Metrics for HairBSDF, Mp, lower

analyze470.0ms (3.6%)

Memory

8.1MiB live, 642.7MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	3%	97%	0%	0%	0%	0
0%	0%	3%	97%	0%	0%	0%	1
0%	0%	3%	97%	0%	0%	0%	2
0%	0%	3%	97%	0%	0%	0%	3
0%	0%	3%	97%	0%	0%	0%	4
0%	0%	3%	97%	0%	0%	0%	5
0%	0%	1.5%	97%	0%	1.5%	0%	6
0%	0%	1.5%	97%	0%	1.5%	0%	7
0%	0%	1.5%	97%	0%	1.5%	0%	8
0%	0%	1.5%	97%	0%	1.5%	0%	9
0%	0%	1.5%	97%	0%	1.5%	0%	10
0%	0%	1.5%	97%	0%	1.5%	0%	11
0%	0%	1.5%	97%	0%	1.5%	0%	12

Compiler

Compiled 65 to 44 computations (32.3% saved)

sample2.8s (21.3%)

Memory

-130.9MiB live, 3 961.3MiB allocated

Samples

1.9s	8 256×	0	valid
30.0ms	119×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

const: 398.0ms (25.6% of total)

ival-div: 263.0ms (16.9% of total)

ival-<=: 245.0ms (15.7% of total)

ival-mult: 224.0ms (14.4% of total)

ival-log: 97.0ms (6.2% of total)

ival-exp: 92.0ms (5.9% of total)

ival-sub: 83.0ms (5.3% of total)

ival-add: 81.0ms (5.2% of total)

ival-and: 53.0ms (3.4% of total)

exact: 17.0ms (1.1% of total)

ival-assert: 4.0ms (0.3% of total)

Bogosity

preprocess289.0ms (2.2%)

Memory

37.6MiB live, 390.6MiB allocated

Algorithm

1×	egg-herbie

Rules

6 404×	`lower-fma.f64`
6 404×	`lower-fma.f32`
3 478×	`lower-*.f64`
3 472×	`lower-*.f32`
1 904×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	159	481
1	462	447
2	1368	440
3	4990	440
0	21	25
0	34	23
1	63	22
2	151	22
3	471	22
4	1717	22
5	5047	22
0	8134	19

Stop Event

1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Calls

Call 1

Inputs

(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

Outputs

(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

(/.f32 (exp.f32 (fma.f32 (/.f32 #s(literal -1 binary32) v) (fma.f32 sinTheta_i sinTheta_O #s(literal 1 binary32)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) #s(literal 6931/10000 binary32)))) (*.f32 v #s(literal 2 binary32)))

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

explain357.0ms (2.7%)

Memory

-33.4MiB live, 451.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
256	0	-	256	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(*.f32 #s(literal 2 binary32) v)`
256	0	-	256	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32))`
256	0	-	256	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(/.f32 #s(literal 1 binary32) v)`
256	0	-	256	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`
256	0	-	256	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(*.f32 sinTheta_i sinTheta_O)`
256	0	-	256	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))`
256	0	-	256	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v))`
256	0	-	252	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`
256	0	-	256	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))`
256	0	-	256	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))`
256	0	-	191	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`
234	0	-	234	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(*.f32 cosTheta_i cosTheta_O)`
170	66	(-5.162230664208124e-23 -7.836358061291899e-24 -1.0578230434778903e-20 -7.991057471338085e-23 7.676521249777579e-7)	170	(-7.1734511948307045e-6 2.4952106353337555e-12 1.983828637044965e-25 4.062455927211772e-10 4.357152550872906e-20)	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`
0	0	-	0	-	`#s(literal 2 binary32)`
0	0	-	0	-	`sinTheta_i`
0	0	-	0	-	`v`
0	0	-	0	-	`cosTheta_i`
0	0	-	0	-	`sinTheta_O`
0	0	-	0	-	`#s(literal 1 binary32)`
0	0	-	0	-	`#s(literal 6931/10000 binary32)`
0	0	-	0	-	`cosTheta_O`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f32`	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`	u/n	11	0
↳	`(*.f32 sinTheta_i sinTheta_O)`	underflow	87
`/.f32`	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`	u/n	7	0
↳	`(*.f32 cosTheta_i cosTheta_O)`	underflow	86
`exp.f32`	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`	sensitivity	4	4

Confusion

	Predicted +	Predicted -
+	0	5
-	22	229

Precision

0.0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	4	1
-	22	0	229

Precision?

0.15384615384615385

Recall?

0.8

Freqs

test

number	freq
0	234
1	22

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

97.0ms

512×

valid

Compiler

Compiled 468 to 109 computations (76.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-log: 27.0ms (36.5% of total)

ival-div: 14.0ms (18.9% of total)

ival-mult: 9.0ms (12.2% of total)

const: 8.0ms (10.8% of total)

ival-sub: 7.0ms (9.5% of total)

ival-exp: 4.0ms (5.4% of total)

ival-add: 4.0ms (5.4% of total)

ival-true: 1.0ms (1.4% of total)

exact: 1.0ms (1.4% of total)

ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 5 to 5 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

Status

Accuracy

Program

▶

99.6%

(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

Compiler

Compiled 30 to 21 computations (30% saved)

simplify263.0ms (2%)

Memory

-2.9MiB live, 273.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))
✓	cost-diff	160	(/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))
✓	cost-diff	320	(-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v))
✓	cost-diff	2944	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

Rules

6 404×	`lower-fma.f64`
6 404×	`lower-fma.f32`
3 478×	`lower-*.f64`
3 472×	`lower-*.f32`
1 904×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	133
0	34	125
1	63	124
2	151	124
3	471	124
4	1717	124
5	5047	124
0	8134	113

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))
(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))
(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32))
(-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v))
(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(*.f32 cosTheta_i cosTheta_O)
cosTheta_i
cosTheta_O
v
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
(*.f32 sinTheta_i sinTheta_O)
sinTheta_i
sinTheta_O
(/.f32 #s(literal 1 binary32) v)
#s(literal 1 binary32)
#s(literal 6931/10000 binary32)
(log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))
(/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))
(*.f32 #s(literal 2 binary32) v)
#s(literal 2 binary32)

Outputs
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))
(/.f32 (exp.f32 (fma.f32 (/.f32 #s(literal -1 binary32) v) (fma.f32 sinTheta_i sinTheta_O #s(literal 1 binary32)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) #s(literal 6931/10000 binary32)))) (*.f32 v #s(literal 2 binary32)))
(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))
(fma.f32 (/.f32 #s(literal -1 binary32) v) (fma.f32 sinTheta_i sinTheta_O #s(literal 1 binary32)) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) #s(literal 6931/10000 binary32)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32))
(fma.f32 (/.f32 #s(literal -1 binary32) v) (fma.f32 sinTheta_i sinTheta_O #s(literal 1 binary32)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) #s(literal 6931/10000 binary32)))
(-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 (/.f32 #s(literal -1 binary32) v) (fma.f32 sinTheta_i sinTheta_O #s(literal 1 binary32))))
(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(fma.f32 sinTheta_i (/.f32 sinTheta_O (neg.f32 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(*.f32 cosTheta_i cosTheta_O)
cosTheta_i
cosTheta_O
v
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
(*.f32 sinTheta_i sinTheta_O)
sinTheta_i
sinTheta_O
(/.f32 #s(literal 1 binary32) v)
#s(literal 1 binary32)
#s(literal 6931/10000 binary32)
(log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))
(neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32))))
(/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))
(/.f32 #s(literal 1/2 binary32) v)
(*.f32 #s(literal 2 binary32) v)
(*.f32 v #s(literal 2 binary32))
#s(literal 2 binary32)

localize72.0ms (0.6%)

Memory

9.7MiB live, 47.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	6.1%	(-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v))
✓	accuracy	4.6%	(/.f32 #s(literal 1 binary32) v)
✓	accuracy	3.1%	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))
✓	accuracy	1.3%	(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32))

Samples

36.0ms

256×

valid

Compiler

Compiled 273 to 44 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-div: 7.0ms (28.8% of total)

ival-mult: 5.0ms (20.5% of total)

const: 4.0ms (16.4% of total)

ival-log: 3.0ms (12.3% of total)

ival-exp: 2.0ms (8.2% of total)

ival-add: 2.0ms (8.2% of total)

ival-sub: 2.0ms (8.2% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series252.0ms (1.9%)

Memory

29.4MiB live, 178.8MiB allocated

Counts

7 → 276

Calls

Call 1

Inputs
#<alt (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))>
#<alt (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v))>
#<alt (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))>
#<alt (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))>
#<alt (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32))>
#<alt (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))>
#<alt (/.f32 #s(literal 1 binary32) v)>

Outputs
#<alt (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) (/ (* cosTheta_O (* cosTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))) v))>
#<alt (+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) (* cosTheta_i (+ (* 1/2 (/ (* (pow cosTheta_O 2) (* cosTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))) (pow v 2))) (/ (* cosTheta_O (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))) v))))>
#<alt (+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ (* (pow cosTheta_O 3) (* cosTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_O 2) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))) (pow v 2))))) (/ (* cosTheta_O (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))) v))))>
#<alt (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
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#<alt (/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt 6931/10000>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt 6931/10000>
#<alt (+ 6931/10000 (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v)))>
#<alt (+ 6931/10000 (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v)))>
#<alt (+ 6931/10000 (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v)))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))>
#<alt (* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))>
#<alt (* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))>
#<alt (* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))>
#<alt (* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))>
#<alt (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (/ cosTheta_i v)>
#<alt (* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ 1 v) (/ (log (/ 1/2 v)) cosTheta_i))) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))>
#<alt (* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ 1 v) (/ (log (/ 1/2 v)) cosTheta_i))) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))>
#<alt (* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ 1 v) (/ (log (/ 1/2 v)) cosTheta_i))) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))>
#<alt (/ cosTheta_i v)>
#<alt (* -1 (* cosTheta_i (- (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_i)) (/ 1 v))))>
#<alt (* -1 (* cosTheta_i (- (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_i)) (/ 1 v))))>
#<alt (* -1 (* cosTheta_i (- (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_i)) (/ 1 v))))>
#<alt (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (+ (/ cosTheta_i v) (/ (log (/ 1/2 v)) cosTheta_O))) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))>
#<alt (* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (+ (/ cosTheta_i v) (/ (log (/ 1/2 v)) cosTheta_O))) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))>
#<alt (* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (+ (/ cosTheta_i v) (/ (log (/ 1/2 v)) cosTheta_O))) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_O)))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_O)))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_O)))))>
#<alt (/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (+ (* cosTheta_O cosTheta_i) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (+ (* cosTheta_O cosTheta_i) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (+ (* cosTheta_O cosTheta_i) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (/ (* cosTheta_O cosTheta_i) v)))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (/ (* cosTheta_O cosTheta_i) v)))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (/ (* cosTheta_O cosTheta_i) v)))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))>
#<alt (+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v)))))>
#<alt (+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v)))))>
#<alt (+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v)))))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (+ (/ (log (/ 1/2 v)) sinTheta_i) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (+ (/ (log (/ 1/2 v)) sinTheta_i) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (+ (/ (log (/ 1/2 v)) sinTheta_i) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ (log (/ 1/2 v)) sinTheta_O) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))>
#<alt (* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ (log (/ 1/2 v)) sinTheta_O) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))>
#<alt (* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ (log (/ 1/2 v)) sinTheta_O) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))>
#<alt (* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))>
#<alt (* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>

Calls

69 calls:

Time	Variable		Point	Expression
99.0ms	sinTheta_i	@	0	(+ (+ (- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v))))
63.0ms	v	@	0	(log (/ 1 (* 2 v)))
20.0ms	v	@	inf	(log (/ 1 (* 2 v)))
11.0ms	v	@	-inf	(log (/ 1 (* 2 v)))
4.0ms	cosTheta_i	@	0	(+ (+ (- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v))))

Compiler

Compiled 1 532 to 1 065 computations (30.5% saved)

rewrite739.0ms (5.7%)

Memory

7.1MiB live, 599.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

9 370×	`lower-fma.f64`
9 370×	`lower-fma.f32`
4 860×	`lower-/.f64`
4 852×	`lower-/.f32`
3 374×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	95
0	34	79
1	147	70
2	1507	70
0	8245	70

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

7 → 621

Calls

Call 1

Inputs
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))
(-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v))
(/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))
(log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))
(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32))
(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))
(/.f32 #s(literal 1 binary32) v)

Outputs
(exp.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))))
(pow.f32 (exp.f32 (fma.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) (.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32))) (pow.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 3 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) (.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (-.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)))))))
(pow.f32 (exp.f32 (fma.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) (neg.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))))) (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))))))
(/.f32 #s(literal 1 binary32) (exp.f32 (-.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)))))
(/.f32 (exp.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32))) (.f32 v #s(literal 2 binary32)))
(/.f32 (exp.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32))) (neg.f32 (.f32 v #s(literal -2 binary32))))
(/.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) v)) (exp.f32 (-.f32 (/.f32 #s(literal 1 binary32) v) (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))))))
(/.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) v)) (exp.f32 (+.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)) (log.f32 (.f32 v #s(literal 2 binary32))))))
(/.f32 (exp.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (exp.f32 (-.f32 (/.f32 (fma.f32 sinTheta_i sinTheta_O #s(literal 1 binary32)) v) (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))))))
(/.f32 (exp.f32 (/.f32 (.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32))) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))))) (exp.f32 (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))))))
(/.f32 (exp.f32 (+.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) #s(literal 0 binary32))) (.f32 v #s(literal 2 binary32)))
(/.f32 (exp.f32 (+.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) v))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
(.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32))))
(.f32 (exp.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32))) (/.f32 #s(literal 1/2 binary32) v))
(.f32 (exp.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v)) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (*.f32 v #s(literal 2 binary32))))
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(.f32 (neg.f32 (fma.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) (neg.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))))) (/.f32 #s(literal 1 binary32) (neg.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))))))
(.f32 (fma.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v)) (pow.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (-.f32 (pow.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 2 binary32)) (.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))))))))
(.f32 (-.f32 (.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v)) (pow.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (-.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (-.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))))))
(.f32 (-.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) (.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)))) (/.f32 #s(literal 1 binary32) (-.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)))))
(neg.f32 (/.f32 #s(literal -1 binary32) v))
(exp.f32 (neg.f32 (log.f32 v)))
(pow.f32 v #s(literal -1 binary32))
(pow.f32 (*.f32 v v) #s(literal -1/2 binary32))
(pow.f32 (neg.f32 (neg.f32 v)) #s(literal -1 binary32))
(pow.f32 (pow.f32 v #s(literal -1/2 binary32)) #s(literal 2 binary32))
(-.f32 #s(literal 0 binary32) (/.f32 #s(literal -1 binary32) v))
(/.f32 #s(literal 1 binary32) v)
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 v)))
(/.f32 #s(literal -1 binary32) (neg.f32 v))
(/.f32 #s(literal -1 binary32) (neg.f32 (neg.f32 (neg.f32 v))))
(*.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) v))
(*.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 1 binary32))
(*.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) v))
(*.f32 (pow.f32 v #s(literal -1/2 binary32)) (pow.f32 v #s(literal -1/2 binary32)))

simplify536.0ms (4.1%)

Memory

3.9MiB live, 516.2MiB allocated

Algorithm

1×	egg-herbie

Rules

9 228×	`lower-fma.f64`
9 228×	`lower-fma.f32`
6 200×	`lower-*.f64`
6 200×	`lower-*.f32`
4 678×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	352	5446
1	1120	5303
2	3789	4618
0	8342	4297

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

Inputs
(exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) (/ (* cosTheta_O (* cosTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))) v))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) (* cosTheta_i (+ (* 1/2 (/ (* (pow cosTheta_O 2) (* cosTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))) (pow v 2))) (/ (* cosTheta_O (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))) v))))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ (* (pow cosTheta_O 3) (* cosTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_O 2) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))) (pow v 2))))) (/ (* cosTheta_O (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) (/ (* cosTheta_O (* cosTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))) v))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) (* cosTheta_O (+ (* 1/2 (/ (* cosTheta_O (* (pow cosTheta_i 2) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))) (pow v 2))) (/ (* cosTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))) v))))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) (* cosTheta_O (+ (* cosTheta_O (+ (* 1/6 (/ (* cosTheta_O (* (pow cosTheta_i 3) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_i 2) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))) (pow v 2))))) (/ (* cosTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v)))))
(+ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i)))) v))
(+ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ (* 1/2 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (pow (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) 2)) (pow v 2))) (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(+ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ (* 1/6 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (pow (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) 3)) (pow v 3))) (+ (* 1/2 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (pow (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) 2)) (pow v 2))) (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i)))) v))))
(exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v)))))
(+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i)))) v)))
(+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (+ (* -1/2 (/ (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (pow (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) 2)) v)) (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))))) v)))
(+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (pow (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) 3)) v)) (* 1/2 (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (pow (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) 2)))) v)) (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))))) v)))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(+ (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))))) v)))
(+ (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))))) (pow v 2))))))
(+ (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))) (pow v 2))))))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(+ (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))))) v)))
(+ (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))))) (pow v 2))))))
(+ (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))) (pow v 2))))))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(* -1 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(- (/ (* cosTheta_O cosTheta_i) v) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(- (/ (* cosTheta_O cosTheta_i) v) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(- (/ (* cosTheta_O cosTheta_i) v) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(/ cosTheta_i v)
(* cosTheta_i (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_i)) (/ 1 v)))
(* cosTheta_i (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_i)) (/ 1 v)))
(* cosTheta_i (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_i)) (/ 1 v)))
(/ cosTheta_i v)
(* -1 (* cosTheta_i (- (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))) (/ 1 v))))
(* -1 (* cosTheta_i (- (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))) (/ 1 v))))
(* -1 (* cosTheta_i (- (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))) (/ 1 v))))
(* -1 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(- (/ (* cosTheta_O cosTheta_i) v) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(- (/ (* cosTheta_O cosTheta_i) v) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(- (/ (* cosTheta_O cosTheta_i) v) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(/ (* cosTheta_O cosTheta_i) v)
(* cosTheta_O (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_O)) (/ cosTheta_i v)))
(* cosTheta_O (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_O)) (/ cosTheta_i v)))
(* cosTheta_O (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_O)) (/ cosTheta_i v)))
(/ (* cosTheta_O cosTheta_i) v)
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))))))
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))))))
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))))))
(/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)
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(/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)
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(* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
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(* -1 (* sinTheta_i (- (* -1 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))
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(/ 1 v)
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(- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
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(/ cosTheta_i v)
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(* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (/ 1 v)) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(/ cosTheta_i v)
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(- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(/ (* cosTheta_O cosTheta_i) v)
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(* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (/ cosTheta_i v)) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (/ cosTheta_i v)) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(/ (* cosTheta_O cosTheta_i) v)
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(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_O)))))
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_O)))))
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(/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) (+ 1 (* sinTheta_O sinTheta_i))) v)
6931/10000
(- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
6931/10000
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(* -1 (/ (* sinTheta_O sinTheta_i) v))
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(* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
(* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
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(* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))
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(* -1 (/ (* sinTheta_O sinTheta_i) v))
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(* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
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(- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(/ cosTheta_i v)
(* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ 1 v) (/ (log (/ 1/2 v)) cosTheta_i))) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ 1 v) (/ (log (/ 1/2 v)) cosTheta_i))) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ 1 v) (/ (log (/ 1/2 v)) cosTheta_i))) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(/ cosTheta_i v)
(* -1 (* cosTheta_i (- (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_i)) (/ 1 v))))
(* -1 (* cosTheta_i (- (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_i)) (/ 1 v))))
(* -1 (* cosTheta_i (- (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_i)) (/ 1 v))))
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(- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(/ (* cosTheta_O cosTheta_i) v)
(* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (+ (/ cosTheta_i v) (/ (log (/ 1/2 v)) cosTheta_O))) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (+ (/ cosTheta_i v) (/ (log (/ 1/2 v)) cosTheta_O))) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (+ (/ cosTheta_i v) (/ (log (/ 1/2 v)) cosTheta_O))) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(/ (* cosTheta_O cosTheta_i) v)
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_O)))))
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_O)))))
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_O)))))
(/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/ (- (+ (* cosTheta_O cosTheta_i) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/ (- (+ (* cosTheta_O cosTheta_i) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/ (- (+ (* cosTheta_O cosTheta_i) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)
(+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))
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(* -1 (/ (* sinTheta_O sinTheta_i) v))
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(* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (+ (/ (log (/ 1/2 v)) sinTheta_i) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
(* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (+ (/ (log (/ 1/2 v)) sinTheta_i) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))
(* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))
(* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))
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(- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ (log (/ 1/2 v)) sinTheta_O) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ (log (/ 1/2 v)) sinTheta_O) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ (log (/ 1/2 v)) sinTheta_O) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ 1 v)

Outputs
(exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) (/ (* cosTheta_O (* cosTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))) v))
(fma.f32 cosTheta_O (.f32 (.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 cosTheta_i v)) (*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) (* cosTheta_i (+ (* 1/2 (/ (* (pow cosTheta_O 2) (* cosTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))) (pow v 2))) (/ (* cosTheta_O (exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))) v))))
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(*.f32 sinTheta_i (-.f32 (/.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) sinTheta_i) (/.f32 sinTheta_O v)))
(- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))
(* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(*.f32 sinTheta_O (+.f32 (-.f32 (/.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v) sinTheta_O) (/.f32 sinTheta_i v)) (/.f32 #s(literal 6931/10000 binary32) sinTheta_O)))
(* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(*.f32 sinTheta_O (+.f32 (-.f32 (/.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v) sinTheta_O) (/.f32 sinTheta_i v)) (/.f32 #s(literal 6931/10000 binary32) sinTheta_O)))
(* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(*.f32 sinTheta_O (+.f32 (-.f32 (/.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v) sinTheta_O) (/.f32 sinTheta_i v)) (/.f32 #s(literal 6931/10000 binary32) sinTheta_O)))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))
(* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(*.f32 sinTheta_O (-.f32 (/.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) sinTheta_O) (/.f32 sinTheta_i v)))
(* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(*.f32 sinTheta_O (-.f32 (/.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) sinTheta_O) (/.f32 sinTheta_i v)))
(* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(*.f32 sinTheta_O (-.f32 (/.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) sinTheta_O) (/.f32 sinTheta_i v)))
(- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
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(- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
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(- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
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(/ cosTheta_i v)
(/.f32 cosTheta_i v)
(* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ 1 v) (/ (log (/ 1/2 v)) cosTheta_i))) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(*.f32 cosTheta_i (+.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) cosTheta_i)) (/.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) cosTheta_i)))
(* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ 1 v) (/ (log (/ 1/2 v)) cosTheta_i))) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(*.f32 cosTheta_i (+.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) cosTheta_i)) (/.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) cosTheta_i)))
(* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ 1 v) (/ (log (/ 1/2 v)) cosTheta_i))) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(*.f32 cosTheta_i (+.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) cosTheta_i)) (/.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) cosTheta_i)))
(/ cosTheta_i v)
(/.f32 cosTheta_i v)
(* -1 (* cosTheta_i (- (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_i)) (/ 1 v))))
(*.f32 cosTheta_i (+.f32 (/.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))) cosTheta_i) (/.f32 #s(literal 1 binary32) v)))
(* -1 (* cosTheta_i (- (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_i)) (/ 1 v))))
(*.f32 cosTheta_i (+.f32 (/.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))) cosTheta_i) (/.f32 #s(literal 1 binary32) v)))
(* -1 (* cosTheta_i (- (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_i)) (/ 1 v))))
(*.f32 cosTheta_i (+.f32 (/.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))) cosTheta_i) (/.f32 #s(literal 1 binary32) v)))
(- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
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(- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
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(- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
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(/ (* cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (+ (/ cosTheta_i v) (/ (log (/ 1/2 v)) cosTheta_O))) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(*.f32 cosTheta_O (+.f32 (+.f32 (/.f32 cosTheta_i v) (/.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) cosTheta_O)) (/.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) cosTheta_O)))
(* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (+ (/ cosTheta_i v) (/ (log (/ 1/2 v)) cosTheta_O))) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(*.f32 cosTheta_O (+.f32 (+.f32 (/.f32 cosTheta_i v) (/.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) cosTheta_O)) (/.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) cosTheta_O)))
(* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (+ (/ cosTheta_i v) (/ (log (/ 1/2 v)) cosTheta_O))) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(*.f32 cosTheta_O (+.f32 (+.f32 (/.f32 cosTheta_i v) (/.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) cosTheta_O)) (/.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) cosTheta_O)))
(/ (* cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_O)))))
(*.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))) cosTheta_O)))
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_O)))))
(*.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))) cosTheta_O)))
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))) cosTheta_O)))))
(*.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))) cosTheta_O)))
(/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v)
(/ (- (+ (* cosTheta_O cosTheta_i) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/.f32 (fma.f32 v (+.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 v)) (log.f32 #s(literal 1/2 binary32))) (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))) v)
(/ (- (+ (* cosTheta_O cosTheta_i) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/.f32 (fma.f32 v (+.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 v)) (log.f32 #s(literal 1/2 binary32))) (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))) v)
(/ (- (+ (* cosTheta_O cosTheta_i) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/.f32 (fma.f32 v (+.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 v)) (log.f32 #s(literal 1/2 binary32))) (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))) v)
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(- (+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (/ (* cosTheta_O cosTheta_i) v)))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
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(- (+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (/ (* cosTheta_O cosTheta_i) v)))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
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(+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v)))))
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(+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v)))))
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(+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v)))))
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(- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))
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(- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))
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(- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))
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(- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))
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(* -1 (/ (* sinTheta_O sinTheta_i) v))
(*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))
(* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (+ (/ (log (/ 1/2 v)) sinTheta_i) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
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(* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (+ (/ (log (/ 1/2 v)) sinTheta_i) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
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(* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (+ (/ (log (/ 1/2 v)) sinTheta_i) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
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(* -1 (/ (* sinTheta_O sinTheta_i) v))
(*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))
(* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))
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(* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))
(*.f32 sinTheta_i (-.f32 (/.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))) sinTheta_i) (/.f32 sinTheta_O v)))
(* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))
(*.f32 sinTheta_i (-.f32 (/.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))) sinTheta_i) (/.f32 sinTheta_O v)))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v)))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (log.f32 (/.f32 #s(literal 1/2 binary32) v))) (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (log.f32 (/.f32 #s(literal 1/2 binary32) v))) (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (log.f32 (/.f32 #s(literal 1/2 binary32) v))) (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))
(* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ (log (/ 1/2 v)) sinTheta_O) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(*.f32 sinTheta_O (+.f32 (+.f32 (-.f32 (/.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v) sinTheta_O) (/.f32 sinTheta_i v)) (/.f32 #s(literal 6931/10000 binary32) sinTheta_O)) (/.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) sinTheta_O)))
(* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ (log (/ 1/2 v)) sinTheta_O) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(*.f32 sinTheta_O (+.f32 (+.f32 (-.f32 (/.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v) sinTheta_O) (/.f32 sinTheta_i v)) (/.f32 #s(literal 6931/10000 binary32) sinTheta_O)) (/.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) sinTheta_O)))
(* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ (log (/ 1/2 v)) sinTheta_O) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)))) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(*.f32 sinTheta_O (+.f32 (+.f32 (-.f32 (/.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v) sinTheta_O) (/.f32 sinTheta_i v)) (/.f32 #s(literal 6931/10000 binary32) sinTheta_O)) (/.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) sinTheta_O)))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))
(* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(*.f32 sinTheta_O (-.f32 (/.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))) sinTheta_O) (/.f32 sinTheta_i v)))
(* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(*.f32 sinTheta_O (-.f32 (/.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))) sinTheta_O) (/.f32 sinTheta_i v)))
(* -1 (* sinTheta_O (- (* -1 (/ (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(*.f32 sinTheta_O (-.f32 (/.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))) sinTheta_O) (/.f32 sinTheta_i v)))
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)

eval105.0ms (0.8%)

Memory: -8.4MiB live, 226.9MiB allocated
Compiler: Compiled 33 749 to 2 791 computations (91.7% saved)

prune164.0ms (1.3%)

Memory

19.8MiB live, 258.9MiB allocated

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	887	10	897
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	888	10	898

Accuracy

99.7%

Counts

898 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.8%	(/.f32 (exp.f32 (/.f32 (.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32))) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))))) (exp.f32 (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))))))
▶	99.6%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
	99.7%	(.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32))))
	99.6%	(exp.f32 (fma.f32 (fma.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) v (neg.f32 v)) (/.f32 #s(literal 1 binary32) (.f32 v v)) (-.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32))))))
	97.5%	(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
▶	47.7%	(exp.f32 (/.f32 cosTheta_i v))
▶	99.5%	(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))))
▶	99.7%	(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
▶	15.4%	(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
	13.2%	(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))

Compiler

Compiled 474 to 286 computations (39.7% saved)

simplify235.0ms (1.8%)

Memory

2.1MiB live, 288.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v)))
✓	cost-diff	128	(log.f32 (/.f32 #s(literal 1/2 binary32) v))
✓	cost-diff	3008	(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))))
✓	cost-diff	0	(exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
✓	cost-diff	0	(/.f32 #s(literal 1/2 binary32) v)
✓	cost-diff	0	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
✓	cost-diff	96	(fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
✓	cost-diff	0	(neg.f32 v)
✓	cost-diff	0	(/.f32 sinTheta_i (neg.f32 v))
✓	cost-diff	0	(*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))
✓	cost-diff	0	(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
✓	cost-diff	0	(/.f32 cosTheta_i v)
✓	cost-diff	0	(exp.f32 (/.f32 cosTheta_i v))
✓	cost-diff	0	(+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
✓	cost-diff	96	(fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
✓	cost-diff	128	(log.f32 (/.f32 #s(literal 1/2 binary32) v))
✓	cost-diff	3008	(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))

Rules

3 452×	`lower-fma.f64`
3 446×	`lower-fma.f32`
3 300×	`lower-*.f64`
3 296×	`lower-*.f32`
2 018×	`lower-/.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	198
0	52	199
1	87	196
2	159	196
3	337	196
4	573	190
5	932	190
6	1393	190
7	1991	190
8	3093	190
9	5654	190
0	8318	190

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
(log.f32 (/.f32 #s(literal 1/2 binary32) v))
(/.f32 #s(literal 1/2 binary32) v)
#s(literal 1/2 binary32)
v
(fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
sinTheta_O
sinTheta_i
#s(literal 1 binary32)
(/.f32 #s(literal -1 binary32) v)
#s(literal -1 binary32)
#s(literal 6931/10000 binary32)
(exp.f32 (/.f32 cosTheta_i v))
(/.f32 cosTheta_i v)
cosTheta_i
v
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))
sinTheta_O
(/.f32 sinTheta_i (neg.f32 v))
sinTheta_i
(neg.f32 v)
v
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(/.f32 #s(literal 1/2 binary32) v)
#s(literal 1/2 binary32)
v
(exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
(fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
sinTheta_O
sinTheta_i
#s(literal 1 binary32)
(/.f32 #s(literal -1 binary32) v)
#s(literal -1 binary32)
#s(literal 6931/10000 binary32)
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))))
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v)))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
#s(literal 6931/10000 binary32)
(/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)
(fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))
cosTheta_O
cosTheta_i
#s(literal -1 binary32)
v
(log.f32 (/.f32 #s(literal 1/2 binary32) v))
(/.f32 #s(literal 1/2 binary32) v)
#s(literal 1/2 binary32)

Outputs
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(/.f32 #s(literal 1/2 binary32) (*.f32 v (exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) #s(literal -6931/10000 binary32)))))
(+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
(+.f32 (neg.f32 (log.f32 (*.f32 #s(literal 2 binary32) v))) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
(log.f32 (/.f32 #s(literal 1/2 binary32) v))
(neg.f32 (log.f32 (*.f32 #s(literal 2 binary32) v)))
(/.f32 #s(literal 1/2 binary32) v)
#s(literal 1/2 binary32)
v
(fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
sinTheta_O
sinTheta_i
#s(literal 1 binary32)
(/.f32 #s(literal -1 binary32) v)
#s(literal -1 binary32)
#s(literal 6931/10000 binary32)
(exp.f32 (/.f32 cosTheta_i v))
(/.f32 cosTheta_i v)
cosTheta_i
v
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O (neg.f32 v))))
(*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))
(*.f32 sinTheta_i (/.f32 sinTheta_O (neg.f32 v)))
sinTheta_O
(/.f32 sinTheta_i (neg.f32 v))
sinTheta_i
(neg.f32 v)
v
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(/.f32 #s(literal 1/2 binary32) (*.f32 v (exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) #s(literal -6931/10000 binary32)))))
(/.f32 #s(literal 1/2 binary32) v)
#s(literal 1/2 binary32)
v
(exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
(exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
(fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
sinTheta_O
sinTheta_i
#s(literal 1 binary32)
(/.f32 #s(literal -1 binary32) v)
#s(literal -1 binary32)
#s(literal 6931/10000 binary32)
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))))
(/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))) (*.f32 #s(literal 2 binary32) v))
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v)))
(+.f32 (neg.f32 (log.f32 (*.f32 #s(literal 2 binary32) v))) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
#s(literal 6931/10000 binary32)
(/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
cosTheta_O
cosTheta_i
#s(literal -1 binary32)
v
(log.f32 (/.f32 #s(literal 1/2 binary32) v))
(neg.f32 (log.f32 (*.f32 #s(literal 2 binary32) v)))
(/.f32 #s(literal 1/2 binary32) v)
#s(literal 1/2 binary32)

localize101.0ms (0.8%)

Memory

-10.5MiB live, 228.4MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	4.4%	(/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)
✓	accuracy	2.1%	(+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v)))
✓	accuracy	1.3%	(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
✓	accuracy	1.3%	(/.f32 #s(literal 1/2 binary32) v)
✓	accuracy	10.8%	(exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
✓	accuracy	5.4%	(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
✓	accuracy	2.1%	(fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
✓	accuracy	1.3%	(/.f32 #s(literal 1/2 binary32) v)
✓	accuracy	12.2%	(*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))
✓	accuracy	10.9%	(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
✓	accuracy	10.0%	(/.f32 sinTheta_i (neg.f32 v))
✓	accuracy	5.4%	(neg.f32 v)
✓	accuracy	11.8%	(exp.f32 (/.f32 cosTheta_i v))
✓	accuracy	10.3%	(/.f32 cosTheta_i v)
✓	accuracy	5.4%	(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
✓	accuracy	3.0%	(+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
✓	accuracy	2.1%	(fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
✓	accuracy	1.3%	(/.f32 #s(literal 1/2 binary32) v)

Samples

63.0ms

256×

valid

Compiler

Compiled 422 to 63 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-exp: 11.0ms (24.9% of total)

ival-div: 10.0ms (22.6% of total)

ival-mult: 7.0ms (15.8% of total)

ival-add: 6.0ms (13.6% of total)

const: 4.0ms (9% of total)

ival-log: 3.0ms (6.8% of total)

ival-neg: 1.0ms (2.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series143.0ms (1.1%)

Memory

0.1MiB live, 203.6MiB allocated

Counts

18 → 528

Calls

Call 1

Inputs
#<alt (exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))>
#<alt (log.f32 (/.f32 #s(literal 1/2 binary32) v))>
#<alt (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))>
#<alt (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))>
#<alt (exp.f32 (/.f32 cosTheta_i v))>
#<alt (/.f32 cosTheta_i v)>
#<alt (exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))>
#<alt (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))>
#<alt (/.f32 sinTheta_i (neg.f32 v))>
#<alt (neg.f32 v)>
#<alt (*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))>
#<alt (/.f32 #s(literal 1/2 binary32) v)>
#<alt (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))>
#<alt (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))))>
#<alt (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v)))>
#<alt (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))>
#<alt (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))>
#<alt (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)>

Outputs
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v)))))>
#<alt (+ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (* -1 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ 1 (* sinTheta_O sinTheta_i))) v)))>
#<alt (+ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ (* -1 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (* 1/2 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2)))))>
#<alt (+ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ (* -1 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (* -1/6 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (pow v 3))) (* 1/2 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))))))>
#<alt (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v)))))>
#<alt (+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (+ 1 (* sinTheta_O sinTheta_i))) v)))>
#<alt (+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (+ (* -1/2 (/ (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) v)) (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))>
#<alt (+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) v)) (* 1/2 (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) v)) (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))>
#<alt (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))>
#<alt (+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))))) v)))>
#<alt (+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))))) (pow v 2))))))>
#<alt (+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))) (pow v 2))))))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))>
#<alt (+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))))) v)))>
#<alt (+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))))) (pow v 2))))))>
#<alt (+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))) (pow v 2))))))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* -1 (log v))>
#<alt (* -1 (log v))>
#<alt (* -1 (log v))>
#<alt (* -1 (log v))>
#<alt (+ (log 1/2) (log (/ 1 v)))>
#<alt (+ (log 1/2) (log (/ 1 v)))>
#<alt (+ (log 1/2) (log (/ 1 v)))>
#<alt (+ (log 1/2) (log (/ 1 v)))>
#<alt (+ (log -1/2) (log (/ -1 v)))>
#<alt (+ (log -1/2) (log (/ -1 v)))>
#<alt (+ (log -1/2) (log (/ -1 v)))>
#<alt (+ (log -1/2) (log (/ -1 v)))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (* -1 (/ sinTheta_O v))>
#<alt (* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* -1 (/ sinTheta_O v))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (/ 1 (* sinTheta_i v))))>
#<alt (* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (/ 1 (* sinTheta_i v))))>
#<alt (* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (/ 1 (* sinTheta_i v))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))>
#<alt (* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))>
#<alt (* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* 6931/10000 v)) v)>
#<alt (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* 6931/10000 v)) v)>
#<alt (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* 6931/10000 v)) v)>
#<alt 6931/10000>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt 6931/10000>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) v)>
#<alt (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) v)>
#<alt (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) v)>
#<alt (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))>
#<alt (+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))>
#<alt (+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (log (/ 1/2 v)) sinTheta_O))) (/ 1 (* sinTheta_O v))))>
#<alt (* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (log (/ 1/2 v)) sinTheta_O))) (/ 1 (* sinTheta_O v))))>
#<alt (* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (log (/ 1/2 v)) sinTheta_O))) (/ 1 (* sinTheta_O v))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))>
#<alt (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (* -1 (/ sinTheta_i v))>
#<alt (* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (log (/ 1/2 v)) sinTheta_i)) (+ (/ 1 v) (/ 1 (* sinTheta_i v)))))>
#<alt (* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (log (/ 1/2 v)) sinTheta_i)) (+ (/ 1 v) (/ 1 (* sinTheta_i v)))))>
#<alt (* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (log (/ 1/2 v)) sinTheta_i)) (+ (/ 1 v) (/ 1 (* sinTheta_i v)))))>
#<alt (* -1 (/ sinTheta_i v))>
#<alt (* -1 (* sinTheta_i (+ (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) sinTheta_i)) (/ 1 v))))>
#<alt (* -1 (* sinTheta_i (+ (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) sinTheta_i)) (/ 1 v))))>
#<alt (* -1 (* sinTheta_i (+ (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) sinTheta_i)) (/ 1 v))))>
#<alt 1>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (* cosTheta_i (+ (* 1/2 (/ cosTheta_i (pow v 2))) (/ 1 v))))>
#<alt (+ 1 (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ cosTheta_i (pow v 3))) (* 1/2 (/ 1 (pow v 2))))) (/ 1 v))))>
#<alt (exp (/ cosTheta_i v))>
#<alt (exp (/ cosTheta_i v))>
#<alt (exp (/ cosTheta_i v))>
#<alt (exp (/ cosTheta_i v))>
#<alt (exp (/ cosTheta_i v))>
#<alt (exp (/ cosTheta_i v))>
#<alt (exp (/ cosTheta_i v))>
#<alt (exp (/ cosTheta_i v))>
#<alt (exp (/ cosTheta_i v))>
#<alt (exp (/ cosTheta_i v))>
#<alt (exp (/ cosTheta_i v))>
#<alt (exp (/ cosTheta_i v))>
#<alt 1>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (+ (* 1/2 (/ (pow cosTheta_i 2) (pow v 2))) (/ cosTheta_i v)))>
#<alt (+ 1 (+ (* 1/6 (/ (pow cosTheta_i 3) (pow v 3))) (+ (* 1/2 (/ (pow cosTheta_i 2) (pow v 2))) (/ cosTheta_i v))))>
#<alt 1>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (* -1 (/ (+ (* -1 cosTheta_i) (* -1/2 (/ (pow cosTheta_i 2) v))) v)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 cosTheta_i) (* -1 (/ (+ (* 1/6 (/ (pow cosTheta_i 3) v)) (* 1/2 (pow cosTheta_i 2))) v))) v)))>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt 1>
#<alt (+ 1 (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (+ 1 (* sinTheta_O (+ (* -1 (/ sinTheta_i v)) (* 1/2 (/ (* sinTheta_O (pow sinTheta_i 2)) (pow v 2))))))>
#<alt (+ 1 (* sinTheta_O (+ (* -1 (/ sinTheta_i v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (pow sinTheta_i 3)) (pow v 3))) (* 1/2 (/ (pow sinTheta_i 2) (pow v 2))))))))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (+ 1 (* sinTheta_i (+ (* -1 (/ sinTheta_O v)) (* 1/2 (/ (* (pow sinTheta_O 2) sinTheta_i) (pow v 2))))))>
#<alt (+ 1 (* sinTheta_i (+ (* -1 (/ sinTheta_O v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) sinTheta_i) (pow v 3))) (* 1/2 (/ (pow sinTheta_O 2) (pow v 2))))))))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (* sinTheta_O sinTheta_i) v)))>
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#<alt (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ cosTheta_O v) (/ (log (/ 1/2 v)) cosTheta_i))) (/ 1 (* cosTheta_i v))))>
#<alt (* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ cosTheta_O v) (/ (log (/ 1/2 v)) cosTheta_i))) (/ 1 (* cosTheta_i v))))>
#<alt (* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ cosTheta_O v) (/ (log (/ 1/2 v)) cosTheta_i))) (/ 1 (* cosTheta_i v))))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) cosTheta_i)))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) cosTheta_i)))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) cosTheta_i)))))>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (+ (* cosTheta_O cosTheta_i) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) 1) v)>
#<alt (/ (- (+ (* cosTheta_O cosTheta_i) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) 1) v)>
#<alt (/ (- (+ (* cosTheta_O cosTheta_i) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) 1) v)>
#<alt (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))>
#<alt (- (+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (/ cosTheta_O v)>
#<alt (* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (/ 1 v)) (/ 1 (* cosTheta_O v))))>
#<alt (* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (/ 1 v)) (/ 1 (* cosTheta_O v))))>
#<alt (* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (/ 1 v)) (/ 1 (* cosTheta_O v))))>
#<alt (/ cosTheta_O v)>
#<alt (* -1 (* cosTheta_O (- (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_O)) (/ 1 v))))>
#<alt (* -1 (* cosTheta_O (- (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_O)) (/ 1 v))))>
#<alt (* -1 (* cosTheta_O (- (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_O)) (/ 1 v))))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (/ cosTheta_O v)) (/ 1 (* cosTheta_i v))))>
#<alt (* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (/ cosTheta_O v)) (/ 1 (* cosTheta_i v))))>
#<alt (* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (/ cosTheta_O v)) (/ 1 (* cosTheta_i v))))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_i)))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_i)))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_i)))))>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) 1) v)>
#<alt (/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) 1) v)>
#<alt (/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) 1) v)>
#<alt 6931/10000>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt 6931/10000>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt 1>
#<alt (+ 1 (* sinTheta_O sinTheta_i))>
#<alt (+ 1 (* sinTheta_O sinTheta_i))>
#<alt (+ 1 (* sinTheta_O sinTheta_i))>
#<alt sinTheta_O>
#<alt (* sinTheta_O (+ 1 (/ 1 sinTheta_O)))>
#<alt (* sinTheta_O (+ 1 (/ 1 sinTheta_O)))>
#<alt (* sinTheta_O (+ 1 (/ 1 sinTheta_O)))>
#<alt sinTheta_O>
#<alt (* sinTheta_O (+ 1 (/ 1 sinTheta_O)))>
#<alt (* sinTheta_O (+ 1 (/ 1 sinTheta_O)))>
#<alt (* sinTheta_O (+ 1 (/ 1 sinTheta_O)))>
#<alt 1>
#<alt (+ 1 (* sinTheta_O sinTheta_i))>
#<alt (+ 1 (* sinTheta_O sinTheta_i))>
#<alt (+ 1 (* sinTheta_O sinTheta_i))>
#<alt (* sinTheta_O sinTheta_i)>
#<alt (* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))>
#<alt (* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))>
#<alt (* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))>
#<alt (* sinTheta_O sinTheta_i)>
#<alt (* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))>
#<alt (* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))>
#<alt (* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))>
#<alt (/ -1 v)>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (/ cosTheta_O v)>
#<alt (* cosTheta_O (- (/ 1 v) (/ 1 (* cosTheta_O v))))>
#<alt (* cosTheta_O (- (/ 1 v) (/ 1 (* cosTheta_O v))))>
#<alt (* cosTheta_O (- (/ 1 v) (/ 1 (* cosTheta_O v))))>
#<alt (/ cosTheta_O v)>
#<alt (* -1 (* cosTheta_O (- (/ 1 (* cosTheta_O v)) (/ 1 v))))>
#<alt (* -1 (* cosTheta_O (- (/ 1 (* cosTheta_O v)) (/ 1 v))))>
#<alt (* -1 (* cosTheta_O (- (/ 1 (* cosTheta_O v)) (/ 1 v))))>
#<alt (/ -1 v)>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_i (- (/ cosTheta_O v) (/ 1 (* cosTheta_i v))))>
#<alt (* cosTheta_i (- (/ cosTheta_O v) (/ 1 (* cosTheta_i v))))>
#<alt (* cosTheta_i (- (/ cosTheta_O v) (/ 1 (* cosTheta_i v))))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ 1 (* cosTheta_i v)))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ 1 (* cosTheta_i v)))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ 1 (* cosTheta_i v)))))>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>

Calls

132 calls:

Time	Variable		Point	Expression
31.0ms	sinTheta_O	@	0	(exp (+ (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v)) 6931/10000))
17.0ms	sinTheta_i	@	-inf	(exp (* sinTheta_O (/ sinTheta_i (neg v))))
9.0ms	v	@	0	(log (/ 1/2 v))
7.0ms	v	@	-inf	(log (/ 1/2 v))
6.0ms	v	@	inf	(log (/ 1/2 v))

Compiler

Compiled 1 752 to 1 322 computations (24.5% saved)

rewrite360.0ms (2.8%)

Memory

13.0MiB live, 610.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 756×	`lower-/.f64`
4 746×	`lower-/.f32`
4 114×	`lower-*.f64`
4 110×	`lower-*.f32`
3 978×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	140
0	52	141
1	189	138
2	1388	138
0	8347	138

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

18 → 641

Calls

Call 1

Inputs
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(log.f32 (/.f32 #s(literal 1/2 binary32) v))
(fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
(+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
(exp.f32 (/.f32 cosTheta_i v))
(/.f32 cosTheta_i v)
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))
(/.f32 sinTheta_i (neg.f32 v))
(neg.f32 v)
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(/.f32 #s(literal 1/2 binary32) v)
(exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))))
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v)))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
(/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)

Outputs
(exp.f32 (+.f32 (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))
(pow.f32 (/.f32 v (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))) #s(literal -1 binary32))
(pow.f32 (exp.f32 (fma.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))) (pow.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 3 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32))))) (pow.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 2 binary32)))))
(pow.f32 (exp.f32 (-.f32 (pow.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 2 binary32)) (.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))) (/.f32 #s(literal 1 binary32) (-.f32 (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))))
(/.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 (log.f32 v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))))
(/.f32 #s(literal 1 binary32) (/.f32 v (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 v (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 v #s(literal 2 binary32)) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 v #s(literal 2 binary32)) (.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 v) (*.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))) #s(literal -1/2 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 v #s(literal 2 binary32)) (.f32 #s(literal 1 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))))
(/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 v) (*.f32 #s(literal -1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 v (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))))))
(/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))) (*.f32 v #s(literal 2 binary32)))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))) v)
(/.f32 (neg.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))) (neg.f32 v))
(/.f32 (.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))) #s(literal 1 binary32)) (.f32 v #s(literal 2 binary32)))
(/.f32 (*.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))) #s(literal -1/2 binary32)) (neg.f32 v))
(/.f32 (.f32 #s(literal 1 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))) (.f32 v #s(literal 2 binary32)))
(/.f32 (*.f32 #s(literal -1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))) (neg.f32 v))
(/.f32 (exp.f32 (/.f32 (pow.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 2 binary32)) (-.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))) (exp.f32 (/.f32 (.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))) (-.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))))
(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))) v)
(/.f32 (neg.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))) (neg.f32 (*.f32 v #s(literal 2 binary32))))
(/.f32 (neg.f32 (neg.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))))) v)
(/.f32 (neg.f32 (.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))) #s(literal 1 binary32))) (neg.f32 (.f32 v #s(literal 2 binary32))))
(/.f32 (neg.f32 (*.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))) #s(literal -1/2 binary32))) v)
(/.f32 (neg.f32 (.f32 #s(literal 1 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))) (neg.f32 (.f32 v #s(literal 2 binary32))))
(/.f32 (neg.f32 (*.f32 #s(literal -1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))) v)
(.f32 #s(literal 1/2 binary32) (.f32 (/.f32 #s(literal 1 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))))
(*.f32 #s(literal 1/2 binary32) (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))) v))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))
(*.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))) (/.f32 #s(literal 1/2 binary32) v))
(.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (.f32 (exp.f32 #s(literal 6931/10000 binary32)) (/.f32 #s(literal 1/2 binary32) v)))
(.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))
(*.f32 #s(literal -1/2 binary32) (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))) (neg.f32 v)))
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simplify443.0ms (3.4%)

Memory

-19.7MiB live, 930.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 576×	`lower-fma.f64`
9 576×	`lower-fma.f32`
7 116×	`lower-*.f64`
7 116×	`lower-*.f32`
3 744×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	640	6834
1	1912	6500
2	6395	6323
0	8861	6003

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 526

Calls

Call 1

Inputs
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v)))))
(+ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (* -1 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ 1 (* sinTheta_O sinTheta_i))) v)))
(+ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ (* -1 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (* 1/2 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2)))))
(+ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ (* -1 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (* -1/6 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (pow v 3))) (* 1/2 (/ (* (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))))))
(exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v)))))
(+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (+ 1 (* sinTheta_O sinTheta_i))) v)))
(+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (+ (* -1/2 (/ (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) v)) (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) v)) (* 1/2 (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) v)) (* (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))))) v)))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))))) (pow v 2))))))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))) (pow v 2))))))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))))) v)))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))))) (pow v 2))))))
(+ (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))) (pow v 2))))))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* -1 (log v))
(* -1 (log v))
(* -1 (log v))
(* -1 (log v))
(+ (log 1/2) (log (/ 1 v)))
(+ (log 1/2) (log (/ 1 v)))
(+ (log 1/2) (log (/ 1 v)))
(+ (log 1/2) (log (/ 1 v)))
(+ (log -1/2) (log (/ -1 v)))
(+ (log -1/2) (log (/ -1 v)))
(+ (log -1/2) (log (/ -1 v)))
(+ (log -1/2) (log (/ -1 v)))
(- 6931/10000 (/ 1 v))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))
(* -1 (/ sinTheta_O v))
(* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))
(* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))
(* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))
(* -1 (/ sinTheta_O v))
(* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ 1 v))))
(* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ 1 v))))
(* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ 1 v))))
(- 6931/10000 (/ 1 v))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (/ 1 (* sinTheta_i v))))
(* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (/ 1 (* sinTheta_i v))))
(* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (/ 1 (* sinTheta_i v))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))
(* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))
(* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* 6931/10000 v)) v)
(/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* 6931/10000 v)) v)
(/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* 6931/10000 v)) v)
6931/10000
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
6931/10000
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) v)
(/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) v)
(/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v)))))) v)
(+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))
(+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(+ 6931/10000 (+ (log 1/2) (+ (log (/ 1 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))
(+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(+ 6931/10000 (+ (log -1/2) (+ (log (/ -1 v)) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (log (/ 1/2 v)) sinTheta_O))) (/ 1 (* sinTheta_O v))))
(* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (log (/ 1/2 v)) sinTheta_O))) (/ 1 (* sinTheta_O v))))
(* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (log (/ 1/2 v)) sinTheta_O))) (/ 1 (* sinTheta_O v))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (* sinTheta_O (+ (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))
(* -1 (* sinTheta_O (+ (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))
(* -1 (* sinTheta_O (+ (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))
(- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))
(- (+ 6931/10000 (+ (log (/ 1/2 v)) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))
(* -1 (/ sinTheta_i v))
(* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (log (/ 1/2 v)) sinTheta_i)) (+ (/ 1 v) (/ 1 (* sinTheta_i v)))))
(* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (log (/ 1/2 v)) sinTheta_i)) (+ (/ 1 v) (/ 1 (* sinTheta_i v)))))
(* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (log (/ 1/2 v)) sinTheta_i)) (+ (/ 1 v) (/ 1 (* sinTheta_i v)))))
(* -1 (/ sinTheta_i v))
(* -1 (* sinTheta_i (+ (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) sinTheta_i)) (/ 1 v))))
(* -1 (* sinTheta_i (+ (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) sinTheta_i)) (/ 1 v))))
(* -1 (* sinTheta_i (+ (* -1 (/ (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)) sinTheta_i)) (/ 1 v))))
1
(+ 1 (/ cosTheta_i v))
(+ 1 (* cosTheta_i (+ (* 1/2 (/ cosTheta_i (pow v 2))) (/ 1 v))))
(+ 1 (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ cosTheta_i (pow v 3))) (* 1/2 (/ 1 (pow v 2))))) (/ 1 v))))
(exp (/ cosTheta_i v))
(exp (/ cosTheta_i v))
(exp (/ cosTheta_i v))
(exp (/ cosTheta_i v))
(exp (/ cosTheta_i v))
(exp (/ cosTheta_i v))
(exp (/ cosTheta_i v))
(exp (/ cosTheta_i v))
(exp (/ cosTheta_i v))
(exp (/ cosTheta_i v))
(exp (/ cosTheta_i v))
(exp (/ cosTheta_i v))
1
(+ 1 (/ cosTheta_i v))
(+ 1 (+ (* 1/2 (/ (pow cosTheta_i 2) (pow v 2))) (/ cosTheta_i v)))
(+ 1 (+ (* 1/6 (/ (pow cosTheta_i 3) (pow v 3))) (+ (* 1/2 (/ (pow cosTheta_i 2) (pow v 2))) (/ cosTheta_i v))))
1
(+ 1 (/ cosTheta_i v))
(+ 1 (* -1 (/ (+ (* -1 cosTheta_i) (* -1/2 (/ (pow cosTheta_i 2) v))) v)))
(+ 1 (* -1 (/ (+ (* -1 cosTheta_i) (* -1 (/ (+ (* 1/6 (/ (pow cosTheta_i 3) v)) (* 1/2 (pow cosTheta_i 2))) v))) v)))
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
(/ cosTheta_i v)
1
(+ 1 (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(+ 1 (* sinTheta_O (+ (* -1 (/ sinTheta_i v)) (* 1/2 (/ (* sinTheta_O (pow sinTheta_i 2)) (pow v 2))))))
(+ 1 (* sinTheta_O (+ (* -1 (/ sinTheta_i v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (pow sinTheta_i 3)) (pow v 3))) (* 1/2 (/ (pow sinTheta_i 2) (pow v 2))))))))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
1
(+ 1 (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(+ 1 (* sinTheta_i (+ (* -1 (/ sinTheta_O v)) (* 1/2 (/ (* (pow sinTheta_O 2) sinTheta_i) (pow v 2))))))
(+ 1 (* sinTheta_i (+ (* -1 (/ sinTheta_O v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) sinTheta_i) (pow v 3))) (* 1/2 (/ (pow sinTheta_O 2) (pow v 2))))))))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(exp (* -1 (/ (* sinTheta_O sinTheta_i) v)))
1
(+ 1 (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(+ 1 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (pow sinTheta_i 2)) (pow v 2)))))
(+ 1 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (+ (* -1/6 (/ (* (pow sinTheta_O 3) (pow sinTheta_i 3)) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (pow sinTheta_i 2)) (pow v 2))))))
1
(+ 1 (* -1 (/ (* sinTheta_O sinTheta_i) v)))
(+ 1 (* -1 (/ (+ (* -1/2 (/ (* (pow sinTheta_O 2) (pow sinTheta_i 2)) v)) (* sinTheta_O sinTheta_i)) v)))
(+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (pow sinTheta_O 3) (pow sinTheta_i 3)) v)) (* 1/2 (* (pow sinTheta_O 2) (pow sinTheta_i 2)))) v)) (* sinTheta_O sinTheta_i)) v)))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ sinTheta_O v))
(* -1 (/ sinTheta_O v))
(* -1 (/ sinTheta_O v))
(* -1 (/ sinTheta_O v))
(* -1 (/ sinTheta_O v))
(* -1 (/ sinTheta_O v))
(* -1 (/ sinTheta_O v))
(* -1 (/ sinTheta_O v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 (/ sinTheta_i v))
(* -1 v)
(* -1 v)
(* -1 v)
(* -1 v)
(* -1 v)
(* -1 v)
(* -1 v)
(* -1 v)
(* -1 v)
(* -1 v)
(* -1 v)
(* -1 v)
(* 1/2 (/ (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))) v))
(* 1/2 (/ (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))) v))
(* 1/2 (/ (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))) v))
(* 1/2 (/ (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))) v))
(* 1/2 (/ (exp 6931/10000) v))
(/ (+ (* -1/2 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)) (* 1/2 (exp 6931/10000))) v)
(/ (+ (* -1/2 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (* 1/4 (/ (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))) (* 1/2 (exp 6931/10000)))) v)
(/ (+ (* -1/2 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (* -1/12 (/ (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (pow v 3))) (+ (* 1/4 (/ (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))) (* 1/2 (exp 6931/10000))))) v)
(* 1/2 (/ (exp 6931/10000) v))
(* -1 (/ (+ (* -1/2 (exp 6931/10000)) (* 1/2 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v))) v))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i)))) (* 1/4 (/ (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) v))) v)) (* -1/2 (exp 6931/10000))) v))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (* 1/12 (/ (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) v))) v)) (* -1/2 (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))))) v)) (* -1/2 (exp 6931/10000))) v))
(* 1/2 (/ (exp (- 6931/10000 (/ 1 v))) v))
(+ (* -1/2 (/ (* sinTheta_O (* sinTheta_i (exp (- 6931/10000 (/ 1 v))))) (pow v 2))) (* 1/2 (/ (exp (- 6931/10000 (/ 1 v))) v)))
(+ (* 1/2 (/ (exp (- 6931/10000 (/ 1 v))) v)) (* sinTheta_O (+ (* -1/2 (/ (* sinTheta_i (exp (- 6931/10000 (/ 1 v)))) (pow v 2))) (* 1/4 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- 6931/10000 (/ 1 v))))) (pow v 3))))))
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(- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))
(/ cosTheta_O v)
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(* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (+ (/ 1 v) (/ (log (/ 1/2 v)) cosTheta_O))) (/ 1 (* cosTheta_O v))))
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(/ cosTheta_O v)
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(* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (+ (/ cosTheta_O v) (/ (log (/ 1/2 v)) cosTheta_i))) (/ 1 (* cosTheta_i v))))
(/ (* cosTheta_O cosTheta_i) v)
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(- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
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(/ cosTheta_O v)
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(* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (/ 1 v)) (/ 1 (* cosTheta_O v))))
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(/ cosTheta_O v)
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(/ (* cosTheta_O cosTheta_i) v)
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(* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (/ cosTheta_O v)) (/ 1 (* cosTheta_i v))))
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(/ (* cosTheta_O cosTheta_i) v)
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(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_i)))))
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(/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) 1) v)
(/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) 1) v)
6931/10000
(- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
(- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
(- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
6931/10000
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(- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
(- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
1
(+ 1 (* sinTheta_O sinTheta_i))
(+ 1 (* sinTheta_O sinTheta_i))
(+ 1 (* sinTheta_O sinTheta_i))
sinTheta_O
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
sinTheta_O
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
1
(+ 1 (* sinTheta_O sinTheta_i))
(+ 1 (* sinTheta_O sinTheta_i))
(+ 1 (* sinTheta_O sinTheta_i))
(* sinTheta_O sinTheta_i)
(* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))
(* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))
(* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))
(* sinTheta_O sinTheta_i)
(* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))
(* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))
(* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))
(/ -1 v)
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(- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))
(- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))
(/ cosTheta_O v)
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(* cosTheta_O (- (/ 1 v) (/ 1 (* cosTheta_O v))))
(* cosTheta_O (- (/ 1 v) (/ 1 (* cosTheta_O v))))
(/ cosTheta_O v)
(* -1 (* cosTheta_O (- (/ 1 (* cosTheta_O v)) (/ 1 v))))
(* -1 (* cosTheta_O (- (/ 1 (* cosTheta_O v)) (/ 1 v))))
(* -1 (* cosTheta_O (- (/ 1 (* cosTheta_O v)) (/ 1 v))))
(/ -1 v)
(- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))
(- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))
(- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))
(/ (* cosTheta_O cosTheta_i) v)
(* cosTheta_i (- (/ cosTheta_O v) (/ 1 (* cosTheta_i v))))
(* cosTheta_i (- (/ cosTheta_O v) (/ 1 (* cosTheta_i v))))
(* cosTheta_i (- (/ cosTheta_O v) (/ 1 (* cosTheta_i v))))
(/ (* cosTheta_O cosTheta_i) v)
(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ 1 (* cosTheta_i v)))))
(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ 1 (* cosTheta_i v)))))
(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ 1 (* cosTheta_i v)))))
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)

Outputs
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(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)

eval128.0ms (1%)

Memory: -0.3MiB live, 363.0MiB allocated
Compiler: Compiled 31 358 to 3 027 computations (90.3% saved)

prune232.0ms (1.8%)

Memory

34.9MiB live, 428.2MiB allocated

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	1 364	18	1 382
Fresh	5	0	5
Picked	4	1	5
Done	0	0	0
Total	1 373	19	1 392

Accuracy

99.9%

Counts

1 392 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.3%	(fma.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)) #s(literal 1 binary32))
▶	3.0%	(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
	99.5%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
▶	99.8%	(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))) v)
	99.6%	(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)
	99.6%	(/.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 (log.f32 v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)))))
	5.3%	(+.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta_i (/.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i cosTheta_i)) v) (.f32 #s(literal 1/2 binary32) (.f32 cosTheta_i cosTheta_i))) v)) v))
	5.8%	(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
	98.8%	(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 (/.f32 (.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal -1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal -1 binary32))) (*.f32 v v)) (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) #s(literal -6931/10000 binary32)))) (exp.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) #s(literal -6931/10000 binary32))))))
	99.7%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
▶	99.5%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
	99.5%	(.f32 (.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))) (exp.f32 #s(literal 6931/10000 binary32)))
	97.5%	(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
	43.3%	(exp.f32 (/.f32 sinTheta_O (neg.f32 v)))
✓	47.7%	(exp.f32 (/.f32 cosTheta_i v))
▶	99.7%	(exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))))
	99.5%	(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))))
	47.7%	(exp.f32 (*.f32 (/.f32 #s(literal 1 binary32) v) cosTheta_i))
▶	6.5%	#s(literal 1 binary32)

Compiler

Compiled 663 to 485 computations (26.8% saved)

simplify248.0ms (1.9%)

Memory

-7.2MiB live, 551.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
✓	cost-diff	64	(+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))
✓	cost-diff	64	(+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32))))))
✓	cost-diff	2944	(exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))))
✓	cost-diff	0	(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
✓	cost-diff	0	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))
✓	cost-diff	0	(/.f32 #s(literal 1/2 binary32) v)
✓	cost-diff	0	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
✓	cost-diff	0	(/.f32 cosTheta_i (.f32 v (.f32 v v)))
✓	cost-diff	160	(fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))
✓	cost-diff	160	(fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v))
✓	cost-diff	160	(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))
✓	cost-diff	0	(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))) v)
✓	cost-diff	64	(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))
✓	cost-diff	3136	(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32))))

Rules

5 668×	`lower-fma.f64`
5 660×	`lower-fma.f32`
3 960×	`lower-*.f64`
3 952×	`lower-*.f32`
1 998×	`lower-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	254
0	68	241
1	127	232
2	272	232
3	601	232
4	1249	232
5	2022	231
6	3569	231
7	7489	230
0	8031	225

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))) v)
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32))))
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))
#s(literal 6931/10000 binary32)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
sinTheta_O
sinTheta_i
#s(literal 1 binary32)
(neg.f32 v)
v
(log.f32 #s(literal 1/2 binary32))
#s(literal 1/2 binary32)
#s(literal 1 binary32)
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
cosTheta_i
(fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v))
(fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))
#s(literal 1/6 binary32)
(/.f32 cosTheta_i (.f32 v (.f32 v v)))
(.f32 v (.f32 v v))
v
(*.f32 v v)
(/.f32 #s(literal 1/2 binary32) (*.f32 v v))
#s(literal 1/2 binary32)
(/.f32 #s(literal 1 binary32) v)
#s(literal 1 binary32)
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(/.f32 #s(literal 1/2 binary32) v)
#s(literal 1/2 binary32)
v
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
#s(literal 6931/10000 binary32)
(/.f32 #s(literal -1 binary32) v)
#s(literal -1 binary32)
(exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))))
(+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32))))))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
sinTheta_O
sinTheta_i
#s(literal 1 binary32)
(neg.f32 v)
v
(+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))
#s(literal 6931/10000 binary32)
(neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32))))
(log.f32 (*.f32 v #s(literal 2 binary32)))
(*.f32 v #s(literal 2 binary32))
#s(literal 2 binary32)

Outputs
(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))) v)
(/.f32 #s(literal 1/2 binary32) (*.f32 v (exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) #s(literal -6931/10000 binary32)))))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))
(+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
#s(literal 6931/10000 binary32)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
sinTheta_O
sinTheta_i
#s(literal 1 binary32)
(neg.f32 v)
v
(log.f32 #s(literal 1/2 binary32))
#s(literal 1/2 binary32)
#s(literal 1 binary32)
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 (/.f32 cosTheta_i v) (fma.f32 (/.f32 cosTheta_i v) (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i v) #s(literal 1/2 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32))
cosTheta_i
(fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v))
(fma.f32 (/.f32 cosTheta_i (*.f32 v v)) (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i v) #s(literal 1/2 binary32)) (/.f32 #s(literal 1 binary32) v))
(fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 v v)) (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i v) #s(literal 1/2 binary32)))
#s(literal 1/6 binary32)
(/.f32 cosTheta_i (.f32 v (.f32 v v)))
(.f32 v (.f32 v v))
v
(*.f32 v v)
(/.f32 #s(literal 1/2 binary32) (*.f32 v v))
#s(literal 1/2 binary32)
(/.f32 #s(literal 1 binary32) v)
#s(literal 1 binary32)
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) (*.f32 v #s(literal 2 binary32)))
(/.f32 #s(literal 1/2 binary32) v)
#s(literal 1/2 binary32)
v
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
#s(literal 6931/10000 binary32)
(/.f32 #s(literal -1 binary32) v)
#s(literal -1 binary32)
(exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))))
(/.f32 #s(literal 1/2 binary32) (*.f32 v (exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) #s(literal -6931/10000 binary32)))))
(+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32))))))
(-.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 (*.f32 v #s(literal 2 binary32))))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
sinTheta_O
sinTheta_i
#s(literal 1 binary32)
(neg.f32 v)
v
(+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))
(-.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32))))
#s(literal 6931/10000 binary32)
(neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32))))
(log.f32 (*.f32 v #s(literal 2 binary32)))
(*.f32 v #s(literal 2 binary32))
#s(literal 2 binary32)

localize124.0ms (1%)

Memory

-7.6MiB live, 361.4MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	10.3%	(+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32))))))
✓	accuracy	9.8%	(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
✓	accuracy	2.1%	(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
✓	accuracy	2.1%	(+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))
✓	accuracy	6.5%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
✓	accuracy	4.6%	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))
✓	accuracy	4.4%	(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
✓	accuracy	2.1%	(/.f32 #s(literal -1 binary32) v)
✓	accuracy	5.4%	(fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v))
✓	accuracy	4.5%	(.f32 v (.f32 v v))
✓	accuracy	4.5%	(fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))
✓	accuracy	3.5%	(/.f32 cosTheta_i (.f32 v (.f32 v v)))
✓	accuracy	6.4%	(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32))))
✓	accuracy	5.2%	(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))) v)
✓	accuracy	2.1%	(+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))
✓	accuracy	2.1%	(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))

Samples

78.0ms

256×

valid

Compiler

Compiled 531 to 82 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-div: 13.0ms (22.8% of total)

ival-add: 12.0ms (21.1% of total)

ival-mult: 11.0ms (19.3% of total)

const: 7.0ms (12.3% of total)

ival-exp: 5.0ms (8.8% of total)

ival-log: 5.0ms (8.8% of total)

ival-neg: 2.0ms (3.5% of total)

exact: 1.0ms (1.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series138.0ms (1.1%)

Memory

-6.6MiB live, 226.2MiB allocated

Counts

19 → 456

Calls

Call 1

Inputs
#<alt (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32))))>
#<alt (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))>
#<alt (/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))) v)>
#<alt (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))>
#<alt (fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))>
#<alt (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v))>
#<alt (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))>
#<alt (/.f32 cosTheta_i (.f32 v (.f32 v v)))>
#<alt (*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))>
#<alt (/.f32 #s(literal 1/2 binary32) v)>
#<alt (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))>
#<alt (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))>
#<alt (exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))))>
#<alt (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32))))))>
#<alt (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))>
#<alt (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))>
#<alt (.f32 v (.f32 v v))>
#<alt (/.f32 #s(literal -1 binary32) v)>
#<alt (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))>

Outputs
#<alt (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))>
#<alt (+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) v)))>
#<alt (+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))))))>
#<alt (+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))))))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))>
#<alt (+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) v)))>
#<alt (+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))))))>
#<alt (+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))))))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (exp (+ 6931/10000 (log 1/2)))>
#<alt (+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)))>
#<alt (+ (exp (+ 6931/10000 (log 1/2))) (+ (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2)))))>
#<alt (+ (exp (+ 6931/10000 (log 1/2))) (+ (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (* -1/6 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (pow v 3))) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))))))>
#<alt (exp (+ 6931/10000 (log 1/2)))>
#<alt (+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)))>
#<alt (+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (+ (* -1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) v)) (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))>
#<alt (+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) v)) (* 1/2 (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) v)) (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (* -1 (/ sinTheta_O v))>
#<alt (* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* -1 (/ sinTheta_O v))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (/ 1 (* sinTheta_i v))))>
#<alt (* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (/ 1 (* sinTheta_i v))))>
#<alt (* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (/ 1 (* sinTheta_i v))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))>
#<alt (* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))>
#<alt (* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* 6931/10000 v)) v)>
#<alt (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* 6931/10000 v)) v)>
#<alt (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* 6931/10000 v)) v)>
#<alt 6931/10000>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt 6931/10000>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v)>
#<alt (+ (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))>
#<alt (+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))>
#<alt (+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 4))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 3))))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v)>
#<alt (+ (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))>
#<alt (+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))>
#<alt (+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 4))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 3))))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))) v)>
#<alt (/ (exp (+ 6931/10000 (log 1/2))) v)>
#<alt (/ (+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v))) v)>
#<alt (/ (+ (exp (+ 6931/10000 (log 1/2))) (+ (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))))) v)>
#<alt (/ (+ (exp (+ 6931/10000 (log 1/2))) (+ (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (* -1/6 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (pow v 3))) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2)))))) v)>
#<alt (/ (exp (+ 6931/10000 (log 1/2))) v)>
#<alt (* -1 (/ (+ (* -1 (exp (+ 6931/10000 (log 1/2)))) (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) v))>
#<alt (* -1 (/ (+ (* -1 (exp (+ 6931/10000 (log 1/2)))) (* -1 (/ (+ (* -1 (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i)))) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) v))) v))) v))>
#<alt (* -1 (/ (+ (* -1 (exp (+ 6931/10000 (log 1/2)))) (* -1 (/ (+ (* -1 (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i)))) (* -1 (/ (+ (* -1/2 (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (* 1/6 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) v))) v))) v))) v))>
#<alt (- (+ 6931/10000 (log 1/2)) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (* -1 (/ sinTheta_O v))>
#<alt (* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (log 1/2) sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (log 1/2) sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (log 1/2) sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* -1 (/ sinTheta_O v))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- (+ 6931/10000 (log 1/2)) (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- (+ 6931/10000 (log 1/2)) (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- (+ 6931/10000 (log 1/2)) (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (- (+ 6931/10000 (log 1/2)) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (log 1/2) sinTheta_i))) (/ 1 (* sinTheta_i v))))>
#<alt (* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (log 1/2) sinTheta_i))) (/ 1 (* sinTheta_i v))))>
#<alt (* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (log 1/2) sinTheta_i))) (/ 1 (* sinTheta_i v))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_i (+ (* -1 (/ (- (+ 6931/10000 (log 1/2)) (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))>
#<alt (* -1 (* sinTheta_i (+ (* -1 (/ (- (+ 6931/10000 (log 1/2)) (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))>
#<alt (* -1 (* sinTheta_i (+ (* -1 (/ (- (+ 6931/10000 (log 1/2)) (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* v (+ 6931/10000 (log 1/2)))) v)>
#<alt (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* v (+ 6931/10000 (log 1/2)))) v)>
#<alt (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* v (+ 6931/10000 (log 1/2)))) v)>
#<alt (+ 6931/10000 (log 1/2))>
#<alt (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))>
#<alt (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))>
#<alt (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))>
#<alt (+ 6931/10000 (log 1/2))>
#<alt (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))>
#<alt (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))>
#<alt (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))>
#<alt 1>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (* cosTheta_i (+ (* 1/2 (/ cosTheta_i (pow v 9))) (/ 1 v))))>
#<alt (+ 1 (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ cosTheta_i (pow v 4))) (* 1/2 (/ 1 (pow v 9))))) (/ 1 v))))>
#<alt (* 1/6 (/ (pow cosTheta_i 13) (pow v 13)))>
#<alt (* 1/6 (/ (pow cosTheta_i 13) (pow v 13)))>
#<alt (* (pow cosTheta_i 13) (+ (* 1/2 (/ 1 (* (pow cosTheta_i 7) (pow v 6)))) (* 1/6 (/ 1 (pow v 13)))))>
#<alt (* (pow cosTheta_i 13) (+ (/ 1/2 (* (pow cosTheta_i 7) (pow v 6))) (+ (/ 1 (* (pow cosTheta_i 12) v)) (* 1/6 (/ 1 (pow v 13))))))>
#<alt (* 1/6 (/ (pow cosTheta_i 3) (pow v 10)))>
#<alt (* (pow cosTheta_i 3) (+ (* 1/6 (/ 1 (pow v 10))) (* 1/2 (/ 1 (* cosTheta_i (pow v 5))))))>
#<alt (* -1 (* (pow cosTheta_i 3) (- (* -1 (/ (+ (/ 1 (* cosTheta_i v)) (* 1/2 (/ 1 (pow v 5)))) cosTheta_i)) (* 1/6 (/ 1 (pow v 10))))))>
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#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* -1 (* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* -1 (* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt v>
#<alt v>
#<alt v>
#<alt v>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt 1>
#<alt (+ 1 (* sinTheta_O sinTheta_i))>
#<alt (+ 1 (* sinTheta_O sinTheta_i))>
#<alt (+ 1 (* sinTheta_O sinTheta_i))>
#<alt sinTheta_O>
#<alt (* sinTheta_O (+ 1 (/ 1 sinTheta_O)))>
#<alt (* sinTheta_O (+ 1 (/ 1 sinTheta_O)))>
#<alt (* sinTheta_O (+ 1 (/ 1 sinTheta_O)))>
#<alt sinTheta_O>
#<alt (* sinTheta_O (+ 1 (/ 1 sinTheta_O)))>
#<alt (* sinTheta_O (+ 1 (/ 1 sinTheta_O)))>
#<alt (* sinTheta_O (+ 1 (/ 1 sinTheta_O)))>
#<alt 1>
#<alt (+ 1 (* sinTheta_O sinTheta_i))>
#<alt (+ 1 (* sinTheta_O sinTheta_i))>
#<alt (+ 1 (* sinTheta_O sinTheta_i))>
#<alt (* sinTheta_O sinTheta_i)>
#<alt (* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))>
#<alt (* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))>
#<alt (* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))>
#<alt (* sinTheta_O sinTheta_i)>
#<alt (* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))>
#<alt (* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))>
#<alt (* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))>

Calls

114 calls:

Time	Variable		Point	Expression
24.0ms	v	@	0	(/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))
13.0ms	v	@	0	(+ 6931/10000 (neg (log (* v 2))))
11.0ms	v	@	-inf	(+ 6931/10000 (neg (log (* v 2))))
6.0ms	v	@	inf	(+ 6931/10000 (neg (log (* v 2))))
3.0ms	sinTheta_O	@	0	(+ (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)) (+ 6931/10000 (neg (log (* v 2)))))

Compiler

Compiled 1 721 to 1 339 computations (22.2% saved)

rewrite392.0ms (3%)

Memory

16.1MiB live, 613.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 090×	`lower-fma.f64`
6 082×	`lower-fma.f32`
4 352×	`lower-/.f64`
4 338×	`lower-/.f32`
4 178×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	192
0	68	179
1	276	170
2	2415	170
0	8965	170

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

19 → 739

Calls

Call 1

Inputs
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32))))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))
(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))) v)
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v))
(fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))
(/.f32 cosTheta_i (.f32 v (.f32 v v)))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(/.f32 #s(literal 1/2 binary32) v)
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
(exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))))
(+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32))))))
(+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(.f32 v (.f32 v v))
(/.f32 #s(literal -1 binary32) v)
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))

Outputs
(exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32))))
(pow.f32 (exp.f32 (fma.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (pow.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 3 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (log.f32 #s(literal 1/2 binary32)) (-.f32 (log.f32 #s(literal 1/2 binary32)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))))
(pow.f32 (exp.f32 (-.f32 (*.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (pow.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 2 binary32)))))
(/.f32 (exp.f32 (/.f32 (*.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 2 binary32))))) (exp.f32 (/.f32 (pow.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 2 binary32)) (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 2 binary32))))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 #s(literal 1/2 binary32) (exp.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))
(*.f32 (exp.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 1/2 binary32)))))
(*.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) #s(literal 1/2 binary32))
(.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))) (exp.f32 #s(literal 6931/10000 binary32)))
(*.f32 (exp.f32 (+.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 6931/10000 binary32))) (exp.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(+.f32 #s(literal 6931/10000 binary32) (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
(+.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) #s(literal 6931/10000 binary32))
(pow.f32 (/.f32 (fma.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) #s(literal 6931/10000 binary32)) #s(literal 48038761/100000000 binary32)) (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (.f32 v (.f32 v v))))) #s(literal -1 binary32))
(pow.f32 (/.f32 (-.f32 #s(literal 6931/10000 binary32) (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (-.f32 #s(literal 48038761/100000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 v v)))) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) #s(literal 6931/10000 binary32))
(fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
(fma.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))) #s(literal 6931/10000 binary32))
(fma.f32 #s(literal -1 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) #s(literal 6931/10000 binary32))
(fma.f32 (/.f32 #s(literal -1 binary32) v) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal 6931/10000 binary32))
(fma.f32 (/.f32 #s(literal -1 binary32) v) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) #s(literal -1 binary32)) #s(literal 6931/10000 binary32))
(fma.f32 (/.f32 #s(literal -1 binary32) v) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal 1 binary32)) #s(literal 6931/10000 binary32))
(fma.f32 (neg.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))
(fma.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) #s(literal -1 binary32) #s(literal 6931/10000 binary32))
(fma.f32 (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))
(fma.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))
(fma.f32 (pow.f32 (/.f32 v (neg.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i)))) #s(literal 6931/10000 binary32))
(fma.f32 (pow.f32 (/.f32 (neg.f32 v) (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))) #s(literal 6931/10000 binary32))
(fma.f32 (/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) v) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i)))) #s(literal -1 binary32)) #s(literal 6931/10000 binary32))
(fma.f32 (/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) #s(literal -1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i)))) v) #s(literal 6931/10000 binary32))
(fma.f32 (/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) v) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))) #s(literal -1 binary32)) #s(literal 6931/10000 binary32))
(fma.f32 (/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) #s(literal -1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))) v) #s(literal 6931/10000 binary32))
(fma.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(-.f32 (/.f32 #s(literal 48038761/100000000 binary32) (-.f32 #s(literal 6931/10000 binary32) (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))) (/.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 v v)) (-.f32 #s(literal 6931/10000 binary32) (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))
(-.f32 (/.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 v v)) (-.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) #s(literal 6931/10000 binary32))) (/.f32 #s(literal 48038761/100000000 binary32) (-.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) #s(literal 6931/10000 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) #s(literal 6931/10000 binary32)) #s(literal 48038761/100000000 binary32)) (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (.f32 v (.f32 v v))))))
(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 6931/10000 binary32) (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (-.f32 #s(literal 48038761/100000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 v v)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (fma.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) #s(literal 6931/10000 binary32)) #s(literal 48038761/100000000 binary32)) (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (.f32 v (.f32 v v)))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (-.f32 #s(literal 6931/10000 binary32) (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (-.f32 #s(literal 48038761/100000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 v v))))))
(/.f32 (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (.f32 v (.f32 v v)))) (fma.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) #s(literal 6931/10000 binary32)) #s(literal 48038761/100000000 binary32)))
(/.f32 (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (.f32 v (.f32 v v)))) (+.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 v v)) (-.f32 #s(literal 48038761/100000000 binary32) (*.f32 #s(literal -6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))
(/.f32 (-.f32 #s(literal 48038761/100000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 v v))) (-.f32 #s(literal 6931/10000 binary32) (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(/.f32 (neg.f32 (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (.f32 v (.f32 v v))))) (neg.f32 (fma.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) #s(literal 6931/10000 binary32)) #s(literal 48038761/100000000 binary32))))
(/.f32 (neg.f32 (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (.f32 v (.f32 v v))))) (neg.f32 (+.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 v v)) (-.f32 #s(literal 48038761/100000000 binary32) (*.f32 #s(literal -6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))))
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(/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) (.f32 (neg.f32 v) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i)))))
(/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) (*.f32 (neg.f32 v) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i))) (neg.f32 v)))
(/.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) #s(literal -1 binary32)) (.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i))) v))
(/.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)) (neg.f32 v)))
(/.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) #s(literal -1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)) v))
(/.f32 (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal 1 binary32)) (neg.f32 v))
(/.f32 (neg.f32 (neg.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (neg.f32 v))
(/.f32 (neg.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32))) (neg.f32 (.f32 (neg.f32 v) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i))))))
(/.f32 (neg.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32))) (neg.f32 (*.f32 (neg.f32 v) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)))))
(/.f32 (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal -1 binary32)) v)
(/.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v)) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i))))
(/.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (*.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) (/.f32 #s(literal -1 binary32) v)) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)))
(/.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal -1 binary32)) v)
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) #s(literal 1 binary32))) (neg.f32 (.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i))) (neg.f32 v))))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) #s(literal -1 binary32))) (neg.f32 (.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i))) v)))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) #s(literal 1 binary32))) (neg.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)) (neg.f32 v))))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) #s(literal -1 binary32))) (neg.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)) v)))
(/.f32 (neg.f32 (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal 1 binary32))) v)
(/.f32 (neg.f32 (neg.f32 (neg.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))))) v)
(/.f32 (neg.f32 (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal -1 binary32))) (neg.f32 v))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v))) (neg.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i)))))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (*.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) (/.f32 #s(literal -1 binary32) v))) (neg.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))))
(/.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal -1 binary32))) (neg.f32 v))
(*.f32 #s(literal 1 binary32) (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
(*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v))
(*.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))))
(*.f32 #s(literal -1 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(*.f32 (/.f32 #s(literal -1 binary32) v) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))
(*.f32 (/.f32 #s(literal -1 binary32) v) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) #s(literal -1 binary32)))
(*.f32 (/.f32 #s(literal -1 binary32) v) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal 1 binary32)))
(*.f32 (neg.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) v))
(*.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) #s(literal -1 binary32))
(.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) v))
(*.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) v))
(.f32 (pow.f32 (/.f32 v (neg.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i)))))
(.f32 (pow.f32 (/.f32 (neg.f32 v) (fma.f32 (.f32 sinTheta_O sinTheta_i) (*.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))))
(.f32 (/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) v) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i)))) #s(literal -1 binary32)))
(.f32 (/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) #s(literal -1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i)))) v))
(.f32 (/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (*.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) v) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))) #s(literal -1 binary32)))
(.f32 (/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (*.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) #s(literal -1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))) v))
(*.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v))
(neg.f32 (.f32 v (.f32 v v)))
(exp.f32 (*.f32 (log.f32 v) #s(literal 3 binary32)))
(exp.f32 (*.f32 (log.f32 (neg.f32 v)) #s(literal 3 binary32)))
(pow.f32 v #s(literal 3 binary32))
(pow.f32 (neg.f32 v) #s(literal 3 binary32))
(pow.f32 (*.f32 v v) #s(literal 3/2 binary32))
(pow.f32 (pow.f32 v #s(literal 3/2 binary32)) #s(literal 2 binary32))
(-.f32 #s(literal 0 binary32) (.f32 v (.f32 v v)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 v (.f32 v v))))
(/.f32 (.f32 v (.f32 v v)) #s(literal 1 binary32))
(/.f32 (.f32 v (.f32 v v)) #s(literal -1 binary32))
(/.f32 (.f32 (.f32 v v) (.f32 (.f32 v (*.f32 v v)) v)) (pow.f32 (+.f32 #s(literal 0 binary32) v) #s(literal 3 binary32)))
(/.f32 (.f32 (.f32 v (.f32 v v)) (.f32 (.f32 v v) (.f32 (.f32 v (.f32 v v)) v))) (pow.f32 (+.f32 #s(literal 0 binary32) (fma.f32 v v (*.f32 #s(literal 0 binary32) v))) #s(literal 3 binary32)))
(.f32 #s(literal 1 binary32) (.f32 v (*.f32 v v)))
(.f32 v (.f32 v v))
(.f32 v (neg.f32 (.f32 v v)))
(.f32 (neg.f32 v) (.f32 v v))
(.f32 (.f32 v v) v)
(.f32 (.f32 v v) (neg.f32 v))
(.f32 (.f32 v (*.f32 v v)) #s(literal 1 binary32))
(.f32 (.f32 v (*.f32 v v)) #s(literal -1 binary32))
(.f32 #s(literal -1 binary32) (.f32 v (*.f32 v v)))
(.f32 (neg.f32 (.f32 v v)) v)
(*.f32 (pow.f32 v #s(literal 3/2 binary32)) (pow.f32 v #s(literal 3/2 binary32)))
(neg.f32 (/.f32 #s(literal 1 binary32) v))
(exp.f32 (*.f32 (log.f32 (neg.f32 v)) #s(literal -1 binary32)))
(pow.f32 (neg.f32 v) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) (neg.f32 v))
(/.f32 #s(literal -1 binary32) v)
(*.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) v))
(*.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -1 binary32))
(*.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) v))
(+.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i))
(+.f32 (*.f32 sinTheta_O sinTheta_i) #s(literal 1 binary32))
(pow.f32 (/.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i))) (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (*.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32))) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)) (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32))) #s(literal -1 binary32))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
(fma.f32 sinTheta_O (*.f32 sinTheta_i #s(literal 1 binary32)) #s(literal 1 binary32))
(fma.f32 sinTheta_i sinTheta_O #s(literal 1 binary32))
(fma.f32 sinTheta_i (*.f32 sinTheta_O #s(literal 1 binary32)) #s(literal 1 binary32))
(fma.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i) #s(literal 1 binary32))
(fma.f32 (*.f32 sinTheta_O sinTheta_i) #s(literal 1 binary32) #s(literal 1 binary32))
(-.f32 (/.f32 (.f32 sinTheta_O (.f32 sinTheta_i (*.f32 sinTheta_O sinTheta_i))) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i))) (/.f32 (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i))) (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (*.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)) (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i))) (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (*.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)) (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)))))
(/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i))))
(/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) (.f32 sinTheta_O sinTheta_i))))
(/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)))
(/.f32 (neg.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32))) (neg.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i)))))
(/.f32 (neg.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32))) (neg.f32 (+.f32 #s(literal 1 binary32) (-.f32 (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) (.f32 sinTheta_O sinTheta_i)))))
(/.f32 (neg.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32))) (neg.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)))) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i)))
(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))))) (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)))) (neg.f32 (neg.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i))))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)))) (neg.f32 (neg.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)))))
(.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i)))))
(.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (*.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))))

simplify402.0ms (3.1%)

Memory

7.0MiB live, 632.1MiB allocated

Algorithm

1×	egg-herbie

Rules

9 278×	`lower-fma.f64`
9 278×	`lower-fma.f32`
6 068×	`lower-*.f64`
6 068×	`lower-*.f32`
3 334×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	656	6445
1	1911	6006
2	5997	5812
0	8533	5525

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 450

Calls

Call 1

Inputs
(exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) v)))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))))))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) v)))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))))))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
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1
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1
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(+ (exp 6931/10000) (* -1 (/ (exp 6931/10000) v)))
(+ (exp 6931/10000) (+ (* -1 (/ (exp 6931/10000) v)) (* 1/2 (/ (exp 6931/10000) (pow v 2)))))
(+ (exp 6931/10000) (+ (* -1 (/ (exp 6931/10000) v)) (+ (* -1/6 (/ (exp 6931/10000) (pow v 3))) (* 1/2 (/ (exp 6931/10000) (pow v 2))))))
(exp 6931/10000)
(+ (exp 6931/10000) (* -1 (/ (exp 6931/10000) v)))
(+ (exp 6931/10000) (* -1 (/ (+ (exp 6931/10000) (* -1/2 (/ (exp 6931/10000) v))) v)))
(+ (exp 6931/10000) (* -1 (/ (+ (exp 6931/10000) (* -1 (/ (+ (* -1/6 (/ (exp 6931/10000) v)) (* 1/2 (exp 6931/10000))) v))) v)))
(/ -1 v)
(/ (- (* 6931/10000 v) 1) v)
(/ (- (* 6931/10000 v) 1) v)
(/ (- (* 6931/10000 v) 1) v)
6931/10000
(- 6931/10000 (/ 1 v))
(- 6931/10000 (/ 1 v))
(- 6931/10000 (/ 1 v))
6931/10000
(- 6931/10000 (/ 1 v))
(- 6931/10000 (/ 1 v))
(- 6931/10000 (/ 1 v))
(exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))
(+ (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))))) v)))
(+ (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))))) (pow v 2))))))
(+ (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))) (pow v 2))))))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))
(+ (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))))) v)))
(+ (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))))) (pow v 2))))))
(+ (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))) (pow v 2))))))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (log (* 2 v))))
(exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v))))))
(+ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (* -1 (/ (* (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)))
(+ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (+ (* -1 (/ (* (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (* 1/2 (/ (* (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2)))))
(+ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (+ (* -1 (/ (* (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (* -1/6 (/ (* (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (pow v 3))) (* 1/2 (/ (* (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))))))
(exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v))))))
(+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (* (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))) v)))
(+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (+ (* -1/2 (/ (* (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) v)) (* (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) v)) (* 1/2 (* (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) v)) (* (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (+ (log (* 2 v)) (/ 1 v)))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (+ (log (* 2 v)) (/ 1 v)))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (+ (log (* 2 v)) (/ 1 v)))
(* -1 (/ sinTheta_O v))
(* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (+ (/ 1 (* sinTheta_O v)) (/ (log (* 2 v)) sinTheta_O)))))
(* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (+ (/ 1 (* sinTheta_O v)) (/ (log (* 2 v)) sinTheta_O)))))
(* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (+ (/ 1 (* sinTheta_O v)) (/ (log (* 2 v)) sinTheta_O)))))
(* -1 (/ sinTheta_O v))
(* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))) sinTheta_O)) (/ 1 v))))
(* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))) sinTheta_O)) (/ 1 v))))
(* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))) sinTheta_O)) (/ 1 v))))
(- 6931/10000 (+ (log (* 2 v)) (/ 1 v)))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (+ (log (* 2 v)) (/ 1 v)))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (+ (log (* 2 v)) (/ 1 v)))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (+ (log (* 2 v)) (/ 1 v)))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (+ (/ 1 (* sinTheta_i v)) (/ (log (* 2 v)) sinTheta_i))))
(* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (+ (/ 1 (* sinTheta_i v)) (/ (log (* 2 v)) sinTheta_i))))
(* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (+ (/ 1 (* sinTheta_i v)) (/ (log (* 2 v)) sinTheta_i))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))) sinTheta_i)) (/ sinTheta_O v))))
(* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))) sinTheta_i)) (/ sinTheta_O v))))
(* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))) sinTheta_i)) (/ sinTheta_O v))))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* v (- 6931/10000 (+ (log 2) (log v))))) v)
(/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* v (- 6931/10000 (+ (log 2) (log v))))) v)
(/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* v (- 6931/10000 (+ (log 2) (log v))))) v)
(- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))
(- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (+ (log 2) (* -1 (log (/ 1 v)))))
(- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (+ (log 2) (* -1 (log (/ 1 v)))))
(- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (+ (log 2) (* -1 (log (/ 1 v)))))
(- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))
(- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (+ (log -2) (* -1 (log (/ -1 v)))))
(- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (+ (log -2) (* -1 (log (/ -1 v)))))
(- (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (+ (log -2) (* -1 (log (/ -1 v)))))
(- 6931/10000 (+ (log 2) (log v)))
(- 6931/10000 (+ (log 2) (log v)))
(- 6931/10000 (+ (log 2) (log v)))
(- 6931/10000 (+ (log 2) (log v)))
(- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))
(- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))
(- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))
(- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))
(- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))
(- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))
(- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))
(- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))
(/ -1 v)
(- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))
(- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))
(- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))
(* -1 (/ sinTheta_O v))
(* -1 (* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))
(* -1 (* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))
(* -1 (* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))
(* -1 (/ sinTheta_O v))
(* -1 (* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))
(* -1 (* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))
(* -1 (* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))
(/ -1 v)
(- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))
(- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))
(- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v))))
(* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v))))
(* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
(* -1 (* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
(* -1 (* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
v
v
v
v
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ -1 v)
(/ -1 v)
(/ -1 v)
(/ -1 v)
(/ -1 v)
(/ -1 v)
(/ -1 v)
(/ -1 v)
1
(+ 1 (* sinTheta_O sinTheta_i))
(+ 1 (* sinTheta_O sinTheta_i))
(+ 1 (* sinTheta_O sinTheta_i))
sinTheta_O
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
sinTheta_O
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
1
(+ 1 (* sinTheta_O sinTheta_i))
(+ 1 (* sinTheta_O sinTheta_i))
(+ 1 (* sinTheta_O sinTheta_i))
(* sinTheta_O sinTheta_i)
(* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))
(* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))
(* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))
(* sinTheta_O sinTheta_i)
(* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))
(* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))
(* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))

Outputs
(exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) v)))
(fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 #s(literal -1/2 binary32) (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) v)) (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))))))
(fma.f32 sinTheta_O (fma.f32 #s(literal 1/2 binary32) (.f32 sinTheta_O (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v)))) (.f32 sinTheta_i (.f32 #s(literal -1/2 binary32) (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) v)))) (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))))))))
(fma.f32 sinTheta_O (fma.f32 sinTheta_O (fma.f32 #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v))) (/.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_i sinTheta_i))))) (.f32 v (.f32 v v)))) (.f32 sinTheta_i (.f32 #s(literal -1/2 binary32) (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) v)))) (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(exp (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) v)))
(fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 #s(literal -1/2 binary32) (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) v)) (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))))))
(fma.f32 sinTheta_i (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (.f32 sinTheta_O (.f32 sinTheta_O sinTheta_i))) (.f32 v v)) (.f32 sinTheta_O (.f32 #s(literal -1/2 binary32) (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) v)))) (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
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(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
v
v
v
v
(pow v 2)
(*.f32 v v)
(pow v 2)
(*.f32 v v)
(pow v 2)
(*.f32 v v)
(pow v 2)
(*.f32 v v)
(pow v 2)
(*.f32 v v)
(pow v 2)
(*.f32 v v)
(pow v 2)
(*.f32 v v)
(pow v 2)
(*.f32 v v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
1
#s(literal 1 binary32)
(+ 1 (* sinTheta_O sinTheta_i))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
(+ 1 (* sinTheta_O sinTheta_i))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
(+ 1 (* sinTheta_O sinTheta_i))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
sinTheta_O
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(+.f32 #s(literal 1 binary32) sinTheta_O)
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(+.f32 #s(literal 1 binary32) sinTheta_O)
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(+.f32 #s(literal 1 binary32) sinTheta_O)
sinTheta_O
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(+.f32 #s(literal 1 binary32) sinTheta_O)
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(+.f32 #s(literal 1 binary32) sinTheta_O)
(* sinTheta_O (+ 1 (/ 1 sinTheta_O)))
(+.f32 #s(literal 1 binary32) sinTheta_O)
1
#s(literal 1 binary32)
(+ 1 (* sinTheta_O sinTheta_i))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
(+ 1 (* sinTheta_O sinTheta_i))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
(+ 1 (* sinTheta_O sinTheta_i))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
(* sinTheta_O sinTheta_i)
(*.f32 sinTheta_O sinTheta_i)
(* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
(* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
(* sinTheta_i (+ sinTheta_O (/ 1 sinTheta_i)))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
(* sinTheta_O sinTheta_i)
(*.f32 sinTheta_O sinTheta_i)
(* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
(* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
(* -1 (* sinTheta_i (- (* -1 sinTheta_O) (/ 1 sinTheta_i))))
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))

eval149.0ms (1.1%)

Memory: 4.1MiB live, 362.8MiB allocated
Compiler: Compiled 33 218 to 3 455 computations (89.6% saved)

prune182.0ms (1.4%)

Memory

23.5MiB live, 412.1MiB allocated

Pruning

27 alts after pruning (23 fresh and 4 done)

	Pruned	Kept	Total
New	1 318	14	1 332
Fresh	4	9	13
Picked	2	3	5
Done	0	1	1
Total	1 324	27	1 351

Accuracy

99.9%

Counts

1 351 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	2.5%	(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
	6.3%	(fma.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)) #s(literal 1 binary32))
	3.4%	(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 (/.f32 cosTheta_i (.f32 v v)) (/.f32 #s(literal 1/6 binary32) v) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
✓	3.0%	(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
	2.0%	(fma.f32 cosTheta_i (fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i #s(literal 1/6 binary32)) (.f32 v v) (.f32 (.f32 v (.f32 v v)) #s(literal 1/2 binary32))) (.f32 (.f32 v v) (.f32 v (*.f32 v v)))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
	4.0%	(fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 #s(literal 1/6 binary32) (.f32 v v)) #s(literal 1 binary32)) v) #s(literal 1 binary32))
	3.1%	(fma.f32 cosTheta_i (/.f32 (fma.f32 #s(literal -1/6 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (.f32 v (.f32 v v)))) #s(literal -1 binary32)) (neg.f32 v)) #s(literal 1 binary32))
	99.5%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
▶	99.8%	(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)
	99.6%	(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 #s(literal 1/2 binary32)))) v)
	99.1%	(/.f32 (exp.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) v)
	99.6%	(/.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 (log.f32 v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)))))
	5.3%	(+.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta_i (/.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i cosTheta_i)) v) (.f32 #s(literal 1/2 binary32) (.f32 cosTheta_i cosTheta_i))) v)) v))
▶	5.8%	(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
	98.9%	(.f32 (/.f32 #s(literal 1 binary32) v) (pow.f32 (/.f32 #s(literal 1 binary32) (.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))) #s(literal -1 binary32)))
	98.7%	(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v)))) (exp.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 v v)) (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v))))))
	97.7%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
	99.7%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
✓	99.5%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
	99.5%	(.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v)) (/.f32 #s(literal 1/2 binary32) v)))
▶	97.5%	(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
	43.3%	(exp.f32 (/.f32 sinTheta_O (neg.f32 v)))
✓	47.7%	(exp.f32 (/.f32 cosTheta_i v))
	99.7%	(exp.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
▶	99.5%	(exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
	47.7%	(exp.f32 (*.f32 (/.f32 #s(literal 1 binary32) v) cosTheta_i))
✓	6.5%	#s(literal 1 binary32)

Compiler

Compiled 935 to 672 computations (28.1% saved)

simplify243.0ms (1.9%)

Memory

-34.2MiB live, 420.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 #s(literal -1 binary32) v)
✓	cost-diff	0	(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
✓	cost-diff	0	(-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32))))
✓	cost-diff	2944	(exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
✓	cost-diff	0	(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
✓	cost-diff	0	(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
✓	cost-diff	0	(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
✓	cost-diff	0	(.f32 v (.f32 v v))
✓	cost-diff	0	(/.f32 cosTheta_i (.f32 v (.f32 v v)))
✓	cost-diff	0	(fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))
✓	cost-diff	544	(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
✓	cost-diff	0	(/.f32 cosTheta_i v)
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
✓	cost-diff	0	(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
✓	cost-diff	0	(+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))
✓	cost-diff	0	(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)
✓	cost-diff	3136	(exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32))))

Rules

4 764×	`lower-fma.f64`
4 756×	`lower-fma.f32`
3 178×	`lower-*.f64`
3 170×	`lower-*.f32`
1 882×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	208
0	67	200
1	106	197
2	187	197
3	419	197
4	819	197
5	1322	197
6	2170	195
7	4042	195
8	7271	195
0	8060	192

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)
(exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32))))
(+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
#s(literal 6931/10000 binary32)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
sinTheta_O
sinTheta_i
#s(literal 1 binary32)
v
(log.f32 #s(literal 1/2 binary32))
#s(literal 1/2 binary32)
(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
#s(literal 1 binary32)
(/.f32 cosTheta_i v)
cosTheta_i
v
(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
(fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))
#s(literal 1/6 binary32)
(/.f32 cosTheta_i (.f32 v (.f32 v v)))
cosTheta_i
(.f32 v (.f32 v v))
v
(*.f32 v v)
(/.f32 #s(literal 1/2 binary32) (*.f32 v v))
#s(literal 1/2 binary32)
(*.f32 cosTheta_i cosTheta_i)
(+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32))
(/.f32 cosTheta_i v)
#s(literal 1 binary32)
(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
cosTheta_i
cosTheta_O
#s(literal -1 binary32)
v
(exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32))))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
#s(literal 6931/10000 binary32)
(/.f32 #s(literal -1 binary32) v)
#s(literal -1 binary32)
v
(log.f32 (*.f32 v #s(literal 2 binary32)))
(*.f32 v #s(literal 2 binary32))
#s(literal 2 binary32)

Outputs
(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)
(/.f32 #s(literal 1/2 binary32) (*.f32 v (exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) #s(literal -6931/10000 binary32)))))
(exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))
(-.f32 (+.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 1/2 binary32))) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
#s(literal 6931/10000 binary32)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))
sinTheta_O
sinTheta_i
#s(literal 1 binary32)
v
(log.f32 #s(literal 1/2 binary32))
#s(literal 1/2 binary32)
(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
#s(literal 1 binary32)
(/.f32 cosTheta_i v)
cosTheta_i
v
(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
(fma.f32 (/.f32 cosTheta_i v) (fma.f32 (/.f32 cosTheta_i v) (fma.f32 cosTheta_i (/.f32 #s(literal 1/6 binary32) v) #s(literal 1/2 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32))
(fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))
(fma.f32 cosTheta_i (/.f32 #s(literal 1/6 binary32) (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))
#s(literal 1/6 binary32)
(/.f32 cosTheta_i (.f32 v (.f32 v v)))
cosTheta_i
(.f32 v (.f32 v v))
v
(*.f32 v v)
(/.f32 #s(literal 1/2 binary32) (*.f32 v v))
#s(literal 1/2 binary32)
(*.f32 cosTheta_i cosTheta_i)
(+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
(/.f32 cosTheta_i v)
#s(literal 1 binary32)
(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
cosTheta_i
cosTheta_O
#s(literal -1 binary32)
v
(exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(/.f32 #s(literal 1/2 binary32) (*.f32 v (exp.f32 (+.f32 #s(literal -6931/10000 binary32) (/.f32 #s(literal 1 binary32) v)))))
(-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32))))
(+.f32 #s(literal 6931/10000 binary32) (-.f32 (/.f32 #s(literal -1 binary32) v) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
#s(literal 6931/10000 binary32)
(/.f32 #s(literal -1 binary32) v)
#s(literal -1 binary32)
v
(log.f32 (*.f32 v #s(literal 2 binary32)))
(*.f32 v #s(literal 2 binary32))
#s(literal 2 binary32)

localize124.0ms (1%)

Memory

18.5MiB live, 208.5MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	9.8%	(/.f32 #s(literal -1 binary32) v)
✓	accuracy	6.3%	(-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32))))
✓	accuracy	3.1%	(*.f32 v #s(literal 2 binary32))
✓	accuracy	2.1%	(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
✓	accuracy	5.7%	(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
✓	accuracy	3.8%	(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
✓	accuracy	3.2%	(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
✓	accuracy	5.8%	(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
✓	accuracy	4.5%	(.f32 v (.f32 v v))
✓	accuracy	3.6%	(fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))
✓	accuracy	3.5%	(/.f32 cosTheta_i (.f32 v (.f32 v v)))
✓	accuracy	100.0%	(/.f32 cosTheta_i v)
✓	accuracy	7.3%	(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
✓	accuracy	5.7%	(exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32))))
✓	accuracy	3.7%	(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
✓	accuracy	2.1%	(+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))
✓	accuracy	2.1%	(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))

Samples

77.0ms

256×

valid

Compiler

Compiled 435 to 80 computations (81.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-div: 15.0ms (25.6% of total)

ival-mult: 12.0ms (20.5% of total)

ival-add: 9.0ms (15.3% of total)

const: 9.0ms (15.3% of total)

ival-log: 6.0ms (10.2% of total)

ival-exp: 5.0ms (8.5% of total)

ival-sub: 2.0ms (3.4% of total)

exact: 1.0ms (1.7% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series90.0ms (0.7%)

Memory

-18.4MiB live, 100.4MiB allocated

Counts

19 → 468

Calls

Call 1

Inputs
#<alt (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32))))>
#<alt (/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)>
#<alt (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))>
#<alt (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))>
#<alt (+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))>
#<alt (/.f32 cosTheta_i v)>
#<alt (fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))>
#<alt (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))>
#<alt (/.f32 cosTheta_i (.f32 v (.f32 v v)))>
#<alt (.f32 v (.f32 v v))>
#<alt (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))>
#<alt (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)>
#<alt (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))>
#<alt (exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))>
#<alt (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32))))>
#<alt (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))>
#<alt (/.f32 #s(literal -1 binary32) v)>
#<alt (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)>
#<alt (*.f32 v #s(literal 2 binary32))>

Outputs
#<alt (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))>
#<alt (+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) v)))>
#<alt (+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))))))>
#<alt (+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))))))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))>
#<alt (+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) v)))>
#<alt (+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))))))>
#<alt (+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))))))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (exp (+ 6931/10000 (log 1/2)))>
#<alt (+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)))>
#<alt (+ (exp (+ 6931/10000 (log 1/2))) (+ (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2)))))>
#<alt (+ (exp (+ 6931/10000 (log 1/2))) (+ (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (* -1/6 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (pow v 3))) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))))))>
#<alt (exp (+ 6931/10000 (log 1/2)))>
#<alt (+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)))>
#<alt (+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (+ (* -1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) v)) (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))>
#<alt (+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) v)) (* 1/2 (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) v)) (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v)>
#<alt (+ (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))>
#<alt (+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))>
#<alt (+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 4))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 3))))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v)>
#<alt (+ (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))>
#<alt (+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))>
#<alt (+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 4))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 3))))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)>
#<alt (/ (exp (+ 6931/10000 (log 1/2))) v)>
#<alt (/ (+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v))) v)>
#<alt (/ (+ (exp (+ 6931/10000 (log 1/2))) (+ (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))))) v)>
#<alt (/ (+ (exp (+ 6931/10000 (log 1/2))) (+ (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (* -1/6 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (pow v 3))) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2)))))) v)>
#<alt (/ (exp (+ 6931/10000 (log 1/2))) v)>
#<alt (* -1 (/ (+ (* -1 (exp (+ 6931/10000 (log 1/2)))) (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) v))>
#<alt (* -1 (/ (+ (* -1 (exp (+ 6931/10000 (log 1/2)))) (* -1 (/ (+ (* -1 (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i)))) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) v))) v))) v))>
#<alt (* -1 (/ (+ (* -1 (exp (+ 6931/10000 (log 1/2)))) (* -1 (/ (+ (* -1 (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i)))) (* -1 (/ (+ (* -1/2 (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (* 1/6 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) v))) v))) v))) v))>
#<alt (- (+ 6931/10000 (log 1/2)) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (* -1 (/ sinTheta_O v))>
#<alt (* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (log 1/2) sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (log 1/2) sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* sinTheta_O (- (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (log 1/2) sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* -1 (/ sinTheta_O v))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- (+ 6931/10000 (log 1/2)) (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- (+ 6931/10000 (log 1/2)) (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- (+ 6931/10000 (log 1/2)) (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (- (+ 6931/10000 (log 1/2)) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (* -1 (/ (* sinTheta_O sinTheta_i) v)))) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (log 1/2) sinTheta_i)) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (log 1/2) sinTheta_i)) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* sinTheta_i (- (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (log 1/2) sinTheta_i)) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (log 1/2)) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (log 1/2)) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- (+ 6931/10000 (log 1/2)) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (/ (- (* v (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (* v (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (* v (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (+ 6931/10000 (log 1/2))>
#<alt (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))>
#<alt (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))>
#<alt (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))>
#<alt (+ 6931/10000 (log 1/2))>
#<alt (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))>
#<alt (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))>
#<alt (+ 6931/10000 (+ (log 1/2) (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (* -1 (/ sinTheta_O v))>
#<alt (* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* sinTheta_O (- (* 6931/10000 (/ 1 sinTheta_O)) (+ (/ 1 v) (/ 1 (* sinTheta_O v)))))>
#<alt (* -1 (/ sinTheta_O v))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ 1 v))))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_i (- (* 6931/10000 (/ 1 sinTheta_i)) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* sinTheta_i (- (* 6931/10000 (/ 1 sinTheta_i)) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* sinTheta_i (- (* 6931/10000 (/ 1 sinTheta_i)) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
#<alt (/ (- (* 6931/10000 v) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (* 6931/10000 v) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (* 6931/10000 v) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt 6931/10000>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt 6931/10000>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt 1>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (/ cosTheta_i v)>
#<alt (* cosTheta_i (+ (/ 1 cosTheta_i) (/ 1 v)))>
#<alt (* cosTheta_i (+ (/ 1 cosTheta_i) (/ 1 v)))>
#<alt (* cosTheta_i (+ (/ 1 cosTheta_i) (/ 1 v)))>
#<alt (/ cosTheta_i v)>
#<alt (* cosTheta_i (+ (/ 1 cosTheta_i) (/ 1 v)))>
#<alt (* cosTheta_i (+ (/ 1 cosTheta_i) (/ 1 v)))>
#<alt (* cosTheta_i (+ (/ 1 cosTheta_i) (/ 1 v)))>
#<alt (/ cosTheta_i v)>
#<alt (/ (+ cosTheta_i v) v)>
#<alt (/ (+ cosTheta_i v) v)>
#<alt (/ (+ cosTheta_i v) v)>
#<alt 1>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt 1>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt (/ cosTheta_i v)>
#<alt 1>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (* cosTheta_i (+ (* 1/2 (/ (pow cosTheta_i 2) (pow v 3))) (/ 1 v))))>
#<alt (+ 1 (* cosTheta_i (+ (* (pow cosTheta_i 2) (+ (* 1/6 (/ cosTheta_i (pow v 6))) (* 1/2 (/ 1 (pow v 3))))) (/ 1 v))))>
#<alt (* 1/2 (/ (pow cosTheta_i 10) (pow v 10)))>
#<alt (* (pow cosTheta_i 10) (+ (* 1/6 (/ 1 (* (pow cosTheta_i 6) (pow v 4)))) (* 1/2 (/ 1 (pow v 10)))))>
#<alt (* (pow cosTheta_i 10) (+ (/ 1/6 (* (pow cosTheta_i 6) (pow v 4))) (+ (/ 1 (* (pow cosTheta_i 9) v)) (* 1/2 (/ 1 (pow v 10))))))>
#<alt (* (pow cosTheta_i 10) (+ (/ 1/6 (* (pow cosTheta_i 6) (pow v 4))) (+ (/ 1 (* (pow cosTheta_i 9) v)) (+ (/ 1 (pow cosTheta_i 10)) (* 1/2 (/ 1 (pow v 10)))))))>
#<alt (* 1/6 (/ (pow cosTheta_i 11) (pow v 11)))>
#<alt (* 1/6 (/ (pow cosTheta_i 11) (pow v 11)))>
#<alt (* (pow cosTheta_i 11) (+ (* 1/6 (/ 1 (pow v 11))) (* 1/2 (/ 1 (* (pow cosTheta_i 7) (pow v 4))))))>
#<alt (* -1 (* (pow cosTheta_i 11) (- (* -1 (/ (+ (/ 1 (* (pow cosTheta_i 3) v)) (* 1/2 (/ 1 (pow v 4)))) (pow cosTheta_i 7))) (* 1/6 (/ 1 (pow v 11))))))>
#<alt (* 1/6 (/ (pow cosTheta_i 4) (pow v 6)))>
#<alt (/ (+ (* 1/6 (pow cosTheta_i 4)) (* 1/2 (* (pow cosTheta_i 3) (pow v 3)))) (pow v 6))>
#<alt (/ (+ (* 1/6 (pow cosTheta_i 4)) (* (pow v 3) (+ (* 1/2 (pow cosTheta_i 3)) (* cosTheta_i (pow v 2))))) (pow v 6))>
#<alt (/ (+ (* 1/6 (pow cosTheta_i 4)) (* (pow v 3) (+ (* 1/2 (pow cosTheta_i 3)) (* (pow v 2) (+ cosTheta_i v))))) (pow v 6))>
#<alt 1>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (+ (* 1/2 (/ (pow cosTheta_i 4) (pow v 4))) (/ cosTheta_i v)))>
#<alt (+ 1 (+ (* 1/6 (/ (pow cosTheta_i 5) (pow v 7))) (+ (* 1/2 (/ (pow cosTheta_i 4) (pow v 4))) (/ cosTheta_i v))))>
#<alt 1>
#<alt (+ 1 (/ cosTheta_i v))>
#<alt (+ 1 (* -1 (/ (+ (* -1 cosTheta_i) (* -1/2 (/ (pow cosTheta_i 6) (pow v 5)))) v)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 cosTheta_i) (* -1 (/ (+ (* 1/6 (/ (pow cosTheta_i 7) (pow v 3))) (* 1/2 (pow cosTheta_i 6))) (pow v 5)))) v)))>
#<alt (/ 1/2 (pow v 9))>
#<alt (+ (* 1/6 (/ cosTheta_i (pow v 3))) (* 1/2 (/ 1 (pow v 9))))>
#<alt (+ (* 1/6 (/ cosTheta_i (pow v 3))) (* 1/2 (/ 1 (pow v 9))))>
#<alt (+ (* 1/6 (/ cosTheta_i (pow v 3))) (* 1/2 (/ 1 (pow v 9))))>
#<alt (* 1/6 (/ cosTheta_i (pow v 4)))>
#<alt (* cosTheta_i (+ (* 1/2 (/ 1 (* cosTheta_i (pow v 10)))) (* 1/6 (/ 1 (pow v 4)))))>
#<alt (* cosTheta_i (+ (* 1/2 (/ 1 (* cosTheta_i (pow v 10)))) (* 1/6 (/ 1 (pow v 4)))))>
#<alt (* cosTheta_i (+ (* 1/2 (/ 1 (* cosTheta_i (pow v 10)))) (* 1/6 (/ 1 (pow v 4)))))>
#<alt (* 1/6 (/ cosTheta_i (pow v 9)))>
#<alt (* cosTheta_i (+ (* 1/6 (/ 1 (pow v 9))) (* 1/2 (/ 1 (* cosTheta_i (pow v 4))))))>
#<alt (* cosTheta_i (+ (* 1/6 (/ 1 (pow v 9))) (* 1/2 (/ 1 (* cosTheta_i (pow v 4))))))>
#<alt (* cosTheta_i (+ (* 1/6 (/ 1 (pow v 9))) (* 1/2 (/ 1 (* cosTheta_i (pow v 4))))))>
#<alt (/ 1/2 (pow v 9))>
#<alt (/ (+ 1/2 (* 1/6 (* cosTheta_i (pow v 6)))) (pow v 9))>
#<alt (/ (+ 1/2 (* 1/6 (* cosTheta_i (pow v 6)))) (pow v 9))>
#<alt (/ (+ 1/2 (* 1/6 (* cosTheta_i (pow v 6)))) (pow v 9))>
#<alt (* 1/6 (/ cosTheta_i (pow v 3)))>
#<alt (/ (+ (* 1/6 cosTheta_i) (* 1/2 (/ 1 (pow v 5)))) (pow v 3))>
#<alt (/ (+ (* 1/6 cosTheta_i) (* 1/2 (/ 1 (pow v 5)))) (pow v 3))>
#<alt (/ (+ (* 1/6 cosTheta_i) (* 1/2 (/ 1 (pow v 5)))) (pow v 3))>
#<alt (* 1/6 (/ cosTheta_i (pow v 3)))>
#<alt (* -1 (/ (- (* -1/6 cosTheta_i) (* 1/2 (/ 1 (pow v 5)))) (pow v 3)))>
#<alt (* -1 (/ (- (* -1/6 cosTheta_i) (* 1/2 (/ 1 (pow v 5)))) (pow v 3)))>
#<alt (* -1 (/ (- (* -1/6 cosTheta_i) (* 1/2 (/ 1 (pow v 5)))) (pow v 3)))>
#<alt (/ cosTheta_i (pow v 2))>
#<alt (/ cosTheta_i (pow v 2))>
#<alt (/ cosTheta_i (pow v 2))>
#<alt (/ cosTheta_i (pow v 2))>
#<alt (/ cosTheta_i (pow v 3))>
#<alt (/ cosTheta_i (pow v 3))>
#<alt (/ cosTheta_i (pow v 3))>
#<alt (/ cosTheta_i (pow v 3))>
#<alt (/ cosTheta_i (pow v 3))>
#<alt (/ cosTheta_i (pow v 3))>
#<alt (/ cosTheta_i (pow v 3))>
#<alt (/ cosTheta_i (pow v 3))>
#<alt (/ cosTheta_i (pow v 2))>
#<alt (/ cosTheta_i (pow v 2))>
#<alt (/ cosTheta_i (pow v 2))>
#<alt (/ cosTheta_i (pow v 2))>
#<alt (/ cosTheta_i (pow v 2))>
#<alt (/ cosTheta_i (pow v 2))>
#<alt (/ cosTheta_i (pow v 2))>
#<alt (/ cosTheta_i (pow v 2))>
#<alt (/ cosTheta_i (pow v 3))>
#<alt (/ cosTheta_i (pow v 3))>
#<alt (/ cosTheta_i (pow v 3))>
#<alt (/ cosTheta_i (pow v 3))>
#<alt v>
#<alt v>
#<alt v>
#<alt v>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (exp (/ -1 v))>
#<alt (+ (exp (/ -1 v)) (/ (* cosTheta_O (* cosTheta_i (exp (/ -1 v)))) v))>
#<alt (+ (exp (/ -1 v)) (* cosTheta_i (+ (* 1/2 (/ (* (pow cosTheta_O 2) (* cosTheta_i (exp (/ -1 v)))) (pow v 2))) (/ (* cosTheta_O (exp (/ -1 v))) v))))>
#<alt (+ (exp (/ -1 v)) (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ (* (pow cosTheta_O 3) (* cosTheta_i (exp (/ -1 v)))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_O 2) (exp (/ -1 v))) (pow v 2))))) (/ (* cosTheta_O (exp (/ -1 v))) v))))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ -1 v))>
#<alt (+ (exp (/ -1 v)) (/ (* cosTheta_O (* cosTheta_i (exp (/ -1 v)))) v))>
#<alt (+ (exp (/ -1 v)) (* cosTheta_O (+ (* 1/2 (/ (* cosTheta_O (* (pow cosTheta_i 2) (exp (/ -1 v)))) (pow v 2))) (/ (* cosTheta_i (exp (/ -1 v))) v))))>
#<alt (+ (exp (/ -1 v)) (* cosTheta_O (+ (* cosTheta_O (+ (* 1/6 (/ (* cosTheta_O (* (pow cosTheta_i 3) (exp (/ -1 v)))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_i 2) (exp (/ -1 v))) (pow v 2))))) (/ (* cosTheta_i (exp (/ -1 v))) v))))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt 1>
#<alt (- (+ 1 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 1 (+ (* 1/2 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 2) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))>
#<alt (- (+ 1 (+ (* 1/6 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 3) (pow v 3))) (+ (* 1/2 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 2) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt 1>
#<alt (- (+ 1 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (- (* cosTheta_O cosTheta_i) 1)) (* -1/2 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 2) v))) v)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (- (* cosTheta_O cosTheta_i) 1)) (* -1 (/ (+ (* 1/6 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 3) v)) (* 1/2 (pow (- (* cosTheta_O cosTheta_i) 1) 2))) v))) v)))>
#<alt (/ -1 v)>
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#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (/ cosTheta_i v)>
#<alt (* cosTheta_i (- (/ 1 v) (/ 1 (* cosTheta_i v))))>
#<alt (* cosTheta_i (- (/ 1 v) (/ 1 (* cosTheta_i v))))>
#<alt (* cosTheta_i (- (/ 1 v) (/ 1 (* cosTheta_i v))))>
#<alt (/ cosTheta_i v)>
#<alt (* -1 (* cosTheta_i (- (/ 1 (* cosTheta_i v)) (/ 1 v))))>
#<alt (* -1 (* cosTheta_i (- (/ 1 (* cosTheta_i v)) (/ 1 v))))>
#<alt (* -1 (* cosTheta_i (- (/ 1 (* cosTheta_i v)) (/ 1 v))))>
#<alt (/ -1 v)>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_O (- (/ cosTheta_i v) (/ 1 (* cosTheta_O v))))>
#<alt (* cosTheta_O (- (/ cosTheta_i v) (/ 1 (* cosTheta_O v))))>
#<alt (* cosTheta_O (- (/ cosTheta_i v) (/ 1 (* cosTheta_O v))))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ 1 (* cosTheta_O v)))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ 1 (* cosTheta_O v)))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ 1 (* cosTheta_O v)))))>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt -1>
#<alt (- (* cosTheta_O cosTheta_i) 1)>
#<alt (- (* cosTheta_O cosTheta_i) 1)>
#<alt (- (* cosTheta_O cosTheta_i) 1)>
#<alt cosTheta_i>
#<alt (* cosTheta_i (- 1 (/ 1 cosTheta_i)))>
#<alt (* cosTheta_i (- 1 (/ 1 cosTheta_i)))>
#<alt (* cosTheta_i (- 1 (/ 1 cosTheta_i)))>
#<alt cosTheta_i>
#<alt (* -1 (* cosTheta_i (- (/ 1 cosTheta_i) 1)))>
#<alt (* -1 (* cosTheta_i (- (/ 1 cosTheta_i) 1)))>
#<alt (* -1 (* cosTheta_i (- (/ 1 cosTheta_i) 1)))>
#<alt -1>
#<alt (- (* cosTheta_O cosTheta_i) 1)>
#<alt (- (* cosTheta_O cosTheta_i) 1)>
#<alt (- (* cosTheta_O cosTheta_i) 1)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O (- cosTheta_i (/ 1 cosTheta_O)))>
#<alt (* cosTheta_O (- cosTheta_i (/ 1 cosTheta_O)))>
#<alt (* cosTheta_O (- cosTheta_i (/ 1 cosTheta_O)))>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* -1 (* cosTheta_O (+ (* -1 cosTheta_i) (/ 1 cosTheta_O))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 cosTheta_i) (/ 1 cosTheta_O))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 cosTheta_i) (/ 1 cosTheta_O))))>
#<alt (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))>
#<alt (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))>
#<alt (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))>
#<alt (exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))>
#<alt (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v))))))>
#<alt (+ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (* -1 (/ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) v)))>
#<alt (+ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (+ (* -1 (/ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) v)) (* 1/2 (/ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (pow v 2)))))>
#<alt (+ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (+ (* -1 (/ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) v)) (+ (* -1/6 (/ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (pow v 3))) (* 1/2 (/ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (pow v 2))))))>
#<alt (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v))))))>
#<alt (+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) v)))>
#<alt (+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1/2 (/ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) v))) v)))>
#<alt (+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (+ (* -1/6 (/ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) v)) (* 1/2 (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))))) v))) v)))>
#<alt (/ -1 v)>
#<alt (/ (- (* v (- 6931/10000 (+ (log 2) (log v)))) 1) v)>
#<alt (/ (- (* v (- 6931/10000 (+ (log 2) (log v)))) 1) v)>
#<alt (/ (- (* v (- 6931/10000 (+ (log 2) (log v)))) 1) v)>
#<alt (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))>
#<alt (- 6931/10000 (+ (log 2) (+ (* -1 (log (/ 1 v))) (/ 1 v))))>
#<alt (- 6931/10000 (+ (log 2) (+ (* -1 (log (/ 1 v))) (/ 1 v))))>
#<alt (- 6931/10000 (+ (log 2) (+ (* -1 (log (/ 1 v))) (/ 1 v))))>
#<alt (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))>
#<alt (- 6931/10000 (+ (log -2) (+ (* -1 (log (/ -1 v))) (/ 1 v))))>
#<alt (- 6931/10000 (+ (log -2) (+ (* -1 (log (/ -1 v))) (/ 1 v))))>
#<alt (- 6931/10000 (+ (log -2) (+ (* -1 (log (/ -1 v))) (/ 1 v))))>
#<alt (/ -1 v)>
#<alt (/ (- (* 6931/10000 v) 1) v)>
#<alt (/ (- (* 6931/10000 v) 1) v)>
#<alt (/ (- (* 6931/10000 v) 1) v)>
#<alt 6931/10000>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt 6931/10000>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ 1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ 1 v)>
#<alt (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))>
#<alt (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))>
#<alt (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))>
#<alt (/ sinTheta_O v)>
#<alt (* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))>
#<alt (* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))>
#<alt (* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))>
#<alt (/ sinTheta_O v)>
#<alt (* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))>
#<alt (* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))>
#<alt (* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))>
#<alt (/ 1 v)>
#<alt (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))>
#<alt (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))>
#<alt (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)))>
#<alt (* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)))>
#<alt (* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)))>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v)))))>
#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
#<alt (* 2 v)>
#<alt (* 2 v)>
#<alt (* 2 v)>
#<alt (* 2 v)>
#<alt v>
#<alt v>
#<alt v>
#<alt v>
#<alt (* -1 v)>
#<alt (* -1 v)>
#<alt (* -1 v)>
#<alt (* -1 v)>

Calls

117 calls:

Time	Variable		Point	Expression
28.0ms	v	@	inf	(* v (* v v))
9.0ms	sinTheta_i	@	0	(+ (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) v)) (log 1/2))
2.0ms	sinTheta_O	@	0	(+ (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) v)) (log 1/2))
2.0ms	v	@	inf	(+ (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) v)) (log 1/2))
2.0ms	v	@	inf	(- (+ 6931/10000 (/ -1 v)) (log (* v 2)))

Compiler

Compiled 1 491 to 1 122 computations (24.7% saved)

rewrite359.0ms (2.8%)

Memory

8.9MiB live, 609.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 708×	`lower-fma.f64`
4 700×	`lower-fma.f32`
4 444×	`lower-/.f64`
4 430×	`lower-/.f32`
3 800×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	157
0	67	149
1	266	146
2	2296	146
0	8654	146

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

19 → 571

Calls

Call 1

Inputs
(exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32))))
(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)
(+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
(/.f32 cosTheta_i v)
(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
(fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v)))
(/.f32 cosTheta_i (.f32 v (.f32 v v)))
(.f32 v (.f32 v v))
(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
(exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32))))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
(/.f32 #s(literal -1 binary32) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(*.f32 v #s(literal 2 binary32))

Outputs
(exp.f32 (-.f32 (+.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 6931/10000 binary32)) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
(pow.f32 (exp.f32 (fma.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (pow.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 3 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (log.f32 #s(literal 1/2 binary32)) (-.f32 (log.f32 #s(literal 1/2 binary32)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))))
(pow.f32 (exp.f32 (fma.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (neg.f32 (pow.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 2 binary32))))) (/.f32 #s(literal 1 binary32) (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 2 binary32)))))
(/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (*.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) #s(literal 2 binary32)))
(/.f32 (exp.f32 (+.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 6931/10000 binary32))) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
(/.f32 (exp.f32 (/.f32 (*.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 2 binary32))))) (exp.f32 (/.f32 (pow.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 2 binary32)) (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 2 binary32))))))
(/.f32 (neg.f32 (exp.f32 #s(literal 6931/10000 binary32))) (neg.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) #s(literal 2 binary32))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(*.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) #s(literal 1/2 binary32))
(*.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (neg.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (log.f32 #s(literal 2 binary32))))))
(*.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (log.f32 #s(literal 1/2 binary32)))))
(*.f32 (exp.f32 (+.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 6931/10000 binary32))) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))
(neg.f32 (*.f32 #s(literal -1/2 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) v)))
(neg.f32 (/.f32 (*.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) #s(literal -1/2 binary32)) v))
(exp.f32 (.f32 (log.f32 (/.f32 v (.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))) #s(literal -1 binary32)))
(pow.f32 (/.f32 v (*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))) #s(literal -1 binary32))
(pow.f32 (/.f32 (/.f32 v (*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))) #s(literal 1 binary32)) #s(literal -1 binary32))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 v)) (*.f32 #s(literal -1/2 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) v)))
(/.f32 #s(literal 1 binary32) (/.f32 v (*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 v (*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (/.f32 v (*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))))))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))) v)
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 v (*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (/.f32 v (*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))) #s(literal 1 binary32))))
(/.f32 (*.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) #s(literal -1/2 binary32)) (neg.f32 v))
(/.f32 (neg.f32 (*.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) #s(literal -1/2 binary32))) (neg.f32 (neg.f32 v)))
(/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))) #s(literal 1 binary32)) v)
(/.f32 (neg.f32 (neg.f32 (*.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) #s(literal -1/2 binary32)))) (neg.f32 (neg.f32 (neg.f32 v))))
(/.f32 (neg.f32 (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))) #s(literal 1 binary32))) (neg.f32 v))
(.f32 #s(literal 1 binary32) (.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (/.f32 #s(literal 1/2 binary32) v)))
(.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))) (/.f32 #s(literal 1 binary32) v))
(*.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (/.f32 #s(literal 1/2 binary32) v))
(.f32 (.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) #s(literal -1/2 binary32)) (/.f32 #s(literal -1 binary32) v))
(.f32 (/.f32 #s(literal 1 binary32) v) (.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))
(.f32 (/.f32 #s(literal 1 binary32) v) (pow.f32 (/.f32 #s(literal 1 binary32) (.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))) #s(literal -1 binary32)))
(*.f32 (/.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) #s(literal -1 binary32)) (/.f32 #s(literal -1/2 binary32) v))
(*.f32 (/.f32 (neg.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))) #s(literal -1 binary32)) (/.f32 #s(literal 1/2 binary32) v))
(+.f32 #s(literal 6931/10000 binary32) (neg.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (log.f32 #s(literal 2 binary32)))))
(+.f32 #s(literal 6931/10000 binary32) (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (log.f32 #s(literal 1/2 binary32))))
(+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))
(+.f32 (log.f32 #s(literal 1/2 binary32)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
(+.f32 (+.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 6931/10000 binary32)) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))
(pow.f32 (/.f32 (fma.f32 (log.f32 #s(literal 1/2 binary32)) (-.f32 (log.f32 #s(literal 1/2 binary32)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))) (fma.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (pow.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 3 binary32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 2 binary32))) (fma.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (neg.f32 (pow.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 2 binary32))))) #s(literal -1 binary32))
(fma.f32 (-.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (.f32 v (.f32 v v)))) (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) #s(literal 48038761/100000000 binary32))) (log.f32 #s(literal 1/2 binary32)))
(fma.f32 (-.f32 #s(literal 48038761/100000000 binary32) (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 v v))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (log.f32 #s(literal 1/2 binary32)))
(-.f32 #s(literal 6931/10000 binary32) (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (log.f32 #s(literal 2 binary32))))
(-.f32 (/.f32 (*.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 2 binary32)))) (/.f32 (pow.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 2 binary32)) (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 2 binary32)))))
(-.f32 (+.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 6931/10000 binary32)) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(-.f32 (/.f32 #s(literal 332956652491/1000000000000 binary32) (+.f32 #s(literal 48038761/100000000 binary32) (+.f32 (pow.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (log.f32 #s(literal 2 binary32))) #s(literal 2 binary32)) (.f32 #s(literal 6931/10000 binary32) (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (log.f32 #s(literal 2 binary32))))))) (/.f32 (pow.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (log.f32 #s(literal 2 binary32))) #s(literal 3 binary32)) (+.f32 #s(literal 48038761/100000000 binary32) (+.f32 (pow.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (log.f32 #s(literal 2 binary32))) #s(literal 2 binary32)) (.f32 #s(literal 6931/10000 binary32) (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (log.f32 #s(literal 2 binary32))))))))
(-.f32 (/.f32 (pow.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 2 binary32)) (-.f32 (log.f32 #s(literal 1/2 binary32)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))) (/.f32 (*.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (-.f32 (log.f32 #s(literal 1/2 binary32)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))
(-.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 #s(literal 6931/10000 binary32) (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (log.f32 #s(literal 2 binary32))))) (/.f32 (pow.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (log.f32 #s(literal 2 binary32))) #s(literal 2 binary32)) (+.f32 #s(literal 6931/10000 binary32) (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (log.f32 #s(literal 2 binary32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (log.f32 #s(literal 1/2 binary32)) (-.f32 (log.f32 #s(literal 1/2 binary32)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))) (fma.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) (pow.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 3 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 2 binary32))) (fma.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (neg.f32 (pow.f32 (log.f32 #s(literal 1/2 binary32)) #s(literal 2 binary32))))))
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(/.f32 (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 #s(literal -1 binary32) (.f32 v (.f32 v v)))) (+.f32 #s(literal 48038761/100000000 binary32) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)) v)))
(/.f32 (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 #s(literal -1 binary32) (.f32 v (.f32 v v)))) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 v v)) (-.f32 #s(literal 48038761/100000000 binary32) (/.f32 #s(literal -6931/10000 binary32) v))))
(/.f32 (-.f32 #s(literal 48038761/100000000 binary32) (/.f32 #s(literal 1 binary32) (*.f32 v v))) (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v)))
(/.f32 (neg.f32 (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 #s(literal -1 binary32) (.f32 v (.f32 v v))))) (neg.f32 (+.f32 #s(literal 48038761/100000000 binary32) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)) v))))
(/.f32 (neg.f32 (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 #s(literal -1 binary32) (.f32 v (.f32 v v))))) (neg.f32 (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 v v)) (-.f32 #s(literal 48038761/100000000 binary32) (/.f32 #s(literal -6931/10000 binary32) v)))))
(/.f32 (neg.f32 (-.f32 #s(literal 48038761/100000000 binary32) (/.f32 #s(literal 1 binary32) (*.f32 v v)))) (neg.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v))))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 v v)) #s(literal 48038761/100000000 binary32)) (-.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
(/.f32 (neg.f32 (neg.f32 (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 #s(literal -1 binary32) (.f32 v (.f32 v v)))))) (neg.f32 (neg.f32 (+.f32 #s(literal 48038761/100000000 binary32) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)) v)))))
(/.f32 (neg.f32 (neg.f32 (-.f32 #s(literal 48038761/100000000 binary32) (/.f32 #s(literal 1 binary32) (*.f32 v v))))) (neg.f32 (neg.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v)))))
(/.f32 (neg.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 v v)) #s(literal 48038761/100000000 binary32))) (neg.f32 (-.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(.f32 (+.f32 #s(literal 332956652491/1000000000000 binary32) (/.f32 #s(literal -1 binary32) (.f32 v (*.f32 v v)))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 48038761/100000000 binary32) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)) v))))
(.f32 (-.f32 #s(literal 48038761/100000000 binary32) (/.f32 #s(literal 1 binary32) (.f32 v v))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v))))
(neg.f32 (/.f32 #s(literal 1 binary32) v))
(exp.f32 (*.f32 (log.f32 (neg.f32 v)) #s(literal -1 binary32)))
(exp.f32 (.f32 (log.f32 (.f32 v #s(literal -1 binary32))) #s(literal -1 binary32)))
(pow.f32 (neg.f32 v) #s(literal -1 binary32))
(pow.f32 (*.f32 v #s(literal -1 binary32)) #s(literal -1 binary32))
(pow.f32 (/.f32 (*.f32 v #s(literal -1 binary32)) #s(literal 1 binary32)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) (neg.f32 v))
(/.f32 #s(literal 1 binary32) (*.f32 v #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 v #s(literal -1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (neg.f32 v))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (*.f32 v #s(literal -1 binary32)))))
(/.f32 #s(literal -1 binary32) v)
(/.f32 #s(literal -1 binary32) (neg.f32 (neg.f32 v)))
(/.f32 #s(literal -1 binary32) (neg.f32 (*.f32 v #s(literal -1 binary32))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (*.f32 v #s(literal -1 binary32)) #s(literal 1 binary32))))
(*.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) v))
(*.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) v))
(*.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -1 binary32))
(neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))
(exp.f32 (*.f32 (log.f32 (/.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) #s(literal -1 binary32)))
(pow.f32 (/.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) #s(literal -1 binary32))
(pow.f32 (/.f32 (/.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) #s(literal 1 binary32)) #s(literal -1 binary32))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 v)) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))
(-.f32 (/.f32 (/.f32 (.f32 sinTheta_O (.f32 sinTheta_i (*.f32 sinTheta_O sinTheta_i))) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))) v) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))) v))
(-.f32 (/.f32 (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) (.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (*.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (/.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))))))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (/.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) #s(literal 1 binary32))))
(/.f32 (neg.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (neg.f32 v))
(/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) (.f32 v (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i)))))
(/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) (*.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))))
(/.f32 (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal 1 binary32)) v)
(/.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i))) v))
(/.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)) v))
(/.f32 (neg.f32 (neg.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (neg.f32 (neg.f32 v)))
(/.f32 (neg.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32))) (neg.f32 (.f32 v (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i))))))
(/.f32 (neg.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32))) (neg.f32 (*.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)))))
(/.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) v)) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i))))
(/.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (*.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) v)) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)))
(/.f32 (neg.f32 (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal 1 binary32))) (neg.f32 v))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) #s(literal 1 binary32))) (neg.f32 (.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (*.f32 sinTheta_O sinTheta_i))) v)))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) #s(literal 1 binary32))) (neg.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)) v)))
(/.f32 (neg.f32 (neg.f32 (neg.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))))) (neg.f32 (neg.f32 (neg.f32 v))))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) v))) (neg.f32 (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i)))))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (*.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) v))) (neg.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))))
(*.f32 #s(literal 1 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) v))
(*.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))))
(*.f32 (neg.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (/.f32 #s(literal -1 binary32) v))
(*.f32 (/.f32 #s(literal 1 binary32) v) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))
(*.f32 (/.f32 #s(literal 1 binary32) v) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 v (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) (-.f32 #s(literal 1 binary32) (.f32 sinTheta_O sinTheta_i)))))
(.f32 (pow.f32 (/.f32 v (fma.f32 (.f32 sinTheta_O sinTheta_i) (*.f32 sinTheta_O sinTheta_i) #s(literal -1 binary32))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))))
(exp.f32 (log.f32 (*.f32 v #s(literal 2 binary32))))
(*.f32 v #s(literal 2 binary32))
(*.f32 #s(literal 2 binary32) v)

simplify434.0ms (3.3%)

Memory

19.0MiB live, 649.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10 620×	`lower-fma.f64`
10 620×	`lower-fma.f32`
6 858×	`lower-*.f64`
6 858×	`lower-*.f32`
3 462×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	574	5385
1	1644	5196
2	5102	4967
0	8568	4698

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 458

Calls

Call 1

Inputs
(exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) v)))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))))))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) v)))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))))))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp (+ 6931/10000 (log 1/2)))
(+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)))
(+ (exp (+ 6931/10000 (log 1/2))) (+ (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2)))))
(+ (exp (+ 6931/10000 (log 1/2))) (+ (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (* -1/6 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (pow v 3))) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))))))
(exp (+ 6931/10000 (log 1/2)))
(+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)))
(+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (+ (* -1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) v)) (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) v)) (* 1/2 (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) v)) (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v)
(+ (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))
(+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))
(+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 4))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 3))))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v)
(+ (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))
(+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))
(+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 4))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 3))))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
(/ (exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))) v)
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(/ -1 v)
(/ (- (* v (- 6931/10000 (+ (log 2) (log v)))) 1) v)
(/ (- (* v (- 6931/10000 (+ (log 2) (log v)))) 1) v)
(/ (- (* v (- 6931/10000 (+ (log 2) (log v)))) 1) v)
(- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))
(- 6931/10000 (+ (log 2) (+ (* -1 (log (/ 1 v))) (/ 1 v))))
(- 6931/10000 (+ (log 2) (+ (* -1 (log (/ 1 v))) (/ 1 v))))
(- 6931/10000 (+ (log 2) (+ (* -1 (log (/ 1 v))) (/ 1 v))))
(- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))
(- 6931/10000 (+ (log -2) (+ (* -1 (log (/ -1 v))) (/ 1 v))))
(- 6931/10000 (+ (log -2) (+ (* -1 (log (/ -1 v))) (/ 1 v))))
(- 6931/10000 (+ (log -2) (+ (* -1 (log (/ -1 v))) (/ 1 v))))
(/ -1 v)
(/ (- (* 6931/10000 v) 1) v)
(/ (- (* 6931/10000 v) 1) v)
(/ (- (* 6931/10000 v) 1) v)
6931/10000
(- 6931/10000 (/ 1 v))
(- 6931/10000 (/ 1 v))
(- 6931/10000 (/ 1 v))
6931/10000
(- 6931/10000 (/ 1 v))
(- 6931/10000 (/ 1 v))
(- 6931/10000 (/ 1 v))
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ 1 v)
(/ -1 v)
(/ -1 v)
(/ -1 v)
(/ -1 v)
(/ -1 v)
(/ -1 v)
(/ -1 v)
(/ -1 v)
(/ 1 v)
(+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))
(+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))
(+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))
(/ sinTheta_O v)
(* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))
(* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))
(* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))
(/ sinTheta_O v)
(* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))
(* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))
(* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))
(/ 1 v)
(+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))
(+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))
(+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))
(/ (* sinTheta_O sinTheta_i) v)
(* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)))
(* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)))
(* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)))
(/ (* sinTheta_O sinTheta_i) v)
(* -1 (* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v)))))
(* -1 (* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v)))))
(* -1 (* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v)))))
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(* 2 v)
(* 2 v)
(* 2 v)
(* 2 v)
v
v
v
v
(* -1 v)
(* -1 v)
(* -1 v)
(* -1 v)

Outputs
(exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) v)))
(fma.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (*.f32 sinTheta_O sinTheta_i)) (neg.f32 v)))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))))))
(fma.f32 sinTheta_O (fma.f32 #s(literal 1/2 binary32) (.f32 (.f32 sinTheta_O (.f32 sinTheta_i sinTheta_i)) (/.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (.f32 v v))) (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (/.f32 sinTheta_i (neg.f32 v)))) (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))))))))
(fma.f32 sinTheta_O (fma.f32 sinTheta_O (fma.f32 #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v))) (.f32 (.f32 #s(literal -1/6 binary32) sinTheta_O) (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i sinTheta_i)) (.f32 v (.f32 v v)))))) (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (/.f32 sinTheta_i (neg.f32 v)))) (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) v)))
(fma.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (*.f32 sinTheta_O sinTheta_i)) (neg.f32 v)))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))))))
(fma.f32 sinTheta_i (fma.f32 #s(literal 1/2 binary32) (.f32 (.f32 sinTheta_O (.f32 sinTheta_O sinTheta_i)) (/.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (.f32 v v))) (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (/.f32 sinTheta_O (neg.f32 v)))) (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
(+ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))))))))
(fma.f32 sinTheta_i (fma.f32 sinTheta_i (fma.f32 #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 v v))) (/.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 sinTheta_O (.f32 sinTheta_O (.f32 sinTheta_O sinTheta_i)))) (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))) (.f32 v (.f32 v v)))) (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (/.f32 sinTheta_O (neg.f32 v)))) (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (- (+ 6931/10000 (log 1/2)) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(*.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(exp (+ 6931/10000 (log 1/2)))
(*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)))
(+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)))
(fma.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (.f32 #s(literal -1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
(+ (exp (+ 6931/10000 (log 1/2))) (+ (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2)))))
(fma.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)) (/.f32 (fma.f32 (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (/.f32 #s(literal 1/2 binary32) v) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (*.f32 #s(literal -1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))))) v))
(+ (exp (+ 6931/10000 (log 1/2))) (+ (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (* -1/6 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (pow v 3))) (* 1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))))))
(fma.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)) (fma.f32 #s(literal -1/6 binary32) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))))) (.f32 v (.f32 v v))) (/.f32 (fma.f32 (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (/.f32 #s(literal 1/2 binary32) v) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (*.f32 #s(literal -1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))))) v)))
(exp (+ 6931/10000 (log 1/2)))
(*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)))
(+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i))) v)))
(fma.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (.f32 #s(literal -1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
(+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (+ (* -1/2 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) v)) (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(fma.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)) (/.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) (.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) v) #s(literal -1/2 binary32)) (.f32 (exp.f32 #s(literal 6931/10000 binary32)) (*.f32 #s(literal 1/2 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))))) (neg.f32 v)))
(+ (exp (+ 6931/10000 (log 1/2))) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) v)) (* 1/2 (* (exp (+ 6931/10000 (log 1/2))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) v)) (* (exp (+ 6931/10000 (log 1/2))) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(fma.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)) (/.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (/.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))))) (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)))) v)) (neg.f32 v))) (neg.f32 v)))
(/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v)
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
(+ (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 2))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))
(fma.f32 sinTheta_O (.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) (neg.f32 (/.f32 sinTheta_i (.f32 v v)))) (/.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v))
(+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v)))) (pow v 2))) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))))) (pow v 3))))) (/ (exp (- (+ 6931/10000 (log 1/2)) (/ 1 v))) v))
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(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
(/ (- (* cosTheta_O cosTheta_i) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)
-1
#s(literal -1 binary32)
(- (* cosTheta_O cosTheta_i) 1)
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
(- (* cosTheta_O cosTheta_i) 1)
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
(- (* cosTheta_O cosTheta_i) 1)
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
cosTheta_i
(* cosTheta_i (- 1 (/ 1 cosTheta_i)))
(+.f32 #s(literal -1 binary32) cosTheta_i)
(* cosTheta_i (- 1 (/ 1 cosTheta_i)))
(+.f32 #s(literal -1 binary32) cosTheta_i)
(* cosTheta_i (- 1 (/ 1 cosTheta_i)))
(+.f32 #s(literal -1 binary32) cosTheta_i)
cosTheta_i
(* -1 (* cosTheta_i (- (/ 1 cosTheta_i) 1)))
(+.f32 #s(literal -1 binary32) cosTheta_i)
(* -1 (* cosTheta_i (- (/ 1 cosTheta_i) 1)))
(+.f32 #s(literal -1 binary32) cosTheta_i)
(* -1 (* cosTheta_i (- (/ 1 cosTheta_i) 1)))
(+.f32 #s(literal -1 binary32) cosTheta_i)
-1
#s(literal -1 binary32)
(- (* cosTheta_O cosTheta_i) 1)
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
(- (* cosTheta_O cosTheta_i) 1)
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
(- (* cosTheta_O cosTheta_i) 1)
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
(* cosTheta_O cosTheta_i)
(*.f32 cosTheta_i cosTheta_O)
(* cosTheta_O (- cosTheta_i (/ 1 cosTheta_O)))
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
(* cosTheta_O (- cosTheta_i (/ 1 cosTheta_O)))
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
(* cosTheta_O (- cosTheta_i (/ 1 cosTheta_O)))
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
(* cosTheta_O cosTheta_i)
(*.f32 cosTheta_i cosTheta_O)
(* -1 (* cosTheta_O (+ (* -1 cosTheta_i) (/ 1 cosTheta_O))))
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
(* -1 (* cosTheta_O (+ (* -1 cosTheta_i) (/ 1 cosTheta_O))))
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
(* -1 (* cosTheta_O (+ (* -1 cosTheta_i) (/ 1 cosTheta_O))))
(fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32))
(exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))
(/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) (*.f32 v #s(literal 2 binary32)))
(exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))
(/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) (*.f32 v #s(literal 2 binary32)))
(exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))
(/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) (*.f32 v #s(literal 2 binary32)))
(exp (- 6931/10000 (+ (log (* 2 v)) (/ 1 v))))
(/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) (*.f32 v #s(literal 2 binary32)))
(exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v))))))
(/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (*.f32 v #s(literal 2 binary32)))
(+ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (* -1 (/ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) v)))
(-.f32 (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 v #s(literal 2 binary32))) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 v (*.f32 v #s(literal 2 binary32)))))
(+ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (+ (* -1 (/ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) v)) (* 1/2 (/ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (pow v 2)))))
(fma.f32 #s(literal 1/2 binary32) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (.f32 v v) (.f32 v #s(literal 2 binary32)))) (-.f32 (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 v #s(literal 2 binary32))) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 v (.f32 v #s(literal 2 binary32))))))
(+ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (+ (* -1 (/ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) v)) (+ (* -1/6 (/ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (pow v 3))) (* 1/2 (/ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (pow v 2))))))
(+.f32 (-.f32 (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 v #s(literal 2 binary32))) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 v (.f32 v #s(literal 2 binary32))))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (.f32 v v) (.f32 v #s(literal 2 binary32)))) (.f32 #s(literal -1/6 binary32) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (.f32 v (.f32 v v)) (*.f32 v #s(literal 2 binary32)))))))
(exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v))))))
(/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (neg.f32 v))))) #s(literal -2 binary32))
(+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) v)))
(-.f32 (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (neg.f32 v))))) #s(literal -2 binary32)) (/.f32 (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (neg.f32 v))))) #s(literal -2 binary32)) v))
(+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1/2 (/ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) v))) v)))
(-.f32 (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (neg.f32 v))))) #s(literal -2 binary32)) (/.f32 (fma.f32 #s(literal -1/2 binary32) (/.f32 (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (neg.f32 v))))) #s(literal -2 binary32)) v) (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (neg.f32 v))))) #s(literal -2 binary32))) v))
(+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (+ (* -1/6 (/ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) v)) (* 1/2 (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))))) v))) v)))
(-.f32 (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (neg.f32 v))))) #s(literal -2 binary32)) (/.f32 (-.f32 (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (neg.f32 v))))) #s(literal -2 binary32)) (/.f32 (fma.f32 #s(literal -1/6 binary32) (/.f32 (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (neg.f32 v))))) #s(literal -2 binary32)) v) (*.f32 #s(literal 1/2 binary32) (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (neg.f32 v))))) #s(literal -2 binary32)))) v)) v))
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ (- (* v (- 6931/10000 (+ (log 2) (log v)))) 1) v)
(fma.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)) #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) v))
(/ (- (* v (- 6931/10000 (+ (log 2) (log v)))) 1) v)
(fma.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)) #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) v))
(/ (- (* v (- 6931/10000 (+ (log 2) (log v)))) 1) v)
(fma.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)) #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) v))
(- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))
(-.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v))
(- 6931/10000 (+ (log 2) (+ (* -1 (log (/ 1 v))) (/ 1 v))))
(+.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)) (/.f32 #s(literal -1 binary32) v))
(- 6931/10000 (+ (log 2) (+ (* -1 (log (/ 1 v))) (/ 1 v))))
(+.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)) (/.f32 #s(literal -1 binary32) v))
(- 6931/10000 (+ (log 2) (+ (* -1 (log (/ 1 v))) (/ 1 v))))
(+.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)) (/.f32 #s(literal -1 binary32) v))
(- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))
(+.f32 #s(literal 6931/10000 binary32) (-.f32 (neg.f32 (log.f32 (neg.f32 v))) (log.f32 #s(literal -2 binary32))))
(- 6931/10000 (+ (log -2) (+ (* -1 (log (/ -1 v))) (/ 1 v))))
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (-.f32 (neg.f32 (log.f32 (neg.f32 v))) (log.f32 #s(literal -2 binary32)))) (/.f32 #s(literal -1 binary32) v))
(- 6931/10000 (+ (log -2) (+ (* -1 (log (/ -1 v))) (/ 1 v))))
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (-.f32 (neg.f32 (log.f32 (neg.f32 v))) (log.f32 #s(literal -2 binary32)))) (/.f32 #s(literal -1 binary32) v))
(- 6931/10000 (+ (log -2) (+ (* -1 (log (/ -1 v))) (/ 1 v))))
(+.f32 (+.f32 #s(literal 6931/10000 binary32) (-.f32 (neg.f32 (log.f32 (neg.f32 v))) (log.f32 #s(literal -2 binary32)))) (/.f32 #s(literal -1 binary32) v))
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ (- (* 6931/10000 v) 1) v)
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
(/ (- (* 6931/10000 v) 1) v)
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
(/ (- (* 6931/10000 v) 1) v)
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
6931/10000
#s(literal 6931/10000 binary32)
(- 6931/10000 (/ 1 v))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
(- 6931/10000 (/ 1 v))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
(- 6931/10000 (/ 1 v))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
6931/10000
#s(literal 6931/10000 binary32)
(- 6931/10000 (/ 1 v))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
(- 6931/10000 (/ 1 v))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
(- 6931/10000 (/ 1 v))
(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v))
(+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v))
(+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v))
(/ sinTheta_O v)
(/.f32 sinTheta_O v)
(* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))
(+.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 sinTheta_O v))
(* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))
(+.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 sinTheta_O v))
(* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))
(+.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 sinTheta_O v))
(/ sinTheta_O v)
(/.f32 sinTheta_O v)
(* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))
(+.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 sinTheta_O v))
(* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))
(+.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 sinTheta_O v))
(* sinTheta_O (+ (/ 1 v) (/ 1 (* sinTheta_O v))))
(+.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 sinTheta_O v))
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v))
(+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v))
(+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v))
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v))
(* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v))
(* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v))
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(* -1 (* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v)))))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v))
(* -1 (* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v)))))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v))
(* -1 (* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v)))))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v))
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
(* 2 v)
(*.f32 v #s(literal 2 binary32))
(* 2 v)
(*.f32 v #s(literal 2 binary32))
(* 2 v)
(*.f32 v #s(literal 2 binary32))
(* 2 v)
(*.f32 v #s(literal 2 binary32))
v
v
v
v
(* -1 v)
(neg.f32 v)
(* -1 v)
(neg.f32 v)
(* -1 v)
(neg.f32 v)
(* -1 v)
(neg.f32 v)

eval381.0ms (2.9%)

Memory: -130.4MiB live, 231.1MiB allocated
Compiler: Compiled 24 665 to 2 584 computations (89.5% saved)

prune221.0ms (1.7%)

Memory

28.5MiB live, 308.8MiB allocated

Pruning

28 alts after pruning (21 fresh and 7 done)

	Pruned	Kept	Total
New	1 078	8	1 086
Fresh	5	13	18
Picked	1	4	5
Done	1	3	4
Total	1 085	28	1 113

Accuracy

99.9%

Counts

1 113 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	2.5%	(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
	6.3%	(fma.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)) #s(literal 1 binary32))
	3.4%	(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 (/.f32 cosTheta_i (.f32 v v)) (/.f32 #s(literal 1/6 binary32) v) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
✓	3.0%	(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
	2.0%	(fma.f32 cosTheta_i (fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i #s(literal 1/6 binary32)) (.f32 v v) (.f32 (.f32 v (.f32 v v)) #s(literal 1/2 binary32))) (.f32 (.f32 v v) (.f32 v (*.f32 v v)))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
	3.5%	(fma.f32 cosTheta_i (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
	4.0%	(fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 #s(literal 1/6 binary32) (.f32 v v)) #s(literal 1 binary32)) v) #s(literal 1 binary32))
	5.8%	(/.f32 (+.f32 v cosTheta_i) v)
	99.5%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
	99.6%	(/.f32 (exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 v))) #s(literal 2 binary32))
✓	99.8%	(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)
	99.6%	(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v)) (log.f32 #s(literal 1/2 binary32)))) v)
	99.1%	(/.f32 (exp.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) v)
	6.4%	(/.f32 cosTheta_i v)
	5.3%	(+.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta_i (/.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i cosTheta_i)) v) (.f32 #s(literal 1/2 binary32) (.f32 cosTheta_i cosTheta_i))) v)) v))
✓	5.8%	(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
	5.8%	(+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 v cosTheta_i)))
	98.9%	(.f32 (/.f32 #s(literal 1 binary32) v) (pow.f32 (/.f32 #s(literal 1 binary32) (.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))) #s(literal -1 binary32)))
	98.7%	(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v)))) (exp.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 v v)) (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v))))))
	97.7%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
	99.7%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
✓	99.5%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
	99.5%	(.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v)) (/.f32 #s(literal 1/2 binary32) v)))
	97.5%	(exp.f32 (/.f32 #s(literal -1 binary32) v))
	97.7%	(exp.f32 (-.f32 (/.f32 #s(literal -1 binary32) v) (log.f32 (*.f32 v #s(literal 2 binary32)))))
	99.7%	(exp.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
✓	99.5%	(exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
✓	6.5%	#s(literal 1 binary32)

Compiler

Compiled 1 257 to 575 computations (54.3% saved)

regimes141.0ms (1.1%)

Memory

2.1MiB live, 284.4MiB allocated

Counts

51 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(/.f32 cosTheta_i v)
(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
(/.f32 (+.f32 v cosTheta_i) v)
(fma.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 v cosTheta_i)))
(fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 #s(literal 1/6 binary32) (.f32 v v)) #s(literal 1 binary32)) v) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (/.f32 (fma.f32 #s(literal -1/6 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (.f32 v (.f32 v v)))) #s(literal -1 binary32)) (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta_i (/.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i cosTheta_i)) v) (.f32 #s(literal 1/2 binary32) (.f32 cosTheta_i cosTheta_i))) v)) v))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 (/.f32 cosTheta_i (.f32 v v)) (/.f32 #s(literal 1/6 binary32) v) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i #s(literal 1/6 binary32)) (.f32 v v) (.f32 (.f32 v (.f32 v v)) #s(literal 1/2 binary32))) (.f32 (.f32 v v) (.f32 v (*.f32 v v)))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(exp.f32 (/.f32 #s(literal -1 binary32) v))
(exp.f32 (/.f32 cosTheta_i v))
(exp.f32 (/.f32 sinTheta_O (neg.f32 v)))
(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(exp.f32 (*.f32 (/.f32 #s(literal 1 binary32) v) cosTheta_i))
(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(/.f32 (exp.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) v)
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32))))
(exp.f32 (-.f32 (/.f32 #s(literal -1 binary32) v) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))))
(exp.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 #s(literal 1/2 binary32)))) v)
(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v)) (log.f32 #s(literal 1/2 binary32)))) v)
(/.f32 (exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 v))) #s(literal 2 binary32))
(exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))))
(.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v)) (/.f32 #s(literal 1/2 binary32) v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))))
(/.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 (log.f32 v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)))))
(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)
(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)
(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))) (log.f32 #s(literal 1/2 binary32)))) v)
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(.f32 (.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))) (exp.f32 #s(literal 6931/10000 binary32)))
(exp.f32 (fma.f32 (fma.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) v (neg.f32 v)) (/.f32 #s(literal 1 binary32) (.f32 v v)) (-.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32))))))
(.f32 (/.f32 #s(literal 1 binary32) v) (pow.f32 (/.f32 #s(literal 1 binary32) (.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))) #s(literal -1 binary32)))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))
(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v)))) (exp.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 v v)) (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v))))))
(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 (/.f32 (.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal -1 binary32)) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal -1 binary32))) (*.f32 v v)) (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) #s(literal -6931/10000 binary32)))) (exp.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) #s(literal -6931/10000 binary32))))))
(/.f32 (exp.f32 (/.f32 (.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32))) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))))) (exp.f32 (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))))))

Outputs
(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)

Calls

9 calls:

23.0ms	v
21.0ms	cosTheta_O
16.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))
15.0ms	sinTheta_O
14.0ms	sinTheta_i

Results

Accuracy	Segments	Branch
99.8%	1	`cosTheta_i`
99.8%	1	`cosTheta_O`
99.8%	1	`sinTheta_i`
99.8%	1	`sinTheta_O`
99.8%	1	`v`
99.8%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`
99.8%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`
99.8%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.8%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 105 to 78 computations (25.7% saved)

regimes158.0ms (1.2%)

Memory

-4.6MiB live, 252.1MiB allocated

Counts

41 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(/.f32 cosTheta_i v)
(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
(/.f32 (+.f32 v cosTheta_i) v)
(fma.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 v cosTheta_i)))
(fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 #s(literal 1/6 binary32) (.f32 v v)) #s(literal 1 binary32)) v) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (/.f32 (fma.f32 #s(literal -1/6 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (.f32 v (.f32 v v)))) #s(literal -1 binary32)) (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta_i (/.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i cosTheta_i)) v) (.f32 #s(literal 1/2 binary32) (.f32 cosTheta_i cosTheta_i))) v)) v))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 (/.f32 cosTheta_i (.f32 v v)) (/.f32 #s(literal 1/6 binary32) v) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i #s(literal 1/6 binary32)) (.f32 v v) (.f32 (.f32 v (.f32 v v)) #s(literal 1/2 binary32))) (.f32 (.f32 v v) (.f32 v (*.f32 v v)))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(exp.f32 (/.f32 #s(literal -1 binary32) v))
(exp.f32 (/.f32 cosTheta_i v))
(exp.f32 (/.f32 sinTheta_O (neg.f32 v)))
(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(exp.f32 (*.f32 (/.f32 #s(literal 1 binary32) v) cosTheta_i))
(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(/.f32 (exp.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) v)
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32))))
(exp.f32 (-.f32 (/.f32 #s(literal -1 binary32) v) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))))
(exp.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 #s(literal 1/2 binary32)))) v)
(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal 1 binary32) v)) (log.f32 #s(literal 1/2 binary32)))) v)
(/.f32 (exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 v))) #s(literal 2 binary32))
(exp.f32 (+.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)) (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))))
(.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v)) (/.f32 #s(literal 1/2 binary32) v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))))
(/.f32 #s(literal 1/2 binary32) (exp.f32 (-.f32 (log.f32 v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)))))
(/.f32 (exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)

Outputs
(exp.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))

Calls

9 calls:

36.0ms	sinTheta_i
34.0ms	cosTheta_O
15.0ms	v
12.0ms	cosTheta_i
12.0ms	(*.f32 sinTheta_i sinTheta_O)

Results

Accuracy	Segments	Branch
99.7%	1	`cosTheta_i`
99.7%	1	`cosTheta_O`
99.7%	1	`sinTheta_i`
99.7%	1	`sinTheta_O`
99.7%	1	`v`
99.7%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`
99.7%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`
99.7%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.7%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 105 to 78 computations (25.7% saved)

regimes90.0ms (0.7%)

Memory

20.8MiB live, 222.1MiB allocated

Counts

32 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(/.f32 cosTheta_i v)
(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
(/.f32 (+.f32 v cosTheta_i) v)
(fma.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 v cosTheta_i)))
(fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 #s(literal 1/6 binary32) (.f32 v v)) #s(literal 1 binary32)) v) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (/.f32 (fma.f32 #s(literal -1/6 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (.f32 v (.f32 v v)))) #s(literal -1 binary32)) (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta_i (/.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i cosTheta_i)) v) (.f32 #s(literal 1/2 binary32) (.f32 cosTheta_i cosTheta_i))) v)) v))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 (/.f32 cosTheta_i (.f32 v v)) (/.f32 #s(literal 1/6 binary32) v) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i #s(literal 1/6 binary32)) (.f32 v v) (.f32 (.f32 v (.f32 v v)) #s(literal 1/2 binary32))) (.f32 (.f32 v v) (.f32 v (*.f32 v v)))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(exp.f32 (/.f32 #s(literal -1 binary32) v))
(exp.f32 (/.f32 cosTheta_i v))
(exp.f32 (/.f32 sinTheta_O (neg.f32 v)))
(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(exp.f32 (*.f32 (/.f32 #s(literal 1 binary32) v) cosTheta_i))
(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(/.f32 (exp.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) v)
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) #s(literal -1 binary32)) v) #s(literal 6931/10000 binary32))))
(exp.f32 (-.f32 (/.f32 #s(literal -1 binary32) v) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)) (log.f32 (/.f32 #s(literal 1/2 binary32) v))))

Outputs
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))

Calls

9 calls:

16.0ms	(*.f32 cosTheta_i cosTheta_O)
10.0ms	cosTheta_O
10.0ms	sinTheta_i
9.0ms	v
9.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))

Results

Accuracy	Segments	Branch
99.7%	1	`cosTheta_i`
99.7%	1	`cosTheta_O`
99.7%	1	`sinTheta_i`
99.7%	1	`sinTheta_O`
99.7%	1	`v`
99.7%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`
99.7%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`
99.7%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.7%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 105 to 78 computations (25.7% saved)

regimes78.0ms (0.6%)

Memory

-52.8MiB live, 168.6MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(/.f32 cosTheta_i v)
(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
(/.f32 (+.f32 v cosTheta_i) v)
(fma.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 v cosTheta_i)))
(fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 #s(literal 1/6 binary32) (.f32 v v)) #s(literal 1 binary32)) v) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (/.f32 (fma.f32 #s(literal -1/6 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (.f32 v (.f32 v v)))) #s(literal -1 binary32)) (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta_i (/.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i cosTheta_i)) v) (.f32 #s(literal 1/2 binary32) (.f32 cosTheta_i cosTheta_i))) v)) v))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 (/.f32 cosTheta_i (.f32 v v)) (/.f32 #s(literal 1/6 binary32) v) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i #s(literal 1/6 binary32)) (.f32 v v) (.f32 (.f32 v (.f32 v v)) #s(literal 1/2 binary32))) (.f32 (.f32 v v) (.f32 v (*.f32 v v)))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(exp.f32 (/.f32 #s(literal -1 binary32) v))
(exp.f32 (/.f32 cosTheta_i v))
(exp.f32 (/.f32 sinTheta_O (neg.f32 v)))
(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(exp.f32 (*.f32 (/.f32 #s(literal 1 binary32) v) cosTheta_i))
(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(/.f32 (exp.f32 (neg.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))) v)
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)

Outputs
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))

Calls

9 calls:

18.0ms	sinTheta_i
8.0ms	v
8.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))
7.0ms	(*.f32 sinTheta_i sinTheta_O)
7.0ms	cosTheta_O

Results

Accuracy	Segments	Branch
99.5%	1	`cosTheta_i`
99.5%	1	`cosTheta_O`
99.5%	1	`sinTheta_i`
99.5%	1	`sinTheta_O`
99.5%	1	`v`
99.5%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`
99.5%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`
99.5%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.5%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 105 to 78 computations (25.7% saved)

regimes101.0ms (0.8%)

Memory

0.4MiB live, 119.7MiB allocated

Counts

23 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(/.f32 cosTheta_i v)
(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
(/.f32 (+.f32 v cosTheta_i) v)
(fma.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 v cosTheta_i)))
(fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 #s(literal 1/6 binary32) (.f32 v v)) #s(literal 1 binary32)) v) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (/.f32 (fma.f32 #s(literal -1/6 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (.f32 v (.f32 v v)))) #s(literal -1 binary32)) (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta_i (/.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i cosTheta_i)) v) (.f32 #s(literal 1/2 binary32) (.f32 cosTheta_i cosTheta_i))) v)) v))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 (/.f32 cosTheta_i (.f32 v v)) (/.f32 #s(literal 1/6 binary32) v) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i #s(literal 1/6 binary32)) (.f32 v v) (.f32 (.f32 v (.f32 v v)) #s(literal 1/2 binary32))) (.f32 (.f32 v v) (.f32 v (*.f32 v v)))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(exp.f32 (/.f32 #s(literal -1 binary32) v))
(exp.f32 (/.f32 cosTheta_i v))
(exp.f32 (/.f32 sinTheta_O (neg.f32 v)))
(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(exp.f32 (*.f32 (/.f32 #s(literal 1 binary32) v) cosTheta_i))
(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))

Outputs
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))

Calls

9 calls:

35.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))
20.0ms	sinTheta_i
7.0ms	cosTheta_O
6.0ms	cosTheta_i
6.0ms	sinTheta_O

Results

Accuracy	Segments	Branch
97.7%	1	`cosTheta_i`
97.7%	1	`cosTheta_O`
97.7%	1	`sinTheta_i`
97.7%	1	`sinTheta_O`
97.7%	1	`v`
97.7%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`
97.7%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`
97.7%	1	`(*.f32 cosTheta_i cosTheta_O)`
97.7%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 105 to 78 computations (25.7% saved)

regimes58.0ms (0.4%)

Memory

12.8MiB live, 129.4MiB allocated

Counts

22 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(/.f32 cosTheta_i v)
(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
(/.f32 (+.f32 v cosTheta_i) v)
(fma.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 v cosTheta_i)))
(fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 #s(literal 1/6 binary32) (.f32 v v)) #s(literal 1 binary32)) v) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (/.f32 (fma.f32 #s(literal -1/6 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (.f32 v (.f32 v v)))) #s(literal -1 binary32)) (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta_i (/.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i cosTheta_i)) v) (.f32 #s(literal 1/2 binary32) (.f32 cosTheta_i cosTheta_i))) v)) v))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 (/.f32 cosTheta_i (.f32 v v)) (/.f32 #s(literal 1/6 binary32) v) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i #s(literal 1/6 binary32)) (.f32 v v) (.f32 (.f32 v (.f32 v v)) #s(literal 1/2 binary32))) (.f32 (.f32 v v) (.f32 v (*.f32 v v)))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(exp.f32 (/.f32 #s(literal -1 binary32) v))
(exp.f32 (/.f32 cosTheta_i v))
(exp.f32 (/.f32 sinTheta_O (neg.f32 v)))
(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(exp.f32 (*.f32 (/.f32 #s(literal 1 binary32) v) cosTheta_i))
(exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O #s(literal -1 binary32)) v))
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))

Outputs
(exp.f32 (/.f32 #s(literal -1 binary32) v))

Calls

9 calls:

7.0ms	cosTheta_O
7.0ms	v
7.0ms	sinTheta_O
6.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))
6.0ms	cosTheta_i

Results

Accuracy	Segments	Branch
97.5%	1	`v`
97.5%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`
97.5%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`
97.5%	1	`cosTheta_O`
97.5%	1	`sinTheta_i`
97.5%	1	`sinTheta_O`
97.5%	1	`(*.f32 cosTheta_i cosTheta_O)`
97.5%	1	`(*.f32 sinTheta_i sinTheta_O)`
97.5%	1	`cosTheta_i`

Compiler

Compiled 105 to 78 computations (25.7% saved)

regimes41.0ms (0.3%)

Memory

-11.4MiB live, 110.3MiB allocated

Accuracy

Total -1.5b remaining (-5.1%)

Threshold costs -1.5b (-5.1%)

Counts

14 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(/.f32 cosTheta_i v)
(+.f32 #s(literal 1 binary32) (/.f32 cosTheta_i v))
(/.f32 (+.f32 v cosTheta_i) v)
(fma.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 v cosTheta_i)))
(fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 #s(literal 1/6 binary32) (.f32 v v)) #s(literal 1 binary32)) v) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (/.f32 (fma.f32 #s(literal -1/6 binary32) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v (.f32 v (.f32 v v)))) #s(literal -1 binary32)) (neg.f32 v)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta_i (/.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i cosTheta_i)) v) (.f32 #s(literal 1/2 binary32) (.f32 cosTheta_i cosTheta_i))) v)) v))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (*.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 (fma.f32 #s(literal 1/6 binary32) (/.f32 cosTheta_i (.f32 v (.f32 v v))) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (.f32 cosTheta_i cosTheta_i) (+.f32 (/.f32 cosTheta_i v) #s(literal 1 binary32)))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 (/.f32 cosTheta_i (.f32 v v)) (/.f32 #s(literal 1/6 binary32) v) (/.f32 #s(literal 1/2 binary32) (.f32 v v))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (/.f32 (fma.f32 (.f32 cosTheta_i #s(literal 1/6 binary32)) (.f32 v v) (.f32 (.f32 v (.f32 v v)) #s(literal 1/2 binary32))) (.f32 (.f32 v v) (.f32 v (*.f32 v v)))) (/.f32 #s(literal 1 binary32) v)) #s(literal 1 binary32))

Outputs
#s(literal 1 binary32)

Calls

9 calls:

6.0ms	v
5.0ms	cosTheta_O
4.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))
4.0ms	sinTheta_i
4.0ms	cosTheta_i

Results

Accuracy	Segments	Branch
6.5%	1	`(*.f32 cosTheta_i cosTheta_O)`
6.5%	1	`cosTheta_i`
6.5%	1	`cosTheta_O`
6.5%	1	`sinTheta_i`
6.5%	1	`sinTheta_O`
6.5%	1	`v`
6.5%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`
6.5%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`
6.5%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 105 to 78 computations (25.7% saved)

simplify7.0ms (0.1%)

Memory

22.7MiB live, 22.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary32`
16×	`+-commutative_binary32`
12×	`sub-neg_binary32`
8×	`neg-sub0_binary32`
8×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	64
1	41	64
2	51	64
3	59	64
4	65	64
5	67	64

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)
(exp.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(exp.f32 (/.f32 #s(literal -1 binary32) v))
#s(literal 1 binary32)

Outputs
(/.f32 (exp.f32 (+.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 #s(literal 1/2 binary32)))) v)
(exp.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(exp.f32 (/.f32 #s(literal -1 binary32) v))
#s(literal 1 binary32)

soundness1.1s (8.3%)

Memory

6.4MiB live, 797.2MiB allocated

Rules

10 620×	`lower-fma.f64`
10 620×	`lower-fma.f32`
9 576×	`lower-fma.f64`
9 576×	`lower-fma.f32`
9 278×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	574	5385
1	1644	5196
2	5102	4967
0	8568	4698
0	656	6445
1	1911	6006
2	5997	5812
0	8533	5525
0	352	5446
1	1120	5303
2	3789	4618
0	8342	4297
0	37	192
0	68	179
1	276	170
2	2415	170
0	8965	170
0	640	6834
1	1912	6500
2	6395	6323
0	8861	6003
0	29	140
0	52	141
1	189	138
2	1388	138
0	8347	138

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 245 to 177 computations (27.8% saved)

preprocess113.0ms (0.9%)

Memory

-12.5MiB live, 109.5MiB allocated

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 274 to 162 computations (40.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze470.0ms (3.6%)

sample2.8s (21.3%)

preprocess289.0ms (2.2%)

explain357.0ms (2.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify263.0ms (2%)

localize72.0ms (0.6%)

series252.0ms (1.9%)

rewrite739.0ms (5.7%)

simplify536.0ms (4.1%)

eval105.0ms (0.8%)

prune164.0ms (1.3%)

simplify235.0ms (1.8%)

localize101.0ms (0.8%)

series143.0ms (1.1%)

rewrite360.0ms (2.8%)

simplify443.0ms (3.4%)

eval128.0ms (1%)

prune232.0ms (1.8%)

simplify248.0ms (1.9%)

localize124.0ms (1%)

series138.0ms (1.1%)

rewrite392.0ms (3%)

simplify402.0ms (3.1%)

eval149.0ms (1.1%)

prune182.0ms (1.4%)

simplify243.0ms (1.9%)

localize124.0ms (1%)

series90.0ms (0.7%)

rewrite359.0ms (2.8%)

simplify434.0ms (3.3%)

eval381.0ms (2.9%)

prune221.0ms (1.7%)

regimes141.0ms (1.1%)

regimes158.0ms (1.2%)

regimes90.0ms (0.7%)

regimes78.0ms (0.6%)

regimes101.0ms (0.8%)

regimes58.0ms (0.4%)

regimes41.0ms (0.3%)

simplify7.0ms (0.1%)

soundness1.1s (8.3%)

preprocess113.0ms (0.9%)

end0.0ms (0%)

Profiling