Details

analyze2.1s (17%)

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)

sample3.1s (25.3%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

3.0s	8256×	body	128	valid
40.0ms	140×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify49.0ms (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	(*.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)))))
✓	0.0b	(-.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))))

series288.0ms (2.4%)

Counts

4 → 180

Calls

4 calls:

145.0ms	(*.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)))))
81.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
53.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
9.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite102.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

561×	`prod-diff_binary32`
190×	`add-sqr-sqrt_binary32`
177×	`log1p-expm1-u_binary32`
177×	`expm1-log1p-u_binary32`
176×	`add-log-exp_binary32`

Counts

4 → 134

Calls

4 calls:

98.0ms	(*.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)))))
98.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
98.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
98.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	81
1	382	81
2	4753	81
3	5777	81
0	0	0
1	0	0

simplify144.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

314 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	7456
1	911	7024
2	4130	6570
3	5010	6570

prune322.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	197	5	202
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	199	5	204

Error

0.1b

Counts

204 → 5

Alt Table

Status	Error	Program
	0.1b	(*.f32 (/.f32 1/2 v) (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))
	0.4b	(pow.f32 (pow.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) 1/3)
	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) (pow.f32 (sqrt.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))
	0.1b	(exp.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 (/.f32 1/2 v))))

Compiler

Compiled 8406 to 5048 computations (39.9% saved)

localize57.0ms (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	(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	(sqrt.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)))))

series91.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

91.0ms

(sqrt.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)))))

rewrite66.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

552×	`prod-diff_binary32`
166×	`add-sqr-sqrt_binary32`
155×	`log1p-expm1-u_binary32`
155×	`expm1-log1p-u_binary32`
154×	`add-log-exp_binary32`

Counts

1 → 24

Calls

1 calls:

65.0ms

(sqrt.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)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	333	25
2	4109	25
3	5154	25
0	0	0
1	0	0

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

890×	`associate-/r*_binary32`
355×	`associate-/r/_binary32`
251×	`cancel-sign-sub-inv_binary32`
218×	`fma-def_binary32`
174×	`times-frac_binary32`

Counts

48 → 47

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	2608
1	591	2198
2	2576	1914
3	6036	1914

prune340.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	189	5	194

Error

0.1b

Counts

194 → 5

Alt Table

Status	Error	Program
	0.1b	(*.f32 (/.f32 1/2 v) (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))
	0.4b	(pow.f32 (pow.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) 1/3)
	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 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))
▶	0.1b	(*.f32 (/.f32 1/2 v) (pow.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)))) 1/4) 2) 2))

Compiler

Compiled 8858 to 5491 computations (38% saved)

localize69.0ms (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))))
✓	1.0b	(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)))) 1/4)

series1.5s (12.4%)

Counts

1 → 60

Calls

1 calls:

1.5s	(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)))) 1/4)

rewrite61.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

552×	`prod-diff_binary32`
178×	`add-sqr-sqrt_binary32`
169×	`log1p-expm1-u_binary32`
169×	`expm1-log1p-u_binary32`
166×	`add-log-exp_binary32`

Counts

1 → 17

Calls

1 calls:

60.0ms

(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)))) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	362	26
2	4355	26
3	5341	26
0	0	0
1	0	0

simplify98.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-def_binary32`
421×	`associate-/r/_binary32`
254×	`times-frac_binary32`
179×	`associate-r_binary32`
163×	`fma-neg_binary32`

Counts

77 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	3402
1	570	3302
2	2630	3228
3	4967	3228
4	5073	3228

prune407.0ms (3.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	181	3	184
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	182	7	189

Error

0.0b

Counts

189 → 7

Alt Table

Status	Error	Program
	0.4b	(*.f32 (/.f32 1/2 v) (pow.f32 (pow.f32 (pow.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)))) 3) 1/3) 1/4) 2) 2))
▶	0.1b	(exp.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 (/.f32 1/2 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) (pow.f32 (pow.f32 (pow.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)))) 1/4) 2) 2))
	0.2b	(*.f32 (/.f32 1/2 v) (pow.f32 (pow.f32 (pow.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))))) 1/4) 2) 2))
✓	0.1b	(*.f32 (/.f32 1/2 v) (pow.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)))) 1/4) 2) 2))
	0.4b	(pow.f32 (pow.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) 1/3)

Compiler

Compiled 9224 to 5970 computations (35.3% saved)

localize53.0ms (0.4%)

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	(+.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 (/.f32 1/2 v)))
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
✓	0.1b	(exp.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 (/.f32 1/2 v))))

series268.0ms (2.2%)

Counts

2 → 120

Calls

2 calls:

209.0ms

(+.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 (/.f32 1/2 v)))

59.0ms

(exp.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 (/.f32 1/2 v))))

rewrite82.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

527×	`prod-diff_binary32`
204×	`add-sqr-sqrt_binary32`
192×	`log1p-expm1-u_binary32`
192×	`expm1-log1p-u_binary32`
190×	`add-log-exp_binary32`

Counts

2 → 63

Calls

2 calls:

79.0ms

(+.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 (/.f32 1/2 v)))

79.0ms

(exp.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 (/.f32 1/2 v))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	58
1	409	58
2	4910	58
3	5881	58
0	0	0
1	0	0

simplify141.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

183 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	285	6298
1	948	5872
2	4518	5432
3	5001	5432

prune457.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	206	7	213

Error

0.0b

Counts

213 → 7

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	(exp.f32 (fma.f32 (pow.f32 (cbrt.f32 (log.f32 (/.f32 1/2 v))) 2) (cbrt.f32 (log.f32 (/.f32 1/2 v))) (-.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) (pow.f32 (pow.f32 (pow.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)))) 1/4) 2) 2))
	0.4b	(*.f32 (/.f32 1/2 v) (pow.f32 (pow.f32 (pow.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)))) 3) 1/3) 1/4) 2) 2))
	0.2b	(*.f32 (/.f32 1/2 v) (pow.f32 (pow.f32 (pow.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))))) 1/4) 2) 2))
✓	0.1b	(*.f32 (/.f32 1/2 v) (pow.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)))) 1/4) 2) 2))
	0.4b	(pow.f32 (pow.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) 1/3)

Compiler

Compiled 8974 to 5524 computations (38.4% saved)

regimes1.9s (15.9%)

Accuracy

Total 0.0b remaining (34%)

Threshold costs 0.0b (34%)

Counts

199 → 1

Compiler

Compiled 48207 to 34882 computations (27.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary32`
3×	`*-commutative_binary32`
2×	`sub-neg_binary32`
1×	`distribute-neg-frac_binary32`
1×	`neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	33
1	27	33
2	33	33
3	35	33
4	36	33
5	34	33

end340.0ms (2.8%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 400 to 304 computations (24% saved)

Details

analyze2.1s (17%)

sample3.1s (25.3%)

simplify49.0ms (0.4%)

prune5.0ms (0%)

localize50.0ms (0.4%)

series288.0ms (2.4%)

rewrite102.0ms (0.8%)

simplify144.0ms (1.2%)

prune322.0ms (2.7%)

localize57.0ms (0.5%)

series91.0ms (0.7%)

rewrite66.0ms (0.5%)

simplify66.0ms (0.5%)

prune340.0ms (2.8%)

localize69.0ms (0.6%)

series1.5s (12.4%)

rewrite61.0ms (0.5%)

simplify98.0ms (0.8%)

prune407.0ms (3.4%)

localize53.0ms (0.4%)

series268.0ms (2.2%)

rewrite82.0ms (0.7%)

simplify141.0ms (1.2%)

prune457.0ms (3.8%)

regimes1.9s (15.9%)

simplify3.0ms (0%)

end340.0ms (2.8%)

Profiling