Details

analyze2.3s (24.8%)

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)

sample88.0ms (0.9%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
13.0ms	257×	pre	128	true
0.0ms	1×	body	128	nan

Compiler

Compiled 86 to 65 computations (24.4% saved)

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

982×	`exp-sum_binary32`
570×	`exp-diff_binary32`
458×	`sub-neg_binary32`
380×	`cancel-sign-sub-inv_binary32`
307×	`div-exp_binary32`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	53	33
2	145	33
3	513	33
4	1979	33
5	3856	33
6	4782	33
7	5305	33

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 2

Alt Table

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

Status

Error

Program

▶

0.1b

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

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)))))

Compiler

Compiled 141 to 101 computations (28.4% saved)

localize63.0ms (0.7%)

Local error

Found 4 expressions with local error:

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 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496))
7.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
8.1b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite132.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

27×	`*-un-lft-identity_binary32`
16×	`add-log-exp_binary32`
14×	`add-cbrt-cube_binary32`
14×	`add-exp-log_binary32`
13×	`add-sqr-sqrt_binary32`

Counts

4 → 86

Calls

4 calls:

19.0ms	(exp.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496))
8.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
4.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
3.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Compiler

Compiled 2345 to 1040 computations (55.7% saved)

series173.0ms (1.8%)

Error

0.1b

Counts

4 → 56

Calls

4 calls:

63.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
47.0ms	(exp.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496))
26.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
26.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 3028 to 2127 computations (29.8% saved)

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Rules

750×	`times-frac_binary32`
533×	`associate-*l/_binary32`
368×	`associate-/l/_binary32`
236×	`associate-/r*_binary32`
200×	`associate-/r/_binary32`

Counts

142 → 79

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	163	1978
1	420	1901
2	1400	1901
3	4640	1901
4	4977	1901

prune59.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Error

0.1b

Counts

81 → 4

Alt Table

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

Compiler

Compiled 1461 to 730 computations (50% saved)

localize64.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f32 (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))
0.2b	(sqrt.f32 (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))
4.1b	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
4.1b	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

rewrite224.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

34×	`*-un-lft-identity_binary32`
26×	`add-sqr-sqrt_binary32`
24×	`add-cube-cbrt_binary32`
18×	`times-frac_binary32`
12×	`sqrt-pow1_binary32`

Counts

4 → 100

Calls

4 calls:

17.0ms	(sqrt.f32 (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))
15.0ms	(sqrt.f32 (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))
7.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
5.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

Compiler

Compiled 4649 to 2026 computations (56.4% saved)

series373.0ms (4%)

Error

0.1b

Counts

4 → 84

Calls

4 calls:

117.0ms	(sqrt.f32 (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))
87.0ms	(sqrt.f32 (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))
61.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
59.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

Compiler

Compiled 7990 to 5182 computations (35.1% saved)

simplify156.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

405×	`times-frac_binary32`
384×	`associate-l_binary32`
379×	`associate-/l*_binary32`
359×	`associate-r_binary32`
279×	`div-sub_binary32`

Counts

184 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	4832
1	336	4286
2	972	4186
3	4723	4174
4	5444	4174

prune112.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	114	4	118

Error

0.0b

Counts

118 → 4

Alt Table

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

Compiler

Compiled 3046 to 1474 computations (51.6% saved)

localize105.0ms (1.1%)

Local error

Found 4 expressions with local error:

4.1b	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
4.1b	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
4.1b	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
4.1b	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

rewrite320.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

36×	`*-un-lft-identity_binary32`
36×	`times-frac_binary32`
36×	`add-sqr-sqrt_binary32`
36×	`add-cube-cbrt_binary32`
12×	`associate-/r*_binary32`

Counts

4 → 120

Calls

4 calls:

6.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
5.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
5.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
5.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

Compiler

Compiled 10309 to 4504 computations (56.3% saved)

series362.0ms (3.8%)

Error

0.0b

Counts

4 → 84

Calls

4 calls:

84.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
78.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
76.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)
75.0ms	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

Compiler

Compiled 13291 to 7627 computations (42.6% saved)

simplify206.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

427×	`distribute-rgt-in_binary32`
419×	`distribute-lft-in_binary32`
342×	`*-commutative_binary32`
341×	`neg-sub0_binary32`
329×	`neg-mul-1_binary32`

Counts

204 → 92

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	72	3608
1	185	3384
2	514	3384
3	1467	3384
4	3862	3384
5	4408	3384
6	4855	3384
7	4884	3384

prune90.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	92	4	96

Error

0.0b

Counts

96 → 4

Alt Table

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

Compiler

Compiled 3430 to 1603 computations (53.3% saved)

localize66.0ms (0.7%)

Local error

Found 4 expressions with local error:

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 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496))
7.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
8.1b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite181.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

28×	`*-un-lft-identity_binary32`
15×	`add-exp-log_binary32`
14×	`add-sqr-sqrt_binary32`
14×	`add-cbrt-cube_binary32`
12×	`add-cube-cbrt_binary32`

Counts

4 → 90

Calls

4 calls:

18.0ms	(pow.f32 E.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496))
8.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
4.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
3.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Compiler

Compiled 2614 to 1118 computations (57.2% saved)

series172.0ms (1.8%)

Error

0.0b

Counts

4 → 56

Calls

4 calls:

55.0ms	(pow.f32 E.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496))
54.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
26.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
25.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Compiler

Compiled 3105 to 2200 computations (29.1% saved)

simplify108.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

741×	`times-frac_binary32`
513×	`associate-*l/_binary32`
389×	`associate-/l/_binary32`
230×	`associate-/r*_binary32`
202×	`associate-/r/_binary32`

Counts

146 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	2272
1	472	2196
2	1518	2194
3	4926	2194
4	4956	2194

prune76.0ms (0.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	86	5	91

Error

0.0b

Counts

91 → 5

Alt Table

Status	Error	Program
	0.1b	(.f32 (/.f32 1/2 v) (pow.f32 E.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496)))
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (sqrt.f32 (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v))))) (sqrt.f32 (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))))
	0.2b	(.f32 (/.f32 1/2 v) (pow.f32 (pow.f32 E.f32 (.f32 (cbrt.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))) (cbrt.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 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496))))
	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) (.f32 (.f32 (.f32 (cbrt.f32 (sqrt.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (+.f32 3121444901730491/4503599627370496 (/.f32 -1 v)))))) (cbrt.f32 (sqrt.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (+.f32 3121444901730491/4503599627370496 (/.f32 -1 v))))))) (cbrt.f32 (sqrt.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (+.f32 3121444901730491/4503599627370496 (/.f32 -1 v))))))) (sqrt.f32 (exp.f32 (+.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 -1 v)))))))

Compiler

Compiled 1518 to 721 computations (52.5% saved)

regimes1.1s (11.4%)

Accuracy

Total 0.0b remaining (26.9%)

Threshold costs 0.0b (26.9%)

Compiler

Compiled 35562 to 23164 computations (34.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	54
1	44	54
2	56	54
3	65	54
4	70	54
5	71	54
6	69	54

end21.0ms (0.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 200 to 140 computations (30% saved)

sample2.7s (28.5%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
372.0ms	8120×	pre	128	true
13.0ms	120×	body	128	nan

Compiler

Compiled 344 to 223 computations (35.2% saved)

Details

analyze2.3s (24.8%)

sample88.0ms (0.9%)

simplify64.0ms (0.7%)

prune4.0ms (0%)

localize63.0ms (0.7%)

rewrite132.0ms (1.4%)

series173.0ms (1.8%)

simplify97.0ms (1%)

prune59.0ms (0.6%)

localize64.0ms (0.7%)

rewrite224.0ms (2.4%)

series373.0ms (4%)

simplify156.0ms (1.7%)

prune112.0ms (1.2%)

localize105.0ms (1.1%)

rewrite320.0ms (3.4%)

series362.0ms (3.8%)

simplify206.0ms (2.2%)

prune90.0ms (1%)

localize66.0ms (0.7%)

rewrite181.0ms (1.9%)

series172.0ms (1.8%)

simplify108.0ms (1.1%)

prune76.0ms (0.8%)

regimes1.1s (11.4%)

simplify5.0ms (0.1%)

end21.0ms (0.2%)

sample2.7s (28.5%)

Profiling