess62.0ms (0.7%)

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)

simplify25.0ms (0.3%)

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

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))

Compiler

Compiled 100 to 68 computations (32% saved)

localize54.0ms (0.6%)

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

series183.0ms (2%)

Counts

4 → 180

Calls

54 calls:

22.0ms	(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))	v	-inf
20.0ms	(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))	v	inf
12.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))	v	-inf
7.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))	v	inf
6.0ms	(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))	sinTheta_i	0

rewrite86.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

561×	`prod-diff_binary32`
190×	`add-sqr-sqrt_binary32`
177×	`add-cbrt-cube_binary32`
177×	`log1p-expm1-u_binary32`
177×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	81
1	382	81
2	4976	81

Stop Event

1×	node limit

Counts

4 → 133

simplify125.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

389×	`times-frac_binary32`
263×	`associate-/l*_binary32`
262×	`associate-+r+_binary32`
246×	`cancel-sign-sub-inv_binary32`
224×	`fma-def_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	7456
1	983	7024
2	4432	6574

Stop Event

1×	node limit

Counts

313 → 203

prune331.0ms (3.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	199	4	203
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	200	4	204

Error

0.1b

Counts

204 → 4

Alt Table

Status	Error	Program
	0.3b	(pow.f32 (cbrt.f32 (*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))) 3)
	0.2b	(*.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 1/2 v))
	0.3b	(*.f32 (pow.f32 (exp.f32 (pow.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)))) 2)) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (/.f32 1/2 v))
▶	0.1b	(/.f32 (/.f32 (*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))

Compiler

Compiled 8394 to 5012 computations (40.3% saved)

localize55.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 (/.f32 (*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1/2) (sqrt.f32 v)) (sqrt.f32 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	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
	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))))

series113.0ms (1.2%)

Counts

1 → 56

Calls

15 calls:

40.0ms	(/.f32 (/.f32 (*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))	v	-inf
22.0ms	(/.f32 (/.f32 (*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))	v	inf
6.0ms	(/.f32 (/.f32 (*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))	sinTheta_O	0
5.0ms	(/.f32 (/.f32 (*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))	sinTheta_i	0
5.0ms	(/.f32 (/.f32 (*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))	cosTheta_O	0

rewrite38.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

211×	`add-sqr-sqrt_binary32`
197×	`add-cbrt-cube_binary32`
197×	`log1p-expm1-u_binary32`
197×	`expm1-log1p-u_binary32`
196×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	29
1	427	29

Stop Event

1×	node limit

Counts

1 → 45

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary32`
452×	`associate-/r/_binary32`
230×	`times-frac_binary32`
167×	`associate-r_binary32`
160×	`associate-/l/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	2944
1	623	2853
2	2774	2786

Stop Event

1×	node limit

Counts

101 → 70

prune396.0ms (4.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	209	4	213
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	211	6	217

Error

0.1b

Counts

217 → 6

Alt Table

Status	Error	Program
	0.1b	(/.f32 (/.f32 (*.f32 (pow.f32 (cbrt.f32 (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) 1/2) (sqrt.f32 v)) (sqrt.f32 v))
	0.2b	(/.f32 (/.f32 (*.f32 (pow.f32 (exp.f32 (pow.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)))) 2)) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))
	0.1b	(exp.f32 (-.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 1/2)) (log.f32 v)))
▶	0.1b	(/.f32 (/.f32 (*.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)))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))
	0.3b	(pow.f32 (cbrt.f32 (*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))) 3)
	0.2b	(*.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 1/2 v))

Compiler

Compiled 9704 to 5557 computations (42.7% saved)

localize56.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 (/.f32 (*.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)))) 1/2) (sqrt.f32 v)) (sqrt.f32 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	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
✓	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))))

series163.0ms (1.8%)

Counts

2 → 116

Calls

30 calls:

42.0ms	(/.f32 (/.f32 (*.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)))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))	v	-inf
23.0ms	(/.f32 (/.f32 (*.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)))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))	v	inf
9.0ms	(/.f32 (/.f32 (*.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)))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))	cosTheta_O	0
9.0ms	(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))))	v	-inf
7.0ms	(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))))	v	inf

rewrite42.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

222×	`add-sqr-sqrt_binary32`
209×	`log1p-expm1-u_binary32`
209×	`expm1-log1p-u_binary32`
207×	`add-cbrt-cube_binary32`
207×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	52
1	455	52

Stop Event

1×	node limit

Counts

2 → 61

simplify112.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

389×	`times-frac_binary32`
262×	`associate-/l*_binary32`
261×	`associate-+r+_binary32`
228×	`cancel-sign-sub-inv_binary32`
222×	`fma-def_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	270	6054
1	960	5871
2	4362	5871

Stop Event

1×	node limit

Counts

177 → 114

prune381.0ms (4.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	206	6	212

Error

0.1b

Counts

212 → 6

Alt Table

Status	Error	Program
▶	0.1b	(/.f32 (/.f32 (*.f32 (pow.f32 (cbrt.f32 (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) 1/2) (sqrt.f32 v)) (sqrt.f32 v))
	0.2b	(/.f32 (/.f32 (*.f32 (pow.f32 (exp.f32 (pow.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)))) 2)) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))
	0.1b	(exp.f32 (-.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 1/2)) (log.f32 v)))
✓	0.1b	(/.f32 (/.f32 (*.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)))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))
	0.3b	(pow.f32 (cbrt.f32 (*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))) 3)
	0.2b	(*.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 1/2 v))

Compiler

Compiled 9622 to 5469 computations (43.2% saved)

localize64.0ms (0.7%)

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	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
	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))))
✓	0.4b	(cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

series964.0ms (10.5%)

Counts

1 → 60

Calls

15 calls:

107.0ms	(cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))	cosTheta_O	-inf
106.0ms	(cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))	cosTheta_O	inf
104.0ms	(cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))	sinTheta_i	-inf
102.0ms	(cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))	sinTheta_i	inf
102.0ms	(cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))	cosTheta_i	inf

rewrite60.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`prod-diff_binary32`
166×	`add-sqr-sqrt_binary32`
155×	`add-cbrt-cube_binary32`
154×	`log1p-expm1-u_binary32`
154×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	332	25
2	4311	25

Stop Event

1×	node limit

Counts

1 → 22

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-def_binary32`
262×	`times-frac_binary32`
189×	`associate-r_binary32`
185×	`associate-+r+_binary32`
160×	`associate-/l*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	3390
1	713	3306
2	3156	3146

Stop Event

1×	node limit

Counts

82 → 49

prune392.0ms (4.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	2	2	4
Picked	0	1	1
Done	1	0	1
Total	192	6	198

Error

0.1b

Counts

198 → 6

Alt Table

Status	Error	Program
✓	0.1b	(/.f32 (/.f32 (*.f32 (pow.f32 (cbrt.f32 (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) 1/2) (sqrt.f32 v)) (sqrt.f32 v))
	0.1b	(/.f32 (/.f32 (.f32 (pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) 2) 1/3) (cbrt.f32 (cbrt.f32 (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) 1/2) (sqrt.f32 v)) (sqrt.f32 v))
	0.1b	(/.f32 (/.f32 (*.f32 (pow.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))))) 3) 1/2) (sqrt.f32 v)) (sqrt.f32 v))
	0.1b	(exp.f32 (-.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 1/2)) (log.f32 v)))
	0.1b	(/.f32 (/.f32 (*.f32 (pow.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1/3) 3) 1/2) (sqrt.f32 v)) (sqrt.f32 v))
	0.2b	(*.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 1/2 v))

Compiler

Compiled 9796 to 5878 computations (40% saved)

regimes778.0ms (8.5%)

Accuracy

Total 0.1b remaining (54.7%)

Threshold costs 0.1b (54.7%)

Counts

78 → 1

Compiler

Compiled 20914 to 14727 computations (29.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary32`
2×	`*-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	24	43
1	30	43
2	34	43
3	36	43
4	37	43

Stop Event

1×

saturated

end240.0ms (2.6%)

Stop Event

1×

fuel

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 404 to 279 computations (30.9% saved)

Details

analyze1.9s (20.4%)

sample2.4s (26.6%)

preprocess62.0ms (0.7%)

simplify25.0ms (0.3%)

prune4.0ms (0%)

localize54.0ms (0.6%)

series183.0ms (2%)

rewrite86.0ms (0.9%)

simplify125.0ms (1.4%)

prune331.0ms (3.6%)

localize55.0ms (0.6%)

series113.0ms (1.2%)

rewrite38.0ms (0.4%)

simplify64.0ms (0.7%)

prune396.0ms (4.3%)

localize56.0ms (0.6%)

series163.0ms (1.8%)

rewrite42.0ms (0.5%)

simplify112.0ms (1.2%)

prune381.0ms (4.1%)

localize64.0ms (0.7%)

series964.0ms (10.5%)

rewrite60.0ms (0.7%)

simplify74.0ms (0.8%)

prune392.0ms (4.3%)

regimes778.0ms (8.5%)

simplify3.0ms (0%)

end240.0ms (2.6%)

Profiling