Details

analyze2.0s (10.4%)

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)

sample2.5s (13.1%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.4s	8256×	body	128	valid
27.0ms	110×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify51.0ms (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

prune4.0ms (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)

localize48.0ms (0.3%)

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)))))
✓	0.1b	(-.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)

series173.0ms (0.9%)

Counts

4 → 180

Calls

4 calls:

93.0ms	(*.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)))))
37.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
34.0ms	(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)

rewrite94.0ms (0.5%)

Algorithm

1×	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 → 138

Calls

4 calls:

91.0ms	(*.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)))))
91.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
91.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
91.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

Iterations

Useful iterations: 0 (0.0ms)

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

simplify140.0ms (0.7%)

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

318 → 205

Iterations

Useful iterations: 2 (0.0ms)

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

prune302.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	200	5	205
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	202	5	207

Error

0.1b

Counts

207 → 5

Alt Table

Status	Error	Program
	0.1b	(/.f32 1 (/.f32 v (*.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)))
	0.4b	(*.f32 (/.f32 1/2 v) (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))
▶	0.1b	(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)
	0.3b	(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)))))

Compiler

Compiled 8470 to 5085 computations (40% saved)

localize53.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(-.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)
✓	0.3b	(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)))

series1.3s (6.8%)

Counts

1 → 60

Calls

1 calls:

1.3s	(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)))

rewrite67.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`prod-diff_binary32`
198×	`add-sqr-sqrt_binary32`
184×	`log1p-expm1-u_binary32`
184×	`expm1-log1p-u_binary32`
183×	`add-cbrt-cube_binary32`

Counts

1 → 24

Calls

1 calls:

66.0ms

(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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	400	31
2	4964	31
3	5901	31

simplify81.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

521×	`associate-r_binary32`
494×	`times-frac_binary32`
302×	`associate-l_binary32`
278×	`fma-def_binary32`
264×	`associate-/r*_binary32`

Counts

84 → 59

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	356	4979
1	1177	4815
2	5063	4815

prune509.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	199	4	203
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	202	6	208

Error

0.0b

Counts

208 → 6

Alt Table

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

Compiler

Compiled 11194 to 7460 computations (33.4% saved)

localize72.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
	0.3b	(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)))
✓	0.7b	(pow.f32 (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))) 2) 1/3)
✓	0.7b	(cbrt.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))))

series7.3s (39%)

Counts

2 → 120

Calls

2 calls:

4.8s

(pow.f32 (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))) 2) 1/3)

2.5s

(cbrt.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))))

rewrite63.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

237×	`add-sqr-sqrt_binary32`
226×	`log1p-expm1-u_binary32`
226×	`expm1-log1p-u_binary32`
222×	`add-cbrt-cube_binary32`
221×	`add-log-exp_binary32`

Counts

2 → 49

Calls

2 calls:

62.0ms

(pow.f32 (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))) 2) 1/3)

62.0ms

(cbrt.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))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	69
1	504	69
2	4834	69
3	4775	69

simplify194.0ms (1%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-def_binary32`
639×	`times-frac_binary32`
361×	`associate-/l*_binary32`
285×	`*-commutative_binary32`
151×	`associate-r_binary32`

Counts

169 → 127

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	619	16320
1	2108	15235
2	4989	15235

prune955.0ms (5.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	298	1	299
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	299	6	305

Error

0.0b

Counts

305 → 6

Alt Table

Status	Error	Program
	0.1b	(pow.f32 (.f32 (cbrt.f32 1/2) (exp.f32 (.f32 1/3 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (log.f32 v)))))) 3)
▶	0.1b	(pow.f32 (.f32 (pow.f32 (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))) 2) 1/3) (.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) v) 1/9) (pow.f32 (cbrt.f32 1/2) 1/3))) 3)
	0.4b	(pow.f32 (cbrt.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)))) 3) 1/3) (/.f32 1/2 v))) 3)
✓	0.1b	(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)
	0.1b	(pow.f32 (exp.f32 (*.f32 1/3 (+.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))))) 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)))))

Compiler

Compiled 31580 to 21912 computations (30.6% saved)

localize115.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(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)))
	0.7b	(pow.f32 (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))) 2) 1/3)
✓	1.1b	(pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) v) 1/9)
✓	7.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series1.1s (5.7%)

Counts

2 → 20

Calls

2 calls:

1.1s	(pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) v) 1/9)
12.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite76.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

295×	`log1p-udef_binary32`
166×	`add-sqr-sqrt_binary32`
160×	`log1p-expm1-u_binary32`
160×	`expm1-log1p-u_binary32`
157×	`add-log-exp_binary32`

Counts

2 → 63

Calls

2 calls:

74.0ms	(pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) v) 1/9)
74.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	35
1	339	33
2	4570	33
3	4902	33

simplify122.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

618×	`associate-/r*_binary32`
555×	`fma-def_binary32`
242×	`fma-neg_binary32`
230×	`cancel-sign-sub-inv_binary32`
227×	`associate-/r/_binary32`

Counts

83 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2070
1	485	2010
2	1926	1900
3	4851	1900
4	4960	1900

prune675.0ms (3.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	211	5	216

Error

0.0b

Counts

216 → 5

Alt Table

Status	Error	Program
✓	0.1b	(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)
	0.1b	(pow.f32 (exp.f32 (*.f32 1/3 (+.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))))) 3)
	0.1b	(pow.f32 (.f32 (pow.f32 (pow.f32 (.f32 (cbrt.f32 1/2) (cbrt.f32 (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (/.f32 -1 v))) v))) 2) 1/3) (.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) v) 1/9) (pow.f32 (cbrt.f32 1/2) 1/3))) 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	(pow.f32 (.f32 (cbrt.f32 1/2) (exp.f32 (.f32 1/3 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (log.f32 v)))))) 3)

Compiler

Compiled 20684 to 14846 computations (28.2% saved)

regimes753.0ms (4%)

Accuracy

Total 0.1b remaining (53%)

Threshold costs 0.1b (53%)

Counts

77 → 1

Compiler

Compiled 21004 to 15223 computations (27.5% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary32`
9×	`+-commutative_binary32`
7×	`sub-neg_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	4294967295
1	47	4294967295
2	54	4294967295
3	65	4294967295
4	79	4294967295
5	87	4294967295
6	92	4294967295
7	94	4294967295
8	92	4294967295

end157.0ms (0.8%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 465 to 363 computations (21.9% saved)

Details

analyze2.0s (10.4%)

sample2.5s (13.1%)

simplify51.0ms (0.3%)

prune4.0ms (0%)

localize48.0ms (0.3%)

series173.0ms (0.9%)

rewrite94.0ms (0.5%)

simplify140.0ms (0.7%)

prune302.0ms (1.6%)

localize53.0ms (0.3%)

series1.3s (6.8%)

rewrite67.0ms (0.4%)

simplify81.0ms (0.4%)

prune509.0ms (2.7%)

localize72.0ms (0.4%)

series7.3s (39%)

rewrite63.0ms (0.3%)

simplify194.0ms (1%)

prune955.0ms (5.1%)

localize115.0ms (0.6%)

series1.1s (5.7%)

rewrite76.0ms (0.4%)

simplify122.0ms (0.6%)

prune675.0ms (3.6%)

regimes753.0ms (4%)

simplify5.0ms (0%)

end157.0ms (0.8%)

Profiling