Details

analyze2.0s (23.8%)

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 51 to 38 computations (25.5% saved)

sample82.0ms (1%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
11.0ms	257×	pre	128	true
0.0ms	1×	body	128	nan

Compiler

Compiled 86 to 65 computations (24.4% saved)

simplify58.0ms (0.7%)

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 (0.1%)

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	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))
	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (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)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))

0.1b

(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize66.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) 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)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))
✓	6.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	8.1b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary32`
54×	`times-frac_binary32`
49×	`prod-diff_binary32`
43×	`add-sqr-sqrt_binary32`
41×	`add-cube-cbrt_binary32`

Counts

4 → 160

Calls

4 calls:

23.0ms	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))
8.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
3.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
3.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

series251.0ms (2.9%)

Counts

4 → 84

Calls

4 calls:

95.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
62.0ms	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))
47.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
46.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

simplify157.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

592×	`times-frac_binary32`
443×	`associate-r_binary32`
392×	`associate-/l*_binary32`
345×	`associate-l_binary32`
283×	`associate-/r*_binary32`

Counts

244 → 426

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	496	8868
1	1378	7767
2	5300	7767

prune408.0ms (4.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	422	4	426
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	424	4	428

Error

0.1b

Counts

428 → 4

Alt Table

Status	Error	Program
	0.1b	(pow.f32 E.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))
	0.1b	(.f32 (sqrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v)))))) (sqrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))))
	0.1b	(.f32 (.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v))))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))))
▶	0.1b	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v)))))) (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v))))))) (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))))

Compiler

Compiled 11822 to 6058 computations (48.8% saved)

localize85.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	6.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	8.1b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
	8.1b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
	8.1b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune283.0ms (3.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	256	4	260

Error

0.1b

Counts

260 → 4

Alt Table

Status	Error	Program
	0.1b	(pow.f32 E.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))
▶	0.1b	(.f32 (sqrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v)))))) (sqrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))))
	0.1b	(.f32 (.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v))))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))))
✓	0.1b	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v)))))) (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v))))))) (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))))

Compiler

Compiled 9636 to 4991 computations (48.2% saved)

localize77.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	6.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	6.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	8.1b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
	8.1b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify19.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune257.0ms (3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	960	0	960
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	960	4	964

Error

0.1b

Counts

964 → 4

Alt Table

Status	Error	Program
▶	0.1b	(pow.f32 E.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))
✓	0.1b	(.f32 (sqrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v)))))) (sqrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))))
	0.1b	(.f32 (.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v))))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))))
✓	0.1b	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v)))))) (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v))))))) (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))))

Compiler

Compiled 6635 to 3428 computations (48.3% saved)

localize81.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
✓	0.1b	(pow.f32 E.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))
	6.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	8.1b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary32`
22×	`distribute-lft-out_binary32`
15×	`pow-unpow_binary32`
12×	`distribute-lft-out--_binary32`
8×	`pow1_binary32`

Counts

1 → 36

Calls

1 calls:

22.0ms

(pow.f32 E.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))

series69.0ms (0.8%)

Counts

1 → 60

Calls

1 calls:

69.0ms

(pow.f32 E.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))

simplify162.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

476×	`times-frac_binary32`
331×	`associate-r_binary32`
271×	`associate-/l*_binary32`
246×	`associate-+r+_binary32`
244×	`associate-/r*_binary32`

Counts

96 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	314	5878
1	994	5681
2	4648	5129
3	5030	5129

prune558.0ms (6.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1651	3	1654
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	1653	5	1658

Error

0.0b

Counts

1658 → 5

Alt Table

Status	Error	Program
	0.1b	(/.f32 (pow.f32 E.f32 (+.f32 3121444901730491/4503599627370496 (-.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 E.f32 (log.f32 (.f32 v 2))))
✓	0.1b	(.f32 (sqrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v)))))) (sqrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))))
✓	0.1b	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v)))))) (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v))))))) (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))))
	0.1b	(.f32 (.f32 (cbrt.f32 (pow.f32 E.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v)))))) (cbrt.f32 (pow.f32 E.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (.f32 2 v))))))) (cbrt.f32 (pow.f32 E.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (log.f32 (/.f32 1 (*.f32 2 v)))))))
	0.1b	(.f32 (pow.f32 E.f32 (+.f32 3121444901730491/4503599627370496 (-.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1/2 v))

Compiler

Compiled 12103 to 6040 computations (50.1% saved)

regimes1.5s (17.8%)

Accuracy

Total 0.0b remaining (35%)

Threshold costs 0.0b (35%)

Compiler

Compiled 51518 to 33785 computations (34.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	39
1	29	39
2	36	39
3	46	39
4	53	39
5	58	39
6	60	39
7	59	39

end22.0ms (0.3%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 150 to 105 computations (30% saved)

sample2.3s (26.7%)

Algorithm

1×

intervals

Results

980.0ms	8000×	body	128	valid
360.0ms	8156×	pre	128	true
18.0ms	156×	body	128	nan

Compiler

Compiled 374 to 244 computations (34.8% saved)

Details

analyze2.0s (23.8%)

sample82.0ms (1%)

simplify58.0ms (0.7%)

prune5.0ms (0.1%)

localize66.0ms (0.8%)

rewrite50.0ms (0.6%)

series251.0ms (2.9%)

simplify157.0ms (1.8%)

prune408.0ms (4.7%)

localize85.0ms (1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify12.0ms (0.1%)

prune283.0ms (3.3%)

localize77.0ms (0.9%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify19.0ms (0.2%)

prune257.0ms (3%)

localize81.0ms (0.9%)

rewrite25.0ms (0.3%)

series69.0ms (0.8%)

simplify162.0ms (1.9%)

prune558.0ms (6.5%)

regimes1.5s (17.8%)

simplify4.0ms (0.1%)

end22.0ms (0.3%)

sample2.3s (26.7%)

Profiling