Details

analyze2.1s (11%)

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)

sample86.0ms (0.5%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
14.0ms	260×	pre	128	true
0.0ms	4×	body	128	nan

Compiler

Compiled 104 to 78 computations (25% saved)

simplify52.0ms (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

0.0b

Counts

3 → 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)))))
▶	0.0b	(*.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)))))

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)))))

▶

0.0b

(*.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)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize51.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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)))
✓	0.0b	(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)

series116.0ms (0.6%)

Counts

4 → 156

Calls

4 calls:

51.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
40.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
15.0ms	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))
10.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary32`
24×	`add-sqr-sqrt_binary32`
20×	`add-cube-cbrt_binary32`
18×	`prod-diff_binary32`
14×	`exp-sum_binary32`

Counts

4 → 83

Calls

4 calls:

4.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
3.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
0.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
0.0ms	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))

simplify161.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

373×	`distribute-rgt-in_binary32`
252×	`times-frac_binary32`
214×	`fma-neg_binary32`
180×	`associate-r_binary32`
152×	`associate-+r+_binary32`

Counts

239 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	6496
1	704	5860
2	3071	5155
3	4888	5155
4	4936	5155

prune239.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	3	162

Error

0.0b

Counts

162 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
	3.5b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 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)))))

Compiler

Compiled 6808 to 3901 computations (42.7% saved)

localize56.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
✓	0.0b	(+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))
✓	0.0b	(exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
✓	0.4b	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))

series4.2s (21.8%)

Counts

4 → 240

Calls

4 calls:

2.2s	(.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
1.8s	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
49.0ms	(exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
35.0ms	(+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))

rewrite47.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary32`
23×	`add-sqr-sqrt_binary32`
19×	`*-un-lft-identity_binary32`
15×	`add-cube-cbrt_binary32`
11×	`pow1_binary32`

Counts

4 → 98

Calls

4 calls:

18.0ms	(.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
8.0ms	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
7.0ms	(exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
6.0ms	(+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))

simplify201.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

688×	`times-frac_binary32`
466×	`fma-def_binary32`
413×	`associate-/l*_binary32`
371×	`associate-/r*_binary32`
201×	`*-commutative_binary32`

Counts

338 → 194

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	571	14649
1	1746	13733
2	5075	13733

prune1.0s (5.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	419	3	422
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	421	4	425

Error

0.0b

Counts

425 → 4

Alt Table

Status	Error	Program
	0.0b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (.f32 (cbrt.f32 (exp.f32 6931/10000)) (cbrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
	3.5b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
▶	0.0b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))) (.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
	0.0b	(.f32 (/.f32 1/2 v) (.f32 (exp.f32 (.f32 2 (log.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))

Compiler

Compiled 35310 to 22355 computations (36.7% saved)

localize63.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))
	0.0b	(exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
✓	0.3b	(sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
	0.4b	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))

series1.8s (9.4%)

Counts

1 → 60

Calls

1 calls:

1.8s	(sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`sqrt-prod_binary32`
5×	`cbrt-prod_binary32`
5×	`add-sqr-sqrt_binary32`
3×	`*-un-lft-identity_binary32`
3×	`add-cube-cbrt_binary32`

Counts

1 → 22

Calls

1 calls:

7.0ms

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

simplify117.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary32`
387×	`times-frac_binary32`
260×	`associate-r_binary32`
224×	`associate-+r+_binary32`
217×	`associate-/l*_binary32`

Counts

82 → 57

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	3857
1	862	3827
2	3218	3599
3	4966	3599
4	4938	3599

prune2.8s (14.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	798	0	798
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	798	4	802

Error

0.0b

Counts

802 → 4

Alt Table

Status	Error	Program
▶	0.0b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (.f32 (cbrt.f32 (exp.f32 6931/10000)) (cbrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
	3.5b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
✓	0.0b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))) (.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
	0.0b	(.f32 (/.f32 1/2 v) (.f32 (exp.f32 (.f32 2 (log.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))

Compiler

Compiled 95438 to 60934 computations (36.2% saved)

localize75.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))
✓	0.4b	(cbrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
	0.4b	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
✓	1.0b	(cbrt.f32 (exp.f32 6931/10000))

series1.4s (7.2%)

Counts

3 → 92

Calls

3 calls:

1.3s

(cbrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))

40.0ms

(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))

0.0ms

(cbrt.f32 (exp.f32 6931/10000))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`exp-prod_binary32`
12×	`*-un-lft-identity_binary32`
12×	`add-sqr-sqrt_binary32`
12×	`add-cube-cbrt_binary32`
9×	`times-frac_binary32`

Counts

3 → 51

Calls

3 calls:

5.0ms

(cbrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))

4.0ms

(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))

1.0ms

(cbrt.f32 (exp.f32 6931/10000))

simplify112.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

285×	`times-frac_binary32`
241×	`associate-+r+_binary32`
215×	`cancel-sign-sub-inv_binary32`
192×	`associate-r_binary32`
190×	`associate-/l*_binary32`

Counts

143 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	5315
1	931	5242
2	3869	5132
3	5073	5132

prune629.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	190	2	192
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	192	4	196

Error

Counts

196 → 4

Alt Table

Status	Error	Program
	0.0b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (.f32 (cbrt.f32 (exp.f32 6931/10000)) (pow.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)) 1/3))))
✓	0.0b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))) (.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
✓	0.0b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (.f32 (cbrt.f32 (exp.f32 6931/10000)) (cbrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
	0.0b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (.f32 (cbrt.f32 (exp.f32 6931/10000)) (cbrt.f32 (pow.f32 (exp.f32 (.f32 (cbrt.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)) (cbrt.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))))

Compiler

Compiled 16572 to 10527 computations (36.5% saved)

regimes1.3s (6.8%)

Accuracy

Total 0.0b remaining (18.3%)

Threshold costs 0.0b (18.3%)

Counts

106 → 1

Compiler

Compiled 41081 to 28141 computations (31.5% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary32`
11×	`+-commutative_binary32`
9×	`sub-neg_binary32`
7×	`neg-sub0_binary32`
7×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	126
1	45	126
2	56	126
3	70	126
4	84	126
5	92	126
6	97	126
7	99	126
8	97	126

end30.0ms (0.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 430 to 290 computations (32.6% saved)

sample2.5s (13%)

Algorithm

1×

intervals

Results

991.0ms	8000×	body	128	valid
437.0ms	8132×	pre	128	true
15.0ms	132×	body	128	nan

Compiler

Compiled 438 to 296 computations (32.4% saved)

Details

analyze2.1s (11%)

sample86.0ms (0.5%)

simplify52.0ms (0.3%)

prune5.0ms (0%)

localize51.0ms (0.3%)

series116.0ms (0.6%)

rewrite17.0ms (0.1%)

simplify161.0ms (0.8%)

prune239.0ms (1.2%)

localize56.0ms (0.3%)

series4.2s (21.8%)

rewrite47.0ms (0.2%)

simplify201.0ms (1.1%)

prune1.0s (5.5%)

localize63.0ms (0.3%)

series1.8s (9.4%)

rewrite9.0ms (0%)

simplify117.0ms (0.6%)

prune2.8s (14.5%)

localize75.0ms (0.4%)

series1.4s (7.2%)

rewrite13.0ms (0.1%)

simplify112.0ms (0.6%)

prune629.0ms (3.3%)

regimes1.3s (6.8%)

simplify7.0ms (0%)

end30.0ms (0.2%)

sample2.5s (13%)

Profiling