Metrics for HairBSDF, Mp, lower

analyze1.1s (5.8%)

Memory

8.6MiB live, 888.4MiB 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)

sample6.0s (32.7%)

Memory

85.8MiB live, 3 858.9MiB allocated

Samples

5.4s	8 256×	0	valid
21.0ms	113×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 4.5s

ival-<=: 957.0ms (21.2% of total)

const: 838.0ms (18.6% of total)

ival-sub: 592.0ms (13.1% of total)

ival-div: 520.0ms (11.5% of total)

ival-add: 518.0ms (11.5% of total)

ival-mult: 405.0ms (9% of total)

ival-log: 306.0ms (6.8% of total)

ival-exp: 304.0ms (6.7% of total)

ival-and: 52.0ms (1.2% of total)

exact: 15.0ms (0.3% of total)

ival-assert: 3.0ms (0.1% of total)

Bogosity

preprocess328.0ms (1.8%)

Memory

-15.9MiB live, 614.0MiB allocated

Algorithm

2×	egg-herbie

Rules

6 404×	`accelerator-lowering-fma.f32`
6 404×	`accelerator-lowering-fma.f64`
3 478×	`-lowering-.f32`
3 478×	`-lowering-.f64`
1 904×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	164	504
1	473	469
2	1379	462
3	5000	462
0	21	23
1	50	22
2	137	22
3	456	22
4	1702	22
5	5011	22
0	8123	19

Stop Event

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

Calls

Call 1

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

Outputs

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

(fma.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 #s(literal 1/2 binary32) v) #s(literal 0 binary32))

Call 2

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

Outputs
(exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))
(* (/ 1/2 v) (exp (- (* cosTheta_i (/ cosTheta_O v)) (+ (* sinTheta_i (/ sinTheta_O v)) (+ (/ 1 v) -6931/10000)))))
(exp (+ (+ (- (- (/ (* (neg cosTheta_i) cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))
(* (/ 1/2 v) (exp (+ 6931/10000 (- (- (/ -1 v) (* sinTheta_i (/ sinTheta_O v))) (* cosTheta_i (/ cosTheta_O v))))))
(exp (+ (+ (- (- (/ (* cosTheta_i (neg cosTheta_O)) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))
(* (/ 1/2 v) (exp (+ 6931/10000 (- (- (/ -1 v) (* sinTheta_i (/ sinTheta_O v))) (* cosTheta_i (/ cosTheta_O v))))))
(exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* (neg sinTheta_i) sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))
(* (exp (+ (* cosTheta_i (/ cosTheta_O v)) (+ (* sinTheta_i (/ sinTheta_O v)) (+ 6931/10000 (/ -1 v))))) (/ 1/2 v))
(exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i (neg sinTheta_O)) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))
(* (exp (+ (* cosTheta_i (/ cosTheta_O v)) (+ (* sinTheta_i (/ sinTheta_O v)) (+ 6931/10000 (/ -1 v))))) (/ 1/2 v))
(exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) (neg v)) (/ (* sinTheta_i sinTheta_O) (neg v))) (/ 1 (neg v))) 6931/10000) (log (/ 1 (* 2 (neg v))))))
(* (exp (- (+ (* sinTheta_i (/ sinTheta_O v)) (+ (/ 1 v) 6931/10000)) (* cosTheta_i (/ cosTheta_O v)))) (/ -1/2 v))
(neg (exp (+ (+ (- (- (/ (* (neg cosTheta_i) cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v))))))
(* (/ -1/2 v) (exp (+ 6931/10000 (- (- (/ -1 v) (* sinTheta_i (/ sinTheta_O v))) (* cosTheta_i (/ cosTheta_O v))))))
(neg (exp (+ (+ (- (- (/ (* cosTheta_i (neg cosTheta_O)) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v))))))
(* (/ -1/2 v) (exp (+ 6931/10000 (- (- (/ -1 v) (* sinTheta_i (/ sinTheta_O v))) (* cosTheta_i (/ cosTheta_O v))))))
(neg (exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* (neg sinTheta_i) sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v))))))
(* (/ -1/2 v) (exp (+ (* cosTheta_i (/ cosTheta_O v)) (+ (* sinTheta_i (/ sinTheta_O v)) (+ 6931/10000 (/ -1 v))))))
(neg (exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i (neg sinTheta_O)) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v))))))
(* (/ -1/2 v) (exp (+ (* cosTheta_i (/ cosTheta_O v)) (+ (* sinTheta_i (/ sinTheta_O v)) (+ 6931/10000 (/ -1 v))))))
(neg (exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) (neg v)) (/ (* sinTheta_i sinTheta_O) (neg v))) (/ 1 (neg v))) 6931/10000) (log (/ 1 (* 2 (neg v)))))))
(* (exp (- (+ (* sinTheta_i (/ sinTheta_O v)) (+ (/ 1 v) 6931/10000)) (* cosTheta_i (/ cosTheta_O v)))) (/ 1/2 v))
(exp (+ (+ (- (- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))
(* (/ 1/2 v) (exp (- (* cosTheta_i (/ cosTheta_O v)) (+ (* sinTheta_i (/ sinTheta_O v)) (+ (/ 1 v) -6931/10000)))))
(exp (+ (+ (- (- (/ (* sinTheta_i cosTheta_O) v) (/ (* cosTheta_i sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))
(* (/ 1/2 v) (exp (+ (* cosTheta_O (/ sinTheta_i v)) (+ (- (/ -1 v) (* cosTheta_i (/ sinTheta_O v))) 6931/10000))))
(exp (+ (+ (- (- (/ (* sinTheta_O cosTheta_O) v) (/ (* sinTheta_i cosTheta_i) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))
(* (/ 1/2 v) (exp (- (* cosTheta_O (/ sinTheta_O v)) (+ (* cosTheta_i (/ sinTheta_i v)) (+ (/ 1 v) -6931/10000)))))
(exp (+ (+ (- (- (/ (* v cosTheta_O) cosTheta_i) (/ (* sinTheta_i sinTheta_O) cosTheta_i)) (/ 1 cosTheta_i)) 6931/10000) (log (/ 1 (* 2 cosTheta_i)))))
(* (exp (+ (- (* cosTheta_O (/ v cosTheta_i)) (* sinTheta_i (/ sinTheta_O cosTheta_i))) (+ 6931/10000 (/ -1 cosTheta_i)))) (/ 1/2 cosTheta_i))
(exp (+ (+ (- (- (/ (* cosTheta_i sinTheta_i) v) (/ (* cosTheta_O sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))
(* (/ 1/2 v) (exp (+ (* cosTheta_i (/ sinTheta_i v)) (+ (- (/ -1 v) (* cosTheta_O (/ sinTheta_O v))) 6931/10000))))
(exp (+ (+ (- (- (/ (* cosTheta_i sinTheta_O) v) (/ (* sinTheta_i cosTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))
(* (/ 1/2 v) (exp (+ (+ 6931/10000 (* cosTheta_i (/ sinTheta_O v))) (- (/ -1 v) (* cosTheta_O (/ sinTheta_i v))))))
(exp (+ (+ (- (- (/ (* cosTheta_i v) cosTheta_O) (/ (* sinTheta_i sinTheta_O) cosTheta_O)) (/ 1 cosTheta_O)) 6931/10000) (log (/ 1 (* 2 cosTheta_O)))))
(* (exp (+ (* cosTheta_i (/ v cosTheta_O)) (+ (- (/ -1 cosTheta_O) (* sinTheta_i (/ sinTheta_O cosTheta_O))) 6931/10000))) (/ 1/2 cosTheta_O))
(exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))
(* (/ 1/2 v) (exp (- (* cosTheta_i (/ cosTheta_O v)) (+ (* sinTheta_i (/ sinTheta_O v)) (+ (/ 1 v) -6931/10000)))))
(exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) sinTheta_i) (/ (* v sinTheta_O) sinTheta_i)) (/ 1 sinTheta_i)) 6931/10000) (log (/ 1 (* 2 sinTheta_i)))))
(* (exp (- (* cosTheta_O (/ cosTheta_i sinTheta_i)) (+ (* v (/ sinTheta_O sinTheta_i)) (+ (/ 1 sinTheta_i) -6931/10000)))) (/ 1/2 sinTheta_i))
(exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) sinTheta_O) (/ (* sinTheta_i v) sinTheta_O)) (/ 1 sinTheta_O)) 6931/10000) (log (/ 1 (* 2 sinTheta_O)))))
(* (exp (+ (- (* cosTheta_O (/ cosTheta_i sinTheta_O)) (* v (/ sinTheta_i sinTheta_O))) (+ 6931/10000 (/ -1 sinTheta_O)))) (/ 1/2 sinTheta_O))

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

explain268.0ms (1.5%)

Memory

-10.0MiB live, 537.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
92	2	(-4.081549223237626e-16 4.498330375083914e-23 -7.846493346202179e-24 1.120816966239906e-23 0.004326848313212395)	36	(-1.1755594734944335e-17 4.596948318404761e-29 -6.8820435935863615e-15 -3.518454332011198e-30 2.5707474909989234e-23)	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`
89	4	(-2.1155458967850336e-38 2.512951043570579e-17 -3.1751745539057307e-18 -1.1256223196807416e-29 4.534151942792164e-10)	37	(1.6646954267001833e-33 5.7678667397809136e-11 -6.7697233134822454e-6 7.708191560595878e-7 1.481973441741502e-7)	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`
1	5	(-4.081549223237626e-16 4.498330375083914e-23 -7.846493346202179e-24 1.120816966239906e-23 0.004326848313212395)	1	(-6.147974677412739e-33 6.662313730991382e-24 -2.276168111685437e-16 6.478670462130004e-24 0.02156561054289341)	`(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)))))`
0	0	-	0	-	`(/.f32 #s(literal 1 binary32) v)`
0	0	-	0	-	`(/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))`
0	0	-	0	-	`#s(literal 2 binary32)`
0	0	-	0	-	`(+.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))))`
0	0	-	0	-	`sinTheta_i`
0	0	-	0	-	`v`
0	0	-	0	-	`cosTheta_i`
0	0	-	0	-	`(+.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))`
0	0	-	0	-	`sinTheta_O`
0	0	-	0	-	`(*.f32 #s(literal 2 binary32) v)`
0	0	-	0	-	`(*.f32 sinTheta_i sinTheta_O)`
0	0	-	0	-	`(log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))`
0	0	-	0	-	`#s(literal 1 binary32)`
0	0	-	0	-	`(*.f32 cosTheta_i cosTheta_O)`
0	0	-	0	-	`#s(literal 6931/10000 binary32)`
0	0	-	0	-	`(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))`
0	0	-	0	-	`(-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v))`
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	8	0
↳	`(*.f32 sinTheta_i sinTheta_O)`	underflow	77
`/.f32`	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`	u/n	7	0
↳	`(*.f32 cosTheta_i cosTheta_O)`	underflow	80
`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	5	4

Confusion

	Predicted +	Predicted -
+	0	2
-	20	234

Precision

0.0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	2	0
-	20	2	232

Precision?

0.08333333333333333

Recall?

1.0

Freqs

test

number	freq
0	236
1	20

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

86.0ms

512×

valid

Compiler

Compiled 330 to 88 computations (73.3% saved)

Precisions

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

ival-div: 14.0ms (24.7% of total)

ival-sub: 11.0ms (19.4% of total)

ival-mult: 9.0ms (15.9% of total)

const: 7.0ms (12.4% of total)

ival-log: 6.0ms (10.6% of total)

ival-exp: 4.0ms (7.1% of total)

ival-add: 4.0ms (7.1% of total)

exact: 1.0ms (1.8% of total)

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

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 5 to 5 computations (0% saved)

prune1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(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

▶

99.7%

(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)

simplify376.0ms (2.1%)

Memory

-13.1MiB live, 462.7MiB 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	2912	(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×	`accelerator-lowering-fma.f32`
6 404×	`accelerator-lowering-fma.f64`
3 478×	`-lowering-.f32`
3 478×	`-lowering-.f64`
1 904×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	125
1	50	124
2	137	124
3	456	124
4	1702	124
5	5011	124
0	8123	113

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize67.0ms (0.4%)

Memory

5.9MiB live, 161.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(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)))))
✓	accuracy	99.8%	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
✓	accuracy	77.7%	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	accuracy	77.3%	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Samples

42.0ms

256×

valid

Compiler

Compiled 135 to 23 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-div: 7.0ms (26.5% of total)

ival-mult: 5.0ms (18.9% of total)

ival-exp: 3.0ms (11.4% of total)

ival-log: 3.0ms (11.4% of total)

const: 3.0ms (11.4% of total)

ival-add: 2.0ms (7.6% of total)

ival-sub: 2.0ms (7.6% of total)

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

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

exact: 0.0ms (0% of total)

series82.0ms (0.5%)

Memory

13.4MiB live, 206.7MiB allocated

Counts

7 → 276

Calls

Call 1

Inputs
#<alt (exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))>
#<alt (- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v))>
#<alt (/ 1 (* 2 v))>
#<alt (log (/ 1 (* 2 v)))>
#<alt (/ (* sinTheta_i sinTheta_O) v)>
#<alt (/ (* cosTheta_i cosTheta_O) v)>
#<alt (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) 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))))>
#<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))))>
#<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))))>
#<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))))>
#<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_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))))>
#<alt (+ (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))))>
#<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))))>
#<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))))>
#<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))))>
#<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))))>
#<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))))>
#<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))))>
#<alt (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v)))))>
#<alt (+ (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))>
#<alt (+ (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)))>
#<alt (+ (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))))>
#<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 (* -1 (* cosTheta_O cosTheta_i))) (* -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 (* -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)))>
#<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 (* -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)))>
#<alt (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))>
#<alt (+ (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)))>
#<alt (+ (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))))))>
#<alt (+ (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))))))))>
#<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))))>
#<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))))>
#<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))))>
#<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))))>
#<alt (exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))>
#<alt (+ (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)))>
#<alt (+ (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))))))>
#<alt (+ (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))))))))>
#<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))))>
#<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))))>
#<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))))>
#<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))))>
#<alt (* -1 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_i (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_i)) (/ cosTheta_O v)))>
#<alt (* cosTheta_i (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_i)) (/ cosTheta_O v)))>
#<alt (* cosTheta_i (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_i)) (/ cosTheta_O v)))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))))))>
#<alt (* -1 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_O (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_O)) (/ cosTheta_i v)))>
#<alt (* cosTheta_O (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_O)) (/ cosTheta_i v)))>
#<alt (* cosTheta_O (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_O)) (/ cosTheta_i v)))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (+ (/ 1 (* cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))))))>
#<alt (/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)>
#<alt (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v))>
#<alt (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v))>
#<alt (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v))>
#<alt (* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))>
#<alt (* 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 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))>
#<alt (* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))>
#<alt (* 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 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))>
#<alt (* -1 (* sinTheta_O (- (* -1 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))>
#<alt (* -1 (* sinTheta_O (- (* -1 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))>
#<alt (/ 1/2 v)>
#<alt (/ 1/2 v)>
#<alt (/ 1/2 v)>
#<alt (/ 1/2 v)>
#<alt (/ 1/2 v)>
#<alt (/ 1/2 v)>
#<alt (/ 1/2 v)>
#<alt (/ 1/2 v)>
#<alt (/ 1/2 v)>
#<alt (/ 1/2 v)>
#<alt (/ 1/2 v)>
#<alt (/ 1/2 v)>
#<alt (+ (log 1/2) (* -1 (log v)))>
#<alt (+ (log 1/2) (* -1 (log v)))>
#<alt (+ (log 1/2) (* -1 (log v)))>
#<alt (+ (log 1/2) (* -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 (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* sinTheta_O sinTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_i (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))) (/ cosTheta_O v)))>
#<alt (* cosTheta_i (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))) (/ cosTheta_O v)))>
#<alt (* cosTheta_i (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))) (/ cosTheta_O v)))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_O (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))) (/ cosTheta_i v)))>
#<alt (* cosTheta_O (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))) (/ cosTheta_i v)))>
#<alt (* cosTheta_O (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))) (/ cosTheta_i v)))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))>
#<alt (/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)>
#<alt (* -1 (/ (- (* -1 (* cosTheta_O cosTheta_i)) (* -1 (* sinTheta_O sinTheta_i))) v))>
#<alt (* -1 (/ (- (* -1 (* cosTheta_O cosTheta_i)) (* -1 (* sinTheta_O sinTheta_i))) v))>
#<alt (* -1 (/ (- (* -1 (* cosTheta_O cosTheta_i)) (* -1 (* sinTheta_O sinTheta_i))) v))>
#<alt (* -1 (/ (- (* -1 (* cosTheta_O cosTheta_i)) (* -1 (* sinTheta_O sinTheta_i))) v))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))>
#<alt (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))>
#<alt (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (/ sinTheta_O v)))>
#<alt (* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (/ sinTheta_O v)))>
#<alt (* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (/ sinTheta_O v)))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (* -1 (/ sinTheta_O v)))))>
#<alt (* -1 (* sinTheta_i (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (* -1 (/ sinTheta_O v)))))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))>
#<alt (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))>
#<alt (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (/ sinTheta_i v)))>
#<alt (* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (/ sinTheta_i v)))>
#<alt (* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (/ sinTheta_i v)))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_O (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (* -1 (/ sinTheta_i v)))))>
#<alt (* -1 (* sinTheta_O (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (* -1 (/ sinTheta_i v)))))>
#<alt (* -1 (* sinTheta_O (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (* -1 (/ sinTheta_i v)))))>

Calls

69 calls:

Time	Variable		Point	Expression
28.0ms	v	@	0	(log (/ 1 (* 2 v)))
21.0ms	v	@	-inf	(log (/ 1 (* 2 v)))
6.0ms	v	@	inf	(log (/ 1 (* 2 v)))
2.0ms	cosTheta_O	@	0	(- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v))
2.0ms	sinTheta_O	@	0	(/ (* sinTheta_i sinTheta_O) v)

rewrite492.0ms (2.7%)

Memory

11.7MiB live, 844.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

9 370×	`accelerator-lowering-fma.f32`
9 370×	`accelerator-lowering-fma.f64`
4 860×	`/-lowering-/.f32`
4 860×	`/-lowering-/.f64`
3 374×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	60
1	134	55
2	1494	55
0	8235	55

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 473

Calls

Call 1

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

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

simplify466.0ms (2.6%)

Memory

1.4MiB live, 806.0MiB allocated

Algorithm

1×	egg-herbie

Rules

11 284×	`accelerator-lowering-fma.f32`
11 284×	`accelerator-lowering-fma.f64`
6 636×	`-lowering-.f32`
6 636×	`-lowering-.f64`
3 122×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	278	4128
1	891	3918
2	3129	3629
0	8250	3465

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_O cosTheta_i) v)
(* cosTheta_i (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_i)) (/ cosTheta_O v)))
(* cosTheta_i (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_i)) (/ cosTheta_O v)))
(* cosTheta_i (+ (* -1 (/ (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)) cosTheta_i)) (/ cosTheta_O v)))
(/ (* cosTheta_O cosTheta_i) v)
(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))))))
(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))))))
(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (+ (/ 1 (* cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_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_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)
(/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)
(/ (- (* cosTheta_O cosTheta_i) (+ 1 (* sinTheta_O sinTheta_i))) v)
(* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v))
(* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v))
(* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v))
(* -1 (/ (- (+ 1 (* -1 (* cosTheta_O cosTheta_i))) (* -1 (* sinTheta_O sinTheta_i))) v))
(- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))
(- (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
(- (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
(- (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
(* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O 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 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))
(* -1 (* sinTheta_i (- (* -1 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))
(* -1 (* sinTheta_i (- (* -1 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_i)) (* -1 (/ sinTheta_O v)))))
(- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))
(- (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
(- (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
(- (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i 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 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(* -1 (* sinTheta_O (- (* -1 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(* -1 (* sinTheta_O (- (* -1 (/ (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v)) sinTheta_O)) (* -1 (/ sinTheta_i v)))))
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(+ (log 1/2) (* -1 (log v)))
(+ (log 1/2) (* -1 (log v)))
(+ (log 1/2) (* -1 (log v)))
(+ (log 1/2) (* -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)))
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))
(- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))
(- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))
(/ (* cosTheta_O cosTheta_i) v)
(* cosTheta_i (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))) (/ cosTheta_O v)))
(* cosTheta_i (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))) (/ cosTheta_O v)))
(* cosTheta_i (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))) (/ cosTheta_O v)))
(/ (* cosTheta_O cosTheta_i) v)
(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))
(- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))
(- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))
(/ (* cosTheta_O cosTheta_i) v)
(* cosTheta_O (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))) (/ cosTheta_i v)))
(* cosTheta_O (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))) (/ cosTheta_i v)))
(* cosTheta_O (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))) (/ cosTheta_i v)))
(/ (* cosTheta_O cosTheta_i) v)
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(* -1 (/ (- (* -1 (* cosTheta_O cosTheta_i)) (* -1 (* sinTheta_O sinTheta_i))) v))
(* -1 (/ (- (* -1 (* cosTheta_O cosTheta_i)) (* -1 (* sinTheta_O sinTheta_i))) v))
(* -1 (/ (- (* -1 (* cosTheta_O cosTheta_i)) (* -1 (* sinTheta_O sinTheta_i))) v))
(* -1 (/ (- (* -1 (* cosTheta_O cosTheta_i)) (* -1 (* sinTheta_O sinTheta_i))) v))
(/ (* cosTheta_O cosTheta_i) v)
(+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))
(+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))
(+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (/ sinTheta_O v)))
(* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (/ sinTheta_O v)))
(* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (/ sinTheta_O v)))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (* sinTheta_i (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (* -1 (/ sinTheta_O v)))))
(* -1 (* sinTheta_i (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (* -1 (/ sinTheta_O v)))))
(* -1 (* sinTheta_i (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (* -1 (/ sinTheta_O v)))))
(/ (* cosTheta_O cosTheta_i) v)
(+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))
(+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))
(+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (/ sinTheta_i v)))
(* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (/ sinTheta_i v)))
(* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (/ sinTheta_i v)))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (* sinTheta_O (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (* -1 (/ sinTheta_i v)))))
(* -1 (* sinTheta_O (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (* -1 (/ sinTheta_i v)))))
(* -1 (* sinTheta_O (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (* -1 (/ sinTheta_i 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 (+.f32 #s(literal 6931/10000 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) 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))
(fma.f32 cosTheta_O (.f32 (.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)) (/.f32 #s(literal -1 binary32) v))))) (/.f32 cosTheta_i 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)) (/.f32 #s(literal -1 binary32) 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))))
(fma.f32 cosTheta_i (fma.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.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)) (/.f32 #s(literal -1 binary32) v))))) cosTheta_i) (/.f32 (.f32 cosTheta_O cosTheta_O) (.f32 v v))) (.f32 (.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)) (/.f32 #s(literal -1 binary32) v))))) (/.f32 cosTheta_O 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)) (/.f32 #s(literal -1 binary32) 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))))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (.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)) (/.f32 #s(literal -1 binary32) v))))) (.f32 cosTheta_O cosTheta_O)) (.f32 v v)) (/.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.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)) (/.f32 #s(literal -1 binary32) v))))) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_O cosTheta_O))))) (.f32 v (.f32 v v)))) (.f32 (.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)) (/.f32 #s(literal -1 binary32) v))))) (/.f32 cosTheta_O 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)) (/.f32 #s(literal -1 binary32) v))))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) 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))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) 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))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) 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))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) 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))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) 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))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) 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))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) 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))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) 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))))
(exp (- (+ 6931/10000 (log (/ 1/2 v))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) 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)) (/.f32 #s(literal -1 binary32) 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))
(fma.f32 cosTheta_O (.f32 (.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)) (/.f32 #s(literal -1 binary32) v))))) (/.f32 cosTheta_i 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)) (/.f32 #s(literal -1 binary32) 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))))
(fma.f32 cosTheta_O (fma.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.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)) (/.f32 #s(literal -1 binary32) v))))) (.f32 cosTheta_i cosTheta_i)) (/.f32 cosTheta_O (.f32 v v))) (.f32 (.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)) (/.f32 #s(literal -1 binary32) v))))) (/.f32 cosTheta_i 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)) (/.f32 #s(literal -1 binary32) 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))))
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eval85.0ms (0.5%)

Memory: 4.9MiB live, 189.5MiB allocated
Compiler: Compiled 25 954 to 2 901 computations (88.8% saved)

prune100.0ms (0.6%)

Memory

29.0MiB live, 223.7MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	746	3	749
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	747	3	750

Accuracy

99.8%

Counts

750 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	86.1%	(/.f32 (exp.f32 (+.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O (neg.f32 sinTheta_i))) v))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
▶	4.6%	(.f32 (/.f32 #s(literal 1 binary32) v) (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))))
▶	99.8%	(.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)) (/.f32 #s(literal -1 binary32) v)))))

Status

Accuracy

Program

▶

86.1%

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

▶

4.6%

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

▶

99.8%

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

Compiler

Compiled 61 to 49 computations (19.7% saved)

simplify257.0ms (1.4%)

Memory

-45.8MiB live, 403.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	32	(fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
✓	cost-diff	64	(+.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O (neg.f32 sinTheta_i))) v))
✓	cost-diff	2944	(exp.f32 (+.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O (neg.f32 sinTheta_i))) v)))
✓	cost-diff	3616	(/.f32 (exp.f32 (+.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O (neg.f32 sinTheta_i))) v))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
✓	cost-diff	0	(exp.f32 #s(literal 6931/10000 binary32))
✓	cost-diff	0	(*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) v)
✓	cost-diff	160	(.f32 (/.f32 #s(literal 1 binary32) v) (.f32 #s(literal 1/2 binary32) (exp.f32 #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 (+.f32 #s(literal 6931/10000 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v)))))
✓	cost-diff	64	(+.f32 #s(literal 6931/10000 binary32) (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v)))
✓	cost-diff	96	(*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v))

Rules

4 358×	`accelerator-lowering-fma.f32`
4 358×	`accelerator-lowering-fma.f64`
2 946×	`-lowering-.f32`
2 946×	`-lowering-.f64`
1 932×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	201
1	74	191
2	153	186
3	376	181
4	989	181
5	2691	181
6	6477	181
0	8041	175

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize110.0ms (0.6%)

Memory

35.0MiB live, 271.4MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(+.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O (neg.f32 sinTheta_i))) v))
✓	accuracy	94.3%	(/.f32 (exp.f32 (+.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O (neg.f32 sinTheta_i))) v))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
✓	accuracy	93.3%	(exp.f32 (+.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O (neg.f32 sinTheta_i))) v)))
✓	accuracy	88.8%	(/.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v)
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) v)
✓	accuracy	100.0%	(*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)))
✓	accuracy	100.0%	(exp.f32 #s(literal 6931/10000 binary32))
✓	accuracy	98.7%	(.f32 (/.f32 #s(literal 1 binary32) v) (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))))
✓	accuracy	100.0%	(.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)) (/.f32 #s(literal -1 binary32) v)))))
✓	accuracy	100.0%	(*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v))
✓	accuracy	99.9%	(+.f32 #s(literal 6931/10000 binary32) (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v)))
✓	accuracy	99.8%	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v))))

Samples

65.0ms	236×	0	valid
5.0ms	20×	0	exit

Compiler

Compiled 194 to 38 computations (80.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 12.0ms (22.7% of total)

ival-exp: 10.0ms (19% of total)

ival-div: 9.0ms (17.1% of total)

ival-add: 8.0ms (15.2% of total)

const: 7.0ms (13.3% of total)

ival-neg: 4.0ms (7.6% of total)

ival-log: 3.0ms (5.7% of total)

exact: 1.0ms (1.9% of total)

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

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

series87.0ms (0.5%)

Memory

-20.0MiB live, 176.6MiB allocated

Counts

14 → 468

Calls

Call 1

Inputs
#<alt (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v))>
#<alt (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v)))>
#<alt (* (/ 1/2 v) (exp (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v)))))>
#<alt (/ 1/2 v)>
#<alt (* (/ 1 v) (* 1/2 (exp 6931/10000)))>
#<alt (/ 1 v)>
#<alt (* 1/2 (exp 6931/10000))>
#<alt (exp 6931/10000)>
#<alt (/ (exp (+ (neg (log (* v 2))) (/ (+ (* cosTheta_i cosTheta_O) (* sinTheta_O (neg sinTheta_i))) v))) (exp (+ (/ 1 v) -6931/10000)))>
#<alt (exp (+ (neg (log (* v 2))) (/ (+ (* cosTheta_i cosTheta_O) (* sinTheta_O (neg sinTheta_i))) v)))>
#<alt (+ (neg (log (* v 2))) (/ (+ (* cosTheta_i cosTheta_O) (* sinTheta_O (neg sinTheta_i))) v))>
#<alt (+ (* cosTheta_i cosTheta_O) (* sinTheta_O (neg sinTheta_i)))>
#<alt (exp (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v))))>
#<alt (/ (+ (* cosTheta_i cosTheta_O) (* sinTheta_O (neg sinTheta_i))) v)>

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

Calls

117 calls:

Time	Variable		Point	Expression
18.0ms	cosTheta_i	@	inf	(+ (* cosTheta_i cosTheta_O) (* sinTheta_O (neg sinTheta_i)))
7.0ms	v	@	-inf	(+ (neg (log (* v 2))) (/ (+ (* cosTheta_i cosTheta_O) (* sinTheta_O (neg sinTheta_i))) v))
3.0ms	cosTheta_i	@	0	(+ (neg (log (* v 2))) (/ (+ (* cosTheta_i cosTheta_O) (* sinTheta_O (neg sinTheta_i))) v))
3.0ms	cosTheta_i	@	0	(/ (exp (+ (neg (log (* v 2))) (/ (+ (* cosTheta_i cosTheta_O) (* sinTheta_O (neg sinTheta_i))) v))) (exp (+ (/ 1 v) -6931/10000)))
2.0ms	sinTheta_i	@	-inf	(* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v))

rewrite603.0ms (3.3%)

Memory

-162.7MiB live, 687.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 940×	`-lowering-.f32`
4 940×	`-lowering-.f64`
4 358×	`accelerator-lowering-fma.f32`
4 358×	`accelerator-lowering-fma.f64`
3 926×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	142
1	173	127
2	1324	126
0	8111	122

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 498

Calls

Call 1

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

Outputs
(+.f32 (/.f32 #s(literal -1 binary32) v) (.f32 (.f32 sinTheta_O sinTheta_i) (/.f32 #s(literal -1 binary32) v)))
(+.f32 (.f32 (/.f32 #s(literal -1 binary32) v) (.f32 sinTheta_O sinTheta_i)) (*.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 1 binary32)))
(+.f32 (.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal -1 binary32) v) (*.f32 sinTheta_O sinTheta_i)))
(+.f32 (.f32 (.f32 sinTheta_O sinTheta_i) (/.f32 #s(literal -1 binary32) v)) (/.f32 #s(literal -1 binary32) v))
(pow.f32 (*.f32 (/.f32 v (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) #s(literal -1 binary32)) #s(literal -1 binary32))
(fma.f32 (*.f32 sinTheta_O sinTheta_i) (/.f32 #s(literal -1 binary32) v) (/.f32 #s(literal -1 binary32) v))
(fma.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) v) (.f32 (.f32 sinTheta_O sinTheta_i) (/.f32 #s(literal -1 binary32) v)))
(fma.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) v) (.f32 (.f32 sinTheta_O sinTheta_i) (/.f32 #s(literal -1 binary32) v)))
(fma.f32 (/.f32 #s(literal -1 binary32) v) (.f32 sinTheta_O sinTheta_i) (.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 1 binary32)))
(fma.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 1 binary32) (.f32 (/.f32 #s(literal -1 binary32) v) (.f32 sinTheta_O sinTheta_i)))
(fma.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -1 binary32) (.f32 (.f32 sinTheta_O sinTheta_i) (/.f32 #s(literal -1 binary32) 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))) (neg.f32 v)) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O sinTheta_i #s(literal -1 binary32))) (neg.f32 v)))
(/.f32 #s(literal 1 binary32) (*.f32 (/.f32 v (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)) (neg.f32 v))
(/.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 (*.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))) (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 sinTheta_O (.f32 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 sinTheta_O (.f32 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 #s(literal 1 binary32) (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 (.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (.f32 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 #s(literal -1 binary32) (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 (.f32 #s(literal -1 binary32) (fma.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i)) #s(literal -1 binary32))) (.f32 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 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (neg.f32 (neg.f32 v)))
(/.f32 (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) #s(literal 1 binary32)) (neg.f32 v))
(/.f32 (.f32 (/.f32 #s(literal -1 binary32) v) (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 (.f32 (/.f32 #s(literal -1 binary32) v) (fma.f32 sinTheta_O (.f32 sinTheta_i (*.f32 sinTheta_O sinTheta_i)) #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)) (/.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 sinTheta_O (.f32 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 #s(literal 1 binary32) (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 (.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 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 sinTheta_i #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 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 sinTheta_i #s(literal -1 binary32)) (neg.f32 v))))
(/.f32 (neg.f32 (.f32 #s(literal 1 binary32) (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))))))
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(/.f32 (neg.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_i cosTheta_O))) (neg.f32 v))
(/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))) (.f32 v (fma.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (-.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (.f32 cosTheta_i cosTheta_O)) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))))
(/.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i))) (.f32 v (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O sinTheta_i))))
(/.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) #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))) (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))) #s(literal 1 binary32)) (.f32 (fma.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (-.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (.f32 cosTheta_i cosTheta_O)) (.f32 cosTheta_i (.f32 cosTheta_O (*.f32 cosTheta_i cosTheta_O)))) v))
(/.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))) #s(literal -1 binary32)) (.f32 (fma.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (-.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (.f32 cosTheta_i cosTheta_O)) (.f32 cosTheta_i (.f32 cosTheta_O (*.f32 cosTheta_i cosTheta_O)))) (neg.f32 v)))
(/.f32 (.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) (.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i)) v))
(/.f32 (.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i))) #s(literal -1 binary32)) (.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i)) (neg.f32 v)))
(/.f32 (neg.f32 (neg.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_i cosTheta_O)))) (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))) (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O)))))) (neg.f32 (.f32 v (fma.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (-.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (.f32 cosTheta_i cosTheta_O)) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O)))))))
(/.f32 (neg.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i)))) (neg.f32 (.f32 v (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O sinTheta_i)))))
(/.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) #s(literal -1 binary32)) (neg.f32 v))
(/.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))) (/.f32 #s(literal 1 binary32) v)) (fma.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (-.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (.f32 cosTheta_i cosTheta_O)) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O)))))
(/.f32 (.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i))) (/.f32 #s(literal 1 binary32) v)) (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O sinTheta_i)))
(/.f32 (neg.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) #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))) (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))) #s(literal 1 binary32))) (neg.f32 (.f32 (fma.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (-.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (.f32 cosTheta_i cosTheta_O)) (.f32 cosTheta_i (.f32 cosTheta_O (*.f32 cosTheta_i cosTheta_O)))) v)))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))) #s(literal -1 binary32))) (neg.f32 (.f32 (fma.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (-.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (.f32 cosTheta_i cosTheta_O)) (.f32 cosTheta_i (.f32 cosTheta_O (*.f32 cosTheta_i cosTheta_O)))) (neg.f32 v))))
(/.f32 (neg.f32 (.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32))) (neg.f32 (.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i)) v)))
(/.f32 (neg.f32 (.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i))) #s(literal -1 binary32))) (neg.f32 (.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i)) (neg.f32 v))))
(/.f32 (neg.f32 (neg.f32 (neg.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_i cosTheta_O))))) (neg.f32 (neg.f32 (neg.f32 v))))
(/.f32 (neg.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) #s(literal -1 binary32))) (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))) (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))) (/.f32 #s(literal 1 binary32) v))) (neg.f32 (fma.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (-.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (.f32 cosTheta_i cosTheta_O)) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))))
(/.f32 (neg.f32 (.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i))) (/.f32 #s(literal 1 binary32) v))) (neg.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O sinTheta_i))))
(.f32 #s(literal 1 binary32) (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) v))
(.f32 (/.f32 #s(literal 1 binary32) v) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)))
(.f32 (/.f32 #s(literal 1 binary32) v) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O))) #s(literal -1 binary32)))
(.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (/.f32 #s(literal 1 binary32) v))
(.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) v) #s(literal 1 binary32))
(.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) v) (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i)) (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i))))
(.f32 (neg.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O))) (/.f32 #s(literal -1 binary32) v))
(.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_i cosTheta_O)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) v))
(.f32 (pow.f32 (/.f32 v (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O)))))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (-.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (.f32 cosTheta_i cosTheta_O)) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))))
(.f32 (pow.f32 (/.f32 v (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O sinTheta_i))))
(.f32 (/.f32 (fma.f32 (.f32 sinTheta_O sinTheta_i) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_i))) (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))) v) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (-.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (.f32 cosTheta_i cosTheta_O)) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))) #s(literal 1 binary32)))
(.f32 (/.f32 (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O sinTheta_i))) v) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)))
(.f32 (/.f32 (fma.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (-.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (.f32 cosTheta_i cosTheta_O)) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O)))) v) (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (fma.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (-.f32 (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i)) (.f32 cosTheta_i cosTheta_O)) (.f32 cosTheta_i (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_O))))))
(.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) #s(literal -1 binary32)) (/.f32 #s(literal -1 binary32) v))

simplify489.0ms (2.7%)

Memory

40.7MiB live, 745.7MiB allocated

Algorithm

1×	egg-herbie

Rules

9 354×	`accelerator-lowering-fma.f32`
9 354×	`accelerator-lowering-fma.f64`
7 326×	`-lowering-.f32`
7 326×	`-lowering-.f64`
3 374×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	665	8987
1	2242	8313
0	8211	8054

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 468

Calls

Call 1

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

Outputs
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))
(fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v))
(- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))
(fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v))
(- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))
(fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(* sinTheta_O (- (* -1 (/ sinTheta_i v)) (/ 1 (* sinTheta_O v))))
(.f32 sinTheta_O (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) (.f32 v sinTheta_O))))
(* sinTheta_O (- (* -1 (/ sinTheta_i v)) (/ 1 (* sinTheta_O v))))
(.f32 sinTheta_O (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) (.f32 v sinTheta_O))))
(* sinTheta_O (- (* -1 (/ sinTheta_i v)) (/ 1 (* sinTheta_O v))))
(.f32 sinTheta_O (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) (.f32 v sinTheta_O))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(* -1 (* sinTheta_O (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(.f32 sinTheta_O (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) (.f32 v sinTheta_O))))
(* -1 (* sinTheta_O (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(.f32 sinTheta_O (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) (.f32 v sinTheta_O))))
(* -1 (* sinTheta_O (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(.f32 sinTheta_O (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) (.f32 v sinTheta_O))))
(/ -1 v)
(/.f32 #s(literal -1 binary32) v)
(- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))
(fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v))
(- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))
(fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v))
(- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))
(fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v))))
(.f32 (+.f32 (/.f32 sinTheta_O v) (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_i))) (neg.f32 sinTheta_i))
(* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v))))
(.f32 (+.f32 (/.f32 sinTheta_O v) (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_i))) (neg.f32 sinTheta_i))
(* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v))))
(.f32 (+.f32 (/.f32 sinTheta_O v) (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_i))) (neg.f32 sinTheta_i))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(* -1 (* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
(.f32 (+.f32 (/.f32 sinTheta_O v) (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_i))) (neg.f32 sinTheta_i))
(* -1 (* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
(.f32 (+.f32 (/.f32 sinTheta_O v) (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_i))) (neg.f32 sinTheta_i))
(* -1 (* sinTheta_i (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))))
(.f32 (+.f32 (/.f32 sinTheta_O v) (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_i))) (neg.f32 sinTheta_i))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(- 6931/10000 (/ 1 v))
(+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))
(+.f32 (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v)) #s(literal 6931/10000 binary32))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))
(+.f32 (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v)) #s(literal 6931/10000 binary32))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))
(+.f32 (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v)) #s(literal 6931/10000 binary32))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (* 6931/10000 (/ 1 sinTheta_O))) (/ 1 (* sinTheta_O v))))
(*.f32 sinTheta_O (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_O)))
(* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (* 6931/10000 (/ 1 sinTheta_O))) (/ 1 (* sinTheta_O v))))
(*.f32 sinTheta_O (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_O)))
(* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (* 6931/10000 (/ 1 sinTheta_O))) (/ 1 (* sinTheta_O v))))
(*.f32 sinTheta_O (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_O)))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))
(*.f32 (-.f32 (/.f32 sinTheta_i v) (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_O)) (neg.f32 sinTheta_O))
(* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))
(*.f32 (-.f32 (/.f32 sinTheta_i v) (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_O)) (neg.f32 sinTheta_O))
(* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))
(*.f32 (-.f32 (/.f32 sinTheta_i v) (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_O)) (neg.f32 sinTheta_O))
(- 6931/10000 (/ 1 v))
(+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))
(+.f32 (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v)) #s(literal 6931/10000 binary32))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))
(+.f32 (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v)) #s(literal 6931/10000 binary32))
(- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))
(+.f32 (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v)) #s(literal 6931/10000 binary32))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (/ 1 (* sinTheta_i v))))
(*.f32 sinTheta_i (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_O v)) (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_i)))
(* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (/ 1 (* sinTheta_i v))))
(*.f32 sinTheta_i (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_O v)) (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_i)))
(* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))) (/ 1 (* sinTheta_i v))))
(*.f32 sinTheta_i (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_O v)) (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_i)))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))
(*.f32 (-.f32 (/.f32 sinTheta_O v) (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_i)) (neg.f32 sinTheta_i))
(* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))
(*.f32 (-.f32 (/.f32 sinTheta_O v) (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_i)) (neg.f32 sinTheta_i))
(* -1 (* sinTheta_i (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_i)) (/ sinTheta_O v))))
(*.f32 (-.f32 (/.f32 sinTheta_O v) (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_i)) (neg.f32 sinTheta_i))
(* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))
(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))
(/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* 6931/10000 v)) v)
(/.f32 (fma.f32 v #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v)
(/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* 6931/10000 v)) v)
(/.f32 (fma.f32 v #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v)
(/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* 6931/10000 v)) v)
(/.f32 (fma.f32 v #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v)
6931/10000
#s(literal 6931/10000 binary32)
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
6931/10000
#s(literal 6931/10000 binary32)
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
(* 1/2 (/ (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))) 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)
(* 1/2 (/ (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))) 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)
(* 1/2 (/ (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))) 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)
(* 1/2 (/ (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))) 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)
(* 1/2 (/ (exp 6931/10000) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v)
(/ (+ (* -1/2 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)) (* 1/2 (exp 6931/10000))) v)
(/.f32 (fma.f32 #s(literal -1/2 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) v)) (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)))) 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)
(/.f32 (fma.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (exp.f32 #s(literal 6931/10000 binary32))) (/.f32 #s(literal -1/2 binary32) v) (fma.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 #s(literal 6931/10000 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 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))))) 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)
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(* 1/2 (/ (exp 6931/10000) v))
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(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (* -1 (/ (- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (log (* 2 v))) cosTheta_i)))))
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(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(* cosTheta_O (- (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))) (/ cosTheta_i v)) (/ (log (* 2 v)) cosTheta_O)))
(.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (neg.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (log.f32 (.f32 v #s(literal 2 binary32))))) cosTheta_O)))
(* cosTheta_O (- (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))) (/ cosTheta_i v)) (/ (log (* 2 v)) cosTheta_O)))
(.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (neg.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (log.f32 (.f32 v #s(literal 2 binary32))))) cosTheta_O)))
(* cosTheta_O (- (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))) (/ cosTheta_i v)) (/ (log (* 2 v)) cosTheta_O)))
(.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (neg.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (log.f32 (.f32 v #s(literal 2 binary32))))) cosTheta_O)))
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(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
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(* -1 (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (/ (log (* 2 v)) sinTheta_O)))
(.f32 sinTheta_O (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (*.f32 v #s(literal 2 binary32)))) sinTheta_O)))
(* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (/ (log (* 2 v)) sinTheta_O)))
(.f32 sinTheta_O (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (*.f32 v #s(literal 2 binary32)))) sinTheta_O)))
(* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (/ (log (* 2 v)) sinTheta_O)))
(.f32 sinTheta_O (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (*.f32 v #s(literal 2 binary32)))) sinTheta_O)))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
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(* -1 (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (/ (log (* 2 v)) sinTheta_i)))
(.f32 sinTheta_i (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_O v)) (/.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (*.f32 v #s(literal 2 binary32)))) sinTheta_i)))
(* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (/ (log (* 2 v)) sinTheta_i)))
(.f32 sinTheta_i (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_O v)) (/.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (*.f32 v #s(literal 2 binary32)))) sinTheta_i)))
(* sinTheta_i (- (+ (* -1 (/ sinTheta_O v)) (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (/ (log (* 2 v)) sinTheta_i)))
(.f32 sinTheta_i (+.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_O v)) (/.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (*.f32 v #s(literal 2 binary32)))) sinTheta_i)))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(* -1 (* sinTheta_i (+ (* -1 (/ (- (/ (* cosTheta_O cosTheta_i) v) (log (* 2 v))) sinTheta_i)) (/ sinTheta_O v))))
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(* -1 (* sinTheta_i (+ (* -1 (/ (- (/ (* cosTheta_O cosTheta_i) v) (log (* 2 v))) sinTheta_i)) (/ sinTheta_O v))))
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(* -1 (* sinTheta_i (+ (* -1 (/ (- (/ (* cosTheta_O cosTheta_i) v) (log (* 2 v))) sinTheta_i)) (/ sinTheta_O v))))
(neg.f32 (.f32 sinTheta_i (-.f32 (/.f32 sinTheta_O v) (/.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (*.f32 v #s(literal 2 binary32)))) sinTheta_i))))
(* -1 (* sinTheta_O sinTheta_i))
(*.f32 sinTheta_O (neg.f32 sinTheta_i))
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(fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))
(* cosTheta_O cosTheta_i)
(*.f32 cosTheta_O cosTheta_i)
(* cosTheta_i (+ cosTheta_O (* -1 (/ (* sinTheta_O sinTheta_i) cosTheta_i))))
(*.f32 cosTheta_i (fma.f32 (neg.f32 sinTheta_O) (/.f32 sinTheta_i cosTheta_i) cosTheta_O))
(* cosTheta_i (+ cosTheta_O (* -1 (/ (* sinTheta_O sinTheta_i) cosTheta_i))))
(*.f32 cosTheta_i (fma.f32 (neg.f32 sinTheta_O) (/.f32 sinTheta_i cosTheta_i) cosTheta_O))
(* cosTheta_i (+ cosTheta_O (* -1 (/ (* sinTheta_O sinTheta_i) cosTheta_i))))
(*.f32 cosTheta_i (fma.f32 (neg.f32 sinTheta_O) (/.f32 sinTheta_i cosTheta_i) cosTheta_O))
(* cosTheta_O cosTheta_i)
(*.f32 cosTheta_O cosTheta_i)
(* -1 (* cosTheta_i (+ (* -1 cosTheta_O) (/ (* sinTheta_O sinTheta_i) cosTheta_i))))
(*.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O cosTheta_i) (neg.f32 cosTheta_O)) (neg.f32 cosTheta_i))
(* -1 (* cosTheta_i (+ (* -1 cosTheta_O) (/ (* sinTheta_O sinTheta_i) cosTheta_i))))
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(* -1 (* sinTheta_O sinTheta_i))
(*.f32 sinTheta_O (neg.f32 sinTheta_i))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))
(* cosTheta_O cosTheta_i)
(*.f32 cosTheta_O cosTheta_i)
(* cosTheta_O (+ cosTheta_i (* -1 (/ (* sinTheta_O sinTheta_i) cosTheta_O))))
(*.f32 cosTheta_O (fma.f32 (neg.f32 sinTheta_O) (/.f32 sinTheta_i cosTheta_O) cosTheta_i))
(* cosTheta_O (+ cosTheta_i (* -1 (/ (* sinTheta_O sinTheta_i) cosTheta_O))))
(*.f32 cosTheta_O (fma.f32 (neg.f32 sinTheta_O) (/.f32 sinTheta_i cosTheta_O) cosTheta_i))
(* cosTheta_O (+ cosTheta_i (* -1 (/ (* sinTheta_O sinTheta_i) cosTheta_O))))
(*.f32 cosTheta_O (fma.f32 (neg.f32 sinTheta_O) (/.f32 sinTheta_i cosTheta_O) cosTheta_i))
(* cosTheta_O cosTheta_i)
(*.f32 cosTheta_O cosTheta_i)
(* -1 (* cosTheta_O (+ (* -1 cosTheta_i) (/ (* sinTheta_O sinTheta_i) cosTheta_O))))
(*.f32 (neg.f32 cosTheta_O) (fma.f32 sinTheta_O (/.f32 sinTheta_i cosTheta_O) (neg.f32 cosTheta_i)))
(* -1 (* cosTheta_O (+ (* -1 cosTheta_i) (/ (* sinTheta_O sinTheta_i) cosTheta_O))))
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(* -1 (* cosTheta_O (+ (* -1 cosTheta_i) (/ (* sinTheta_O sinTheta_i) cosTheta_O))))
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(* cosTheta_O cosTheta_i)
(*.f32 cosTheta_O cosTheta_i)
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))
(* -1 (* sinTheta_O sinTheta_i))
(*.f32 sinTheta_O (neg.f32 sinTheta_i))
(* sinTheta_O (+ (* -1 sinTheta_i) (/ (* cosTheta_O cosTheta_i) sinTheta_O)))
(*.f32 sinTheta_O (fma.f32 cosTheta_O (/.f32 cosTheta_i sinTheta_O) (neg.f32 sinTheta_i)))
(* sinTheta_O (+ (* -1 sinTheta_i) (/ (* cosTheta_O cosTheta_i) sinTheta_O)))
(*.f32 sinTheta_O (fma.f32 cosTheta_O (/.f32 cosTheta_i sinTheta_O) (neg.f32 sinTheta_i)))
(* sinTheta_O (+ (* -1 sinTheta_i) (/ (* cosTheta_O cosTheta_i) sinTheta_O)))
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(* -1 (* sinTheta_O sinTheta_i))
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(* -1 (* sinTheta_O (+ sinTheta_i (* -1 (/ (* cosTheta_O cosTheta_i) sinTheta_O)))))
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(* -1 (* sinTheta_O (+ sinTheta_i (* -1 (/ (* cosTheta_O cosTheta_i) sinTheta_O)))))
(-.f32 #s(literal 0 binary32) (*.f32 sinTheta_O (fma.f32 (neg.f32 cosTheta_O) (/.f32 cosTheta_i sinTheta_O) sinTheta_i)))
(* -1 (* sinTheta_O (+ sinTheta_i (* -1 (/ (* cosTheta_O cosTheta_i) sinTheta_O)))))
(-.f32 #s(literal 0 binary32) (*.f32 sinTheta_O (fma.f32 (neg.f32 cosTheta_O) (/.f32 cosTheta_i sinTheta_O) sinTheta_i)))
(* cosTheta_O cosTheta_i)
(*.f32 cosTheta_O cosTheta_i)
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))
(* -1 (* sinTheta_O sinTheta_i))
(*.f32 sinTheta_O (neg.f32 sinTheta_i))
(* sinTheta_i (+ (* -1 sinTheta_O) (/ (* cosTheta_O cosTheta_i) sinTheta_i)))
(.f32 sinTheta_i (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) sinTheta_i) sinTheta_O))
(* sinTheta_i (+ (* -1 sinTheta_O) (/ (* cosTheta_O cosTheta_i) sinTheta_i)))
(.f32 sinTheta_i (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) sinTheta_i) sinTheta_O))
(* sinTheta_i (+ (* -1 sinTheta_O) (/ (* cosTheta_O cosTheta_i) sinTheta_i)))
(.f32 sinTheta_i (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) sinTheta_i) sinTheta_O))
(* -1 (* sinTheta_O sinTheta_i))
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(exp (- 6931/10000 (/ 1 v)))
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(exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))
(exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
(exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))
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(exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))
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(exp (- 6931/10000 (/ 1 v)))
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(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)

eval103.0ms (0.6%)

Memory: 3.5MiB live, 228.8MiB allocated
Compiler: Compiled 31 713 to 2 893 computations (90.9% saved)

prune176.0ms (1%)

Memory

-44.4MiB live, 254.6MiB allocated

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	977	15	992
Fresh	0	0	0
Picked	3	0	3
Done	0	0	0
Total	980	15	995

Accuracy

99.9%

Counts

995 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	93.5%	(/.f32 (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_O (neg.f32 sinTheta_i)) v)) (.f32 v #s(literal 2 binary32))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
	91.6%	(/.f32 (/.f32 (exp.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (.f32 v #s(literal 2 binary32))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
	99.8%	(/.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)
	4.6%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v)
	86.1%	(/.f32 (exp.f32 (/.f32 (fma.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (+.f32 #s(literal 0 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) (.f32 v (-.f32 #s(literal 0 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))))) (.f32 v (+.f32 #s(literal 0 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
	91.6%	(/.f32 (exp.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (.f32 v #s(literal 2 binary32))))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
	86.1%	(/.f32 (exp.f32 (-.f32 (-.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) v) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal -6931/10000 binary32))) (exp.f32 (/.f32 #s(literal 1 binary32) v)))
	84.2%	(/.f32 (exp.f32 (.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (neg.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (log.f32 (.f32 v #s(literal 2 binary32))))) cosTheta_O)))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
▶	99.8%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))))))
	4.6%	(/.f32 #s(literal 1 binary32) (*.f32 (/.f32 v (exp.f32 #s(literal 6931/10000 binary32))) #s(literal 2 binary32)))
▶	99.7%	(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 binary32) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))) (exp.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 v 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 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))))
	98.6%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))
▶	99.4%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
▶	4.6%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 #s(literal 6931/10000 binary32)))
▶	99.8%	(.f32 (exp.f32 (neg.f32 (log.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)) (/.f32 #s(literal -1 binary32) v)))))

Compiler

Compiled 714 to 512 computations (28.3% saved)

simplify276.0ms (1.5%)

Memory

14.8MiB live, 485.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	96	(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))
✓	cost-diff	160	(.f32 (/.f32 #s(literal 1 binary32) (.f32 v v)) (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))))
✓	cost-diff	192	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 v 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 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))
✓	cost-diff	3520	(/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 1 binary32) (.f32 v 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 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))))
✓	cost-diff	0	(.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))))
✓	cost-diff	160	(-.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_i cosTheta_O)) v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))
✓	cost-diff	224	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))))))
✓	cost-diff	480	(/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))))
✓	cost-diff	0	(+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
✓	cost-diff	0	(exp.f32 (+.f32 (/.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 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
✓	cost-diff	0	(exp.f32 #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 #s(literal 6931/10000 binary32)))
✓	cost-diff	0	(.f32 (exp.f32 (neg.f32 (log.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)) (/.f32 #s(literal -1 binary32) v)))))
✓	cost-diff	64	(*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v))
✓	cost-diff	96	(+.f32 #s(literal 6931/10000 binary32) (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v)))
✓	cost-diff	6272	(exp.f32 (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))

Rules

6 624×	`accelerator-lowering-fma.f32`
6 624×	`accelerator-lowering-fma.f64`
4 496×	`-lowering-.f32`
4 496×	`-lowering-.f64`
1 628×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	522
1	129	489
2	356	472
3	1160	466
4	4869	466
0	8214	428

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (exp (neg (log (* v 2)))) (exp (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v)))))
(exp (neg (log (* v 2))))
(neg (log (* v 2)))
(log (* v 2))
(* v 2)
v
2
(exp (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v))))
(+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v)))
6931/10000
(* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v))
(+ (* sinTheta_O sinTheta_i) 1)
sinTheta_O
sinTheta_i
1
(/ -1 v)
-1
(* (/ 1/2 v) (exp 6931/10000))
(/ 1/2 v)
1/2
v
(exp 6931/10000)
6931/10000
(* (/ 1/2 v) (exp (+ (/ -1 v) 6931/10000)))
(/ 1/2 v)
1/2
v
(exp (+ (/ -1 v) 6931/10000))
(+ (/ -1 v) 6931/10000)
(/ -1 v)
-1
6931/10000
(/ 1 (/ 1 (* (/ 1/2 v) (exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000))))))
1
(/ 1 (* (/ 1/2 v) (exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000)))))
(* (/ 1/2 v) (exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000))))
(/ 1/2 v)
1/2
v
(exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000)))
(- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000))
(/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v)
(+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O))
sinTheta_O
(neg sinTheta_i)
sinTheta_i
(* cosTheta_i cosTheta_O)
cosTheta_i
cosTheta_O
(+ (/ 1 v) -6931/10000)
(/ 1 v)
-6931/10000
(* (/ 1/2 v) (/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1))) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))))))
(/ 1/2 v)
1/2
v
(/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1))) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))))
(exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))))
(/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))
48038761/100000000
(- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))
6931/10000
(/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))
(+ (* sinTheta_O sinTheta_i) 1)
sinTheta_O
sinTheta_i
1
(neg v)
(exp (/ (* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1))) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))))
(/ (* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1))) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))
(* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1)))
(/ 1 (* v v))
(* v v)
(* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1))

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

localize237.0ms (1.3%)

Memory

13.3MiB live, 331.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(exp.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 v 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 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))
✓	accuracy	99.8%	(/.f32 #s(literal 1 binary32) (*.f32 v v))
✓	accuracy	99.7%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 v 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 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))
✓	accuracy	99.7%	(/.f32 #s(literal 48038761/100000000 binary32) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))))))
✓	accuracy	99.9%	(+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))
✓	accuracy	99.8%	(exp.f32 (-.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_i cosTheta_O)) v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
✓	accuracy	98.9%	(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_i cosTheta_O)) v)
✓	accuracy	100.0%	(/.f32 #s(literal -1 binary32) v)
✓	accuracy	100.0%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
✓	accuracy	99.9%	(+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))
✓	accuracy	99.8%	(exp.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)))
✓	accuracy	100.0%	(/.f32 #s(literal 1/2 binary32) v)
✓	accuracy	100.0%	(exp.f32 #s(literal 6931/10000 binary32))
✓	accuracy	99.7%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 #s(literal 6931/10000 binary32)))
✓	accuracy	100.0%	(*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v))
✓	accuracy	99.9%	(+.f32 #s(literal 6931/10000 binary32) (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v)))
✓	accuracy	99.8%	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v))))
✓	accuracy	98.8%	(exp.f32 (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))

Samples

113.0ms	203×	0	exit
23.0ms	53×	0	valid

Compiler

Compiled 483 to 56 computations (88.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 108.0ms

ival-mult: 49.0ms (45.5% of total)

ival-div: 18.0ms (16.7% of total)

ival-exp: 14.0ms (13% of total)

const: 10.0ms (9.3% of total)

ival-add: 7.0ms (6.5% of total)

ival-log: 3.0ms (2.8% of total)

ival-neg: 3.0ms (2.8% of total)

ival-sub: 2.0ms (1.9% of total)

exact: 1.0ms (0.9% of total)

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

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

series185.0ms (1%)

Memory

4.1MiB live, 273.0MiB allocated

Counts

26 → 828

Calls

Call 1

Inputs
#<alt (exp (neg (log (* v 2))))>
#<alt (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v)))>
#<alt (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v))>
#<alt (* (exp (neg (log (* v 2)))) (exp (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v)))))>
#<alt (* (/ 1/2 v) (exp 6931/10000))>
#<alt (/ 1/2 v)>
#<alt (exp 6931/10000)>
#<alt (* (/ 1/2 v) (exp (+ (/ -1 v) 6931/10000)))>
#<alt (exp (+ (/ -1 v) 6931/10000))>
#<alt (+ (/ -1 v) 6931/10000)>
#<alt (/ 1 (* (/ 1/2 v) (exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000)))))>
#<alt (/ 1 (/ 1 (* (/ 1/2 v) (exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000))))))>
#<alt (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000))>
#<alt (* (/ 1/2 v) (exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000))))>
#<alt (/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1))) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))))>
#<alt (/ (* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1))) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))>
#<alt (* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1)))>
#<alt (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))>
#<alt (exp (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v))))>
#<alt (/ -1 v)>
#<alt (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v)>
#<alt (exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000)))>
#<alt (+ (/ 1 v) -6931/10000)>
#<alt (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))>
#<alt (/ 1 (* v v))>
#<alt (exp (/ (* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1))) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))))>

Outputs
#<alt (exp (neg (+ (log 2) (log v))))>
#<alt (exp (neg (+ (log 2) (log v))))>
#<alt (exp (neg (+ (log 2) (log v))))>
#<alt (exp (neg (+ (log 2) (log v))))>
#<alt (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))>
#<alt (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))>
#<alt (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))>
#<alt (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))>
#<alt (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))>
#<alt (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))>
#<alt (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))>
#<alt (exp (neg (+ (log -2) (* -1 (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 sinTheta_i) v))>
#<alt (* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (* 6931/10000 (/ 1 sinTheta_O))) (/ 1 (* sinTheta_O v))))>
#<alt (* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (* 6931/10000 (/ 1 sinTheta_O))) (/ 1 (* sinTheta_O v))))>
#<alt (* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (* 6931/10000 (/ 1 sinTheta_O))) (/ 1 (* sinTheta_O v))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))>
#<alt (* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) 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 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 v)>
#<alt (- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))>
#<alt (- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))>
#<alt (- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_O (- (* -1 (/ sinTheta_i v)) (/ 1 (* sinTheta_O v))))>
#<alt (* sinTheta_O (- (* -1 (/ sinTheta_i v)) (/ 1 (* sinTheta_O v))))>
#<alt (* sinTheta_O (- (* -1 (/ sinTheta_i v)) (/ 1 (* sinTheta_O v))))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* -1 (* sinTheta_O (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))>
#<alt (* -1 (* sinTheta_O (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))>
#<alt (* -1 (* sinTheta_O (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))>
#<alt (/ -1 v)>
#<alt (- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))>
#<alt (- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))>
#<alt (- (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ 1 v))>
#<alt (* -1 (/ (* sinTheta_O sinTheta_i) v))>
#<alt (* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v))))>
#<alt (* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v))))>
#<alt (* sinTheta_i (- (* -1 (/ sinTheta_O v)) (/ 1 (* sinTheta_i v))))>
#<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 (* (exp (neg (+ (log 2) (log v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (+ (log 2) (log v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (+ (log 2) (log v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (+ (log 2) (log v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))))>
#<alt (+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))))>
#<alt (+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (+ (* 1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))))))>
#<alt (+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (+ (* -1/6 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) (pow v 3))) (+ (* 1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))))))>
#<alt (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))))>
#<alt (+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v)) (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) v)) (* 1/2 (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) v)) (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))>
#<alt (+ (* -1 (/ (* sinTheta_O (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) v)) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))>
#<alt (+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 2))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))>
#<alt (+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) (pow v 2))))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))>
#<alt (+ (* -1 (/ (* sinTheta_O (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) v)) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))>
#<alt (+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 2))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))>
#<alt (+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) (pow v 2))))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
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#<alt 6931/10000>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (- (* -10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) v)) (* -1 (+ 1 (* sinTheta_O sinTheta_i)))) v)))>
#<alt (+ 6931/10000 (* -1 (/ (- (* -1 (/ (- (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) v)) (* -10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v)) (* -1 (+ 1 (* sinTheta_O sinTheta_i)))) v)))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt 1>
#<alt (+ 1 (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))))>
#<alt (+ 1 (+ (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) (pow v 3))) (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2)))))>
#<alt (+ 1 (+ (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) (pow v 3))) (+ (* 50000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 4) (pow v 4))) (+ (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))) (* 1000000000000/332956652491 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 4) (pow v 4)))))))>
#<alt 1>
#<alt (+ 1 (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))))>
#<alt (+ 1 (+ (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) (pow v 3))) (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2)))))>
#<alt (+ 1 (+ (* -1 (/ (+ (* -1 (/ (+ (* 50000000/48038761 (pow (+ 1 (* sinTheta_O sinTheta_i)) 4)) (* 1000000000000/332956652491 (pow (+ 1 (* sinTheta_O sinTheta_i)) 4))) v)) (* 100000000/48038761 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) (pow v 3))) (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2)))))>
#<alt (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))>
#<alt (+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))))))>
#<alt (+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (+ (* sinTheta_O (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (+ (* 1/2 (pow (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 2)) (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))))))>
#<alt (+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (+ (* sinTheta_O (+ (* sinTheta_O (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* -1 (/ (* sinTheta_i (- (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))) (* v (+ 6931/10000 (/ 1 v))))) (+ (* 1/6 (pow (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 3)) (* (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (- (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (+ (* 1/2 (pow (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 2)) (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))>
#<alt (+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))))))>
#<alt (+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (+ (* sinTheta_i (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (+ (* 1/2 (pow (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 2)) (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))))))>
#<alt (+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (+ (* sinTheta_i (+ (* sinTheta_i (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* -1 (/ (* sinTheta_O (- (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))) (* v (+ 6931/10000 (/ 1 v))))) (+ (* 1/6 (pow (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 3)) (* (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (- (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (+ (* 1/2 (pow (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 2)) (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>

Calls

207 calls:

Time	Variable		Point	Expression
17.0ms	sinTheta_i	@	inf	(/ 1 (/ 1 (* (/ 1/2 v) (exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000))))))
13.0ms	v	@	0	(exp (neg (log (* v 2))))
13.0ms	sinTheta_i	@	-inf	(/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1))) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))))
11.0ms	sinTheta_O	@	inf	(* (exp (neg (log (* v 2)))) (exp (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v)))))
10.0ms	v	@	-inf	(exp (neg (log (* v 2))))

rewrite478.0ms (2.6%)

Memory

-20.9MiB live, 919.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 340×	`accelerator-lowering-fma.f32`
5 340×	`accelerator-lowering-fma.f64`
5 044×	`/-lowering-/.f32`
5 044×	`/-lowering-/.f64`
4 462×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	357
1	280	258
2	2439	255
0	9299	243

Stop Event

1×	iter limit
1×	node limit

Counts

26 → 1 314

Calls

Call 1

Inputs
(exp (neg (log (* v 2))))
(+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v)))
(* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v))
(* (exp (neg (log (* v 2)))) (exp (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v)))))
(* (/ 1/2 v) (exp 6931/10000))
(/ 1/2 v)
(exp 6931/10000)
(* (/ 1/2 v) (exp (+ (/ -1 v) 6931/10000)))
(exp (+ (/ -1 v) 6931/10000))
(+ (/ -1 v) 6931/10000)
(/ 1 (* (/ 1/2 v) (exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000)))))
(/ 1 (/ 1 (* (/ 1/2 v) (exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000))))))
(- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000))
(* (/ 1/2 v) (exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000))))
(/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1))) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))))
(/ (* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1))) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))
(* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1)))
(- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))
(exp (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v))))
(/ -1 v)
(/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v)
(exp (- (/ (+ (* sinTheta_O (neg sinTheta_i)) (* cosTheta_i cosTheta_O)) v) (+ (/ 1 v) -6931/10000)))
(+ (/ 1 v) -6931/10000)
(/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))
(/ 1 (* v v))
(exp (/ (* (/ 1 (* v v)) (* (+ (* sinTheta_O sinTheta_i) 1) (+ (* sinTheta_O sinTheta_i) 1))) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))))

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

simplify824.0ms (4.5%)

Memory

27.5MiB live, 1 043.2MiB allocated

Algorithm

1×	egg-herbie

Rules

7 404×	`-lowering-.f32`
7 404×	`-lowering-.f64`
6 316×	`accelerator-lowering-fma.f32`
6 316×	`accelerator-lowering-fma.f64`
4 762×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1730	23906
1	5696	23039
0	9322	22155

Stop Event

1×	iter limit
1×	node limit

Counts

828 → 828

Calls

Call 1

Inputs
(exp (neg (+ (log 2) (log v))))
(exp (neg (+ (log 2) (log v))))
(exp (neg (+ (log 2) (log v))))
(exp (neg (+ (log 2) (log v))))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(exp (neg (+ (log -2) (* -1 (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 sinTheta_i) v))
(* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (* 6931/10000 (/ 1 sinTheta_O))) (/ 1 (* sinTheta_O v))))
(* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (* 6931/10000 (/ 1 sinTheta_O))) (/ 1 (* sinTheta_O v))))
(* sinTheta_O (- (+ (* -1 (/ sinTheta_i v)) (* 6931/10000 (/ 1 sinTheta_O))) (/ 1 (* sinTheta_O v))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))
(* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ sinTheta_i v))))
(* -1 (* sinTheta_O (+ (* -1 (/ (- 6931/10000 (/ 1 v)) sinTheta_O)) (/ sinTheta_i 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 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_O (- (* -1 (/ sinTheta_i v)) (/ 1 (* sinTheta_O v))))
(* sinTheta_O (- (* -1 (/ sinTheta_i v)) (/ 1 (* sinTheta_O v))))
(* sinTheta_O (- (* -1 (/ sinTheta_i v)) (/ 1 (* sinTheta_O v))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(* -1 (* sinTheta_O (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(* -1 (* sinTheta_O (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v))))
(* -1 (* sinTheta_O (+ (/ 1 (* sinTheta_O v)) (/ 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)) (/ 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))
(* (exp (neg (+ (log 2) (log v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (+ (log 2) (log v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (+ (log 2) (log v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (+ (log 2) (log v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))))
(+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))))
(+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (+ (* 1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))))))
(+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (+ (* -1/6 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) (pow v 3))) (+ (* 1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))))))
(* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))))
(+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))
(+ (* -1 (/ (+ (* -1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v)) (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) v)) (* 1/2 (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) v)) (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))
(+ (* -1 (/ (* sinTheta_O (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) v)) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))
(+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 2))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))
(+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) (pow v 2))))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))
(+ (* -1 (/ (* sinTheta_O (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) v)) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))
(+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 2))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))
(+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) (pow v 2))))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* (exp (neg (log (* 2 v)))) (exp (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(* 1/2 (/ (exp (- 6931/10000 (/ 1 v))) v))
(* 1/2 (/ (exp (- 6931/10000 (/ 1 v))) v))
(* 1/2 (/ (exp (- 6931/10000 (/ 1 v))) v))
(* 1/2 (/ (exp (- 6931/10000 (/ 1 v))) v))
(* 1/2 (/ (exp 6931/10000) v))
(/ (+ (* -1/2 (/ (exp 6931/10000) v)) (* 1/2 (exp 6931/10000))) v)
(/ (+ (* -1/2 (/ (exp 6931/10000) v)) (+ (* 1/4 (/ (exp 6931/10000) (pow v 2))) (* 1/2 (exp 6931/10000)))) v)
(/ (+ (* -1/2 (/ (exp 6931/10000) v)) (+ (* -1/12 (/ (exp 6931/10000) (pow v 3))) (+ (* 1/4 (/ (exp 6931/10000) (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) v))) v))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (exp 6931/10000)) (* 1/4 (/ (exp 6931/10000) v))) v)) (* -1/2 (exp 6931/10000))) v))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (exp 6931/10000)) (* 1/12 (/ (exp 6931/10000) v))) v)) (* -1/2 (exp 6931/10000))) v)) (* -1/2 (exp 6931/10000))) v))
(exp (- 6931/10000 (/ 1 v)))
(exp (- 6931/10000 (/ 1 v)))
(exp (- 6931/10000 (/ 1 v)))
(exp (- 6931/10000 (/ 1 v)))
(exp 6931/10000)
(+ (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))
(* 2 (/ v (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))))
(* 2 (/ v (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))))
(* 2 (/ v (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))))
(* 2 (/ v (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))))
(* 2 (/ v (exp 6931/10000)))
(* v (+ (* -2 (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) (* v (exp 6931/10000)))) (* 2 (/ 1 (exp 6931/10000)))))
(* v (- (+ (* -1 (/ (+ (* -2 (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2) (exp 6931/10000))) (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2) (exp 6931/10000))) (pow v 2))) (* 2 (/ 1 (exp 6931/10000)))) (* 2 (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) (* v (exp 6931/10000))))))
(* v (- (+ (* -1 (/ (+ (* -1 (* (+ (* -2 (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2) (exp 6931/10000))) (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2) (exp 6931/10000))) (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1))) (+ (* -1 (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 3) (exp 6931/10000))) (* 1/3 (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 3) (exp 6931/10000))))) (pow v 3))) (* 2 (/ 1 (exp 6931/10000)))) (+ (* -2 (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2) (* (pow v 2) (exp 6931/10000)))) (+ (* 2 (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) (* v (exp 6931/10000)))) (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2) (* (pow v 2) (exp 6931/10000)))))))
(* 2 (/ v (exp 6931/10000)))
(* -1 (* v (- (* -2 (/ (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) (* v (exp 6931/10000)))) (* 2 (/ 1 (exp 6931/10000))))))
(* -1 (* v (- (* -1 (/ (- (+ (* -1 (/ (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 2) (* v (exp 6931/10000)))) (* 2 (/ (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 2) (* v (exp 6931/10000))))) (* -2 (/ (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) (exp 6931/10000)))) v)) (* 2 (/ 1 (exp 6931/10000))))))
(* -1 (* v (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) (+ (* -1 (/ (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 2) (exp 6931/10000))) (* 2 (/ (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 2) (exp 6931/10000))))) v)) (+ (* -1/3 (/ (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 3) (* v (exp 6931/10000)))) (/ (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 3) (* v (exp 6931/10000))))) (+ (* -1 (/ (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 2) (exp 6931/10000))) (* 2 (/ (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 2) (exp 6931/10000))))) v)) (* -2 (/ (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) (exp 6931/10000)))) v)) (* 2 (/ 1 (exp 6931/10000))))))
(* 2 (/ v (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))))
(+ (* 2 (/ v (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))))) (* 2 (/ (* sinTheta_O sinTheta_i) (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))))))
(+ (* 2 (/ v (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))))) (* sinTheta_O (+ (* -2 (* sinTheta_O (+ (* -1 (/ (pow sinTheta_i 2) (* v (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))))) (* 1/2 (/ (pow sinTheta_i 2) (* v (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))))))))) (* 2 (/ sinTheta_i (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))))))))
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(/ (* cosTheta_O cosTheta_i) v)
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6931/10000
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6931/10000
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(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
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(* 1/2 (/ (exp 6931/10000) v))
(/ (+ (* 1/2 (exp 6931/10000)) (* 1/2 (/ (* (exp 6931/10000) (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1)) v))) v)
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(* 1/2 (/ (exp 6931/10000) v))
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(+ (* 1/2 (/ (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))) v)) (* sinTheta_O (+ (* -1/2 (/ (* sinTheta_i (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))) (pow v 2))) (* 1/4 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))))) (pow v 3))))))
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(+ (* 1/2 (/ (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))) v)) (* cosTheta_i (+ (* 1/2 (/ (* cosTheta_O (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v)))) (pow v 2))) (* cosTheta_i (+ (* 1/12 (/ (* (pow cosTheta_O 3) (* cosTheta_i (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))))) (pow v 4))) (* 1/4 (/ (* (pow cosTheta_O 2) (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v)))) (pow v 3))))))))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
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(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))) v))
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(+ (* 1/2 (/ (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))) v)) (* cosTheta_O (+ (* 1/2 (/ (* cosTheta_i (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v)))) (pow v 2))) (* cosTheta_O (+ (* 1/12 (/ (* cosTheta_O (* (pow cosTheta_i 3) (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))))) (pow v 4))) (* 1/4 (/ (* (pow cosTheta_i 2) (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v)))) (pow v 3))))))))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
(* 1/2 (/ (exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))) v))
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(/ 1 (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))))
(+ (* 48038761/100000000 (/ v (* (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (+ 1 (* sinTheta_O sinTheta_i))))) (/ 1 (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))))
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(+ (* v (+ (* v (- (* 535804164344572917445081/6000000000000000000000000 (/ v (* (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)))) (* 4351410491404879/20000000000000000 (/ 1 (* (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))))) (* 48038761/100000000 (/ 1 (* (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (+ 1 (* sinTheta_O sinTheta_i))))))) (/ 1 (exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))))
(exp 6931/10000)
(+ (exp 6931/10000) (* -1 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)))
(- (+ (exp 6931/10000) (+ (* -1 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)) (/ (* (exp 6931/10000) (+ (* 1/2 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) (pow v 2)))) (* 10000/6931 (/ (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))))
(- (+ (exp 6931/10000) (+ (* -1 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (/ (* (exp 6931/10000) (+ (* -100000000/48038761 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (+ (* -10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (* -1/6 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))))) (pow v 3)) (/ (* (exp 6931/10000) (+ (* 1/2 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) (pow v 2))))) (+ (* -100000000/48038761 (/ (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (pow v 3))) (+ (* -10000/6931 (/ (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (pow v 3))) (* 10000/6931 (/ (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (pow v 2))))))
(exp 6931/10000)
(+ (exp 6931/10000) (* -1 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)))
(+ (exp 6931/10000) (* -1 (/ (+ (* -1 (/ (- (* (exp 6931/10000) (+ (* 1/2 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) (* 10000/6931 (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) v)) (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(+ (exp 6931/10000) (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* (exp 6931/10000) (+ (* 1/6 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (+ (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (* 100000000/48038761 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))))) (+ (* 10000/6931 (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) (* 100000000/48038761 (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))))) v)) (* (exp 6931/10000) (+ (* 1/2 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) (* 10000/6931 (* (exp 6931/10000) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) v)) (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(/ (+ 1 (* sinTheta_O sinTheta_i)) v)
(/ (+ 1 (+ (* -6931/10000 v) (* sinTheta_O sinTheta_i))) v)
(/ (+ 1 (+ (* sinTheta_O sinTheta_i) (* v (- (* 48038761/100000000 (/ v (+ 1 (* sinTheta_O sinTheta_i)))) 6931/10000)))) v)
(/ (+ 1 (+ (* sinTheta_O sinTheta_i) (* v (- (* v (+ (* -332956652491/1000000000000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (* 48038761/100000000 (/ 1 (+ 1 (* sinTheta_O sinTheta_i)))))) 6931/10000)))) v)
(* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2)))
(/ (+ (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) v)) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))
(/ (- (+ (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (* 1000000000000/332956652491 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 4) (pow v 2)))) (* 100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) v))) (pow v 2))
(/ (- (+ (* -10000000000000000/2307722558415121 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 5) (pow v 3))) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (+ (* -1000000000000/332956652491 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 4) (pow v 2))) (* 100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) v)))) (pow v 2))
(* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2)))
(/ (+ (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) v)) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))
(/ (+ (* -1 (/ (- (* -1000000000000/332956652491 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 4) v)) (* -100000000/48038761 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) v)) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (* -10000000000000000/2307722558415121 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 5) v)) (* -1000000000000/332956652491 (pow (+ 1 (* sinTheta_O sinTheta_i)) 4))) v)) (* -100000000/48038761 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) v)) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))
(/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))
(+ (* sinTheta_O (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(+ (* sinTheta_O (- (+ (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (- (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(+ (* sinTheta_O (- (+ (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (- (+ (* -1 (/ (* sinTheta_O (* sinTheta_i (- (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (* v (+ 6931/10000 (/ 1 v))))) (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(/ (* sinTheta_O sinTheta_i) v)
(* sinTheta_O (- (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v)) (* 6931/10000 (/ 1 sinTheta_O))))
(* sinTheta_O (- (+ (/ 1 (* sinTheta_O v)) (+ (/ 1 (* (pow sinTheta_O 2) (* sinTheta_i v))) (/ sinTheta_i v))) (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) (* (pow sinTheta_O 2) sinTheta_i)))))
(* sinTheta_O (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 (* sinTheta_i v)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) sinTheta_i)))) (* (pow sinTheta_O 3) sinTheta_i))) (+ (/ 1 (* sinTheta_O v)) (+ (/ 1 (* (pow sinTheta_O 2) (* sinTheta_i v))) (/ sinTheta_i v)))) (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) (* (pow sinTheta_O 2) sinTheta_i)))))
(/ (* sinTheta_O sinTheta_i) v)
(* -1 (* sinTheta_O (+ (* -1 (/ sinTheta_i v)) (* -1 (/ (- (/ 1 v) 6931/10000) sinTheta_O)))))
(* -1 (* sinTheta_O (+ (* -1 (/ sinTheta_i v)) (* -1 (/ (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) (* sinTheta_O sinTheta_i))) (+ (/ 1 v) (/ 1 (* sinTheta_O (* sinTheta_i v))))) 6931/10000) sinTheta_O)))))
(* -1 (* sinTheta_O (+ (* -1 (/ sinTheta_i v)) (* -1 (/ (- (+ (* -1 (/ (- (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) sinTheta_i)) (/ 1 (* sinTheta_i v))))) (* sinTheta_O sinTheta_i)) (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) sinTheta_i)) (/ 1 (* sinTheta_i v)))) sinTheta_O)) (/ 1 v)) 6931/10000) sinTheta_O)))))
(/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))
(+ (* sinTheta_i (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(+ (* sinTheta_i (- (+ (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (- (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(+ (* sinTheta_i (- (+ (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (- (+ (* -1 (/ (* sinTheta_O (* sinTheta_i (- (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (* v (+ 6931/10000 (/ 1 v))))) (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(/ (* sinTheta_O sinTheta_i) v)
(* sinTheta_i (- (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))))
(* sinTheta_i (- (+ (/ 1 (* sinTheta_O (* (pow sinTheta_i 2) v))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))) (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) (* sinTheta_O (pow sinTheta_i 2))))))
(* sinTheta_i (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 (* sinTheta_O v)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) sinTheta_O)))) (* sinTheta_O (pow sinTheta_i 3)))) (+ (/ 1 (* sinTheta_O (* (pow sinTheta_i 2) v))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)))) (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) (* sinTheta_O (pow sinTheta_i 2))))))
(/ (* sinTheta_O sinTheta_i) v)
(* -1 (* sinTheta_i (+ (* -1 (/ sinTheta_O v)) (* -1 (/ (- (/ 1 v) 6931/10000) sinTheta_i)))))
(* -1 (* sinTheta_i (+ (* -1 (/ sinTheta_O v)) (* -1 (/ (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) (* sinTheta_O sinTheta_i))) (+ (/ 1 v) (/ 1 (* sinTheta_O (* sinTheta_i v))))) 6931/10000) sinTheta_i)))))
(* -1 (* sinTheta_i (+ (* -1 (/ sinTheta_O v)) (* -1 (/ (- (+ (* -1 (/ (- (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) sinTheta_O)) (/ 1 (* sinTheta_O v))))) (* sinTheta_O sinTheta_i)) (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) sinTheta_O)) (/ 1 (* sinTheta_O v)))) sinTheta_i)) (/ 1 v)) 6931/10000) sinTheta_i)))))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/ 1 (pow v 2))
(+ (* 2 (/ (* sinTheta_O sinTheta_i) (pow v 2))) (/ 1 (pow v 2)))
(+ (* sinTheta_O (+ (* 2 (/ sinTheta_i (pow v 2))) (/ (* sinTheta_O (pow sinTheta_i 2)) (pow v 2)))) (/ 1 (pow v 2)))
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6931/10000
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6931/10000
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp 6931/10000)
(+ (exp 6931/10000) (/ (* (exp 6931/10000) (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1)) v))
(+ (exp 6931/10000) (+ (* 1/2 (/ (* (exp 6931/10000) (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2)) (pow v 2))) (/ (* (exp 6931/10000) (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1)) v)))
(+ (exp 6931/10000) (+ (* 1/6 (/ (* (exp 6931/10000) (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 3)) (pow v 3))) (+ (* 1/2 (/ (* (exp 6931/10000) (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2)) (pow v 2))) (/ (* (exp 6931/10000) (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1)) v))))
(exp 6931/10000)
(+ (exp 6931/10000) (* -1 (/ (* (exp 6931/10000) (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))))) v)))
(+ (exp 6931/10000) (* -1 (/ (+ (* -1/2 (/ (* (exp 6931/10000) (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 2)) v)) (* (exp 6931/10000) (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))))) v)))
(+ (exp 6931/10000) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp 6931/10000) (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 3)) v)) (* 1/2 (* (exp 6931/10000) (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 2)))) v)) (* (exp 6931/10000) (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))))) v)))
(/ 1 v)
(/ (+ 1 (* -6931/10000 v)) v)
(/ (+ 1 (* -6931/10000 v)) v)
(/ (+ 1 (* -6931/10000 v)) v)
-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) 6931/10000)
(/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))
(+ (* -48038761/100000000 (/ (* sinTheta_O sinTheta_i) (* v (pow (+ 6931/10000 (/ 1 v)) 2)))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))
(+ (* sinTheta_O (- (* 48038761/100000000 (/ (* sinTheta_O (pow sinTheta_i 2)) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 3)))) (* 48038761/100000000 (/ sinTheta_i (* v (pow (+ 6931/10000 (/ 1 v)) 2)))))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))
(+ (* sinTheta_O (- (* sinTheta_O (- (* -48038761/100000000 (/ (* sinTheta_O (pow sinTheta_i 3)) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 4)))) (* -48038761/100000000 (/ (pow sinTheta_i 2) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 3)))))) (* 48038761/100000000 (/ sinTheta_i (* v (pow (+ 6931/10000 (/ 1 v)) 2)))))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))
(* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))
(/ (+ (* -48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* sinTheta_O (pow sinTheta_i 2)))) (* 48038761/100000000 (/ v sinTheta_i))) sinTheta_O)
(/ (- (+ (* 48038761/100000000 (/ v sinTheta_i)) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 2) (pow sinTheta_i 3))))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* sinTheta_O (pow sinTheta_i 2))))) sinTheta_O)
(/ (- (+ (* -48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* (pow sinTheta_O 3) (pow sinTheta_i 4)))) (* 48038761/100000000 (/ v sinTheta_i))) (+ (* -48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 2) (pow sinTheta_i 3)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* sinTheta_O (pow sinTheta_i 2)))))) sinTheta_O)
(* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))
(* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_i)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* sinTheta_O (pow sinTheta_i 2))))) sinTheta_O))
(* -1 (/ (+ (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* sinTheta_O (pow sinTheta_i 3)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_i 2)))) sinTheta_O)) (* -48038761/100000000 (/ v sinTheta_i))) sinTheta_O))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* sinTheta_O (pow sinTheta_i 4)))) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (pow sinTheta_i 3)))) sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_i 2)))) sinTheta_O)) (* -48038761/100000000 (/ v sinTheta_i))) sinTheta_O))
(/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))
(+ (* -48038761/100000000 (/ (* sinTheta_O sinTheta_i) (* v (pow (+ 6931/10000 (/ 1 v)) 2)))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))
(+ (* sinTheta_i (- (* 48038761/100000000 (/ (* (pow sinTheta_O 2) sinTheta_i) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 3)))) (* 48038761/100000000 (/ sinTheta_O (* v (pow (+ 6931/10000 (/ 1 v)) 2)))))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))
(+ (* sinTheta_i (- (* sinTheta_i (- (* -48038761/100000000 (/ (* (pow sinTheta_O 3) sinTheta_i) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 4)))) (* -48038761/100000000 (/ (pow sinTheta_O 2) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 3)))))) (* 48038761/100000000 (/ sinTheta_O (* v (pow (+ 6931/10000 (/ 1 v)) 2)))))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))
(* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))
(/ (+ (* -48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i))) (* 48038761/100000000 (/ v sinTheta_O))) sinTheta_i)
(/ (- (+ (* 48038761/100000000 (/ v sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) (pow sinTheta_i 2))))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i)))) sinTheta_i)
(/ (- (+ (* -48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* (pow sinTheta_O 4) (pow sinTheta_i 3)))) (* 48038761/100000000 (/ v sinTheta_O))) (+ (* -48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) (pow sinTheta_i 2)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i))))) sinTheta_i)
(* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))
(* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i)))) sinTheta_i))
(* -1 (/ (+ (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) sinTheta_i))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_O 2)))) sinTheta_i)) (* -48038761/100000000 (/ v sinTheta_O))) sinTheta_i))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* (pow sinTheta_O 4) sinTheta_i))) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (pow sinTheta_O 3)))) sinTheta_i)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_O 2)))) sinTheta_i)) (* -48038761/100000000 (/ v sinTheta_O))) sinTheta_i))
(* 48038761/100000000 (/ v (+ 1 (* sinTheta_O sinTheta_i))))
(* v (+ (* -332956652491/1000000000000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (* 48038761/100000000 (/ 1 (+ 1 (* sinTheta_O sinTheta_i))))))
(* v (+ (* v (- (* 2307722558415121/10000000000000000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) (* 332956652491/1000000000000 (/ 1 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) (* 48038761/100000000 (/ 1 (+ 1 (* sinTheta_O sinTheta_i))))))
(* v (+ (* v (- (* v (+ (* -15994825052375203651/100000000000000000000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 4))) (* 2307722558415121/10000000000000000 (/ 1 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))))) (* 332956652491/1000000000000 (/ 1 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) (* 48038761/100000000 (/ 1 (+ 1 (* sinTheta_O sinTheta_i))))))
6931/10000
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(- (+ 6931/10000 (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2)))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(- (+ 6931/10000 (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) (pow v 3)))) (+ (* -10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
6931/10000
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(+ 6931/10000 (* -1 (/ (- (* -10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) v)) (* -1 (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(+ 6931/10000 (* -1 (/ (- (* -1 (/ (- (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) v)) (* -10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v)) (* -1 (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
1
(+ 1 (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))))
(+ 1 (+ (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) (pow v 3))) (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2)))))
(+ 1 (+ (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) (pow v 3))) (+ (* 50000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 4) (pow v 4))) (+ (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))) (* 1000000000000/332956652491 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 4) (pow v 4)))))))
1
(+ 1 (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))))
(+ 1 (+ (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) (pow v 3))) (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2)))))
(+ 1 (+ (* -1 (/ (+ (* -1 (/ (+ (* 50000000/48038761 (pow (+ 1 (* sinTheta_O sinTheta_i)) 4)) (* 1000000000000/332956652491 (pow (+ 1 (* sinTheta_O sinTheta_i)) 4))) v)) (* 100000000/48038761 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) (pow v 3))) (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2)))))
(exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (+ (* sinTheta_O (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (+ (* 1/2 (pow (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 2)) (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (+ (* sinTheta_O (+ (* sinTheta_O (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* -1 (/ (* sinTheta_i (- (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))) (* v (+ 6931/10000 (/ 1 v))))) (+ (* 1/6 (pow (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 3)) (* (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (- (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (+ (* 1/2 (pow (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 2)) (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (+ (* sinTheta_i (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (+ (* 1/2 (pow (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 2)) (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (+ (* sinTheta_i (+ (* sinTheta_i (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* -1 (/ (* sinTheta_O (- (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))) (* v (+ 6931/10000 (/ 1 v))))) (+ (* 1/6 (pow (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 3)) (* (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (- (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (+ (* 1/2 (pow (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 2)) (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))

Outputs
(exp (neg (+ (log 2) (log v))))
(exp.f32 (neg.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v))))
(exp (neg (+ (log 2) (log v))))
(exp.f32 (neg.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v))))
(exp (neg (+ (log 2) (log v))))
(exp.f32 (neg.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v))))
(exp (neg (+ (log 2) (log v))))
(exp.f32 (neg.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v))))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp.f32 (neg.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v))))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp.f32 (neg.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v))))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp.f32 (neg.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v))))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp.f32 (neg.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) v)) (-.f32 #s(literal 0 binary32) (log.f32 #s(literal -2 binary32)))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) v)) (-.f32 #s(literal 0 binary32) (log.f32 #s(literal -2 binary32)))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
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(exp.f32 #s(literal 6931/10000 binary32))
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(exp.f32 #s(literal 6931/10000 binary32))
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(+ (* sinTheta_O (- (+ (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (- (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
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(+ (* sinTheta_O (- (+ (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (- (+ (* -1 (/ (* sinTheta_O (* sinTheta_i (- (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (* v (+ 6931/10000 (/ 1 v))))) (/ (pow sinTheta_i 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_i (- (* 2 (/ sinTheta_i (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(fma.f32 sinTheta_O (fma.f32 #s(literal 2 binary32) (/.f32 sinTheta_i (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (fma.f32 sinTheta_O (fma.f32 sinTheta_O (/.f32 (.f32 sinTheta_i (-.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 (.f32 sinTheta_i (fma.f32 #s(literal 2 binary32) (/.f32 sinTheta_i (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 (neg.f32 sinTheta_i) (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))))) (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32))))) (neg.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)))) (-.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 (.f32 sinTheta_i (fma.f32 #s(literal 2 binary32) (/.f32 sinTheta_i (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 (neg.f32 sinTheta_i) (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))))) (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32))))) (/.f32 (neg.f32 sinTheta_i) (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))))) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))
(/ (* sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(* sinTheta_O (- (+ (/ 1 (* sinTheta_O v)) (/ sinTheta_i v)) (* 6931/10000 (/ 1 sinTheta_O))))
(.f32 sinTheta_O (+.f32 (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_O)) (+.f32 (/.f32 sinTheta_i v) (/.f32 #s(literal -6931/10000 binary32) sinTheta_O))))
(* sinTheta_O (- (+ (/ 1 (* sinTheta_O v)) (+ (/ 1 (* (pow sinTheta_O 2) (* sinTheta_i v))) (/ sinTheta_i v))) (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) (* (pow sinTheta_O 2) sinTheta_i)))))
(.f32 sinTheta_O (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_O)) (+.f32 (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) (.f32 (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_O)) v)))) (+.f32 (/.f32 #s(literal 6931/10000 binary32) sinTheta_O) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))) (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_O))))))
(* sinTheta_O (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 (* sinTheta_i v)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) sinTheta_i)))) (* (pow sinTheta_O 3) sinTheta_i))) (+ (/ 1 (* sinTheta_O v)) (+ (/ 1 (* (pow sinTheta_O 2) (* sinTheta_i v))) (/ sinTheta_i v)))) (+ (* 6931/10000 (/ 1 sinTheta_O)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) (* (pow sinTheta_O 2) sinTheta_i)))))
(.f32 sinTheta_O (-.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_O)) (+.f32 (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) (.f32 (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_O)) v)))) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_i)) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))) sinTheta_i))) (.f32 sinTheta_i (.f32 sinTheta_O (.f32 sinTheta_O sinTheta_O))))) (+.f32 (/.f32 #s(literal 6931/10000 binary32) sinTheta_O) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))) (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_O))))))
(/ (* sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(* -1 (* sinTheta_O (+ (* -1 (/ sinTheta_i v)) (* -1 (/ (- (/ 1 v) 6931/10000) sinTheta_O)))))
(*.f32 (-.f32 (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_O) (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(* -1 (* sinTheta_O (+ (* -1 (/ sinTheta_i v)) (* -1 (/ (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) (* sinTheta_O sinTheta_i))) (+ (/ 1 v) (/ 1 (* sinTheta_O (* sinTheta_i v))))) 6931/10000) sinTheta_O)))))
(.f32 (-.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (+.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 #s(literal 1 binary32) (.f32 sinTheta_O (.f32 v sinTheta_i)))) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))) (*.f32 sinTheta_O sinTheta_i))) #s(literal -6931/10000 binary32)) sinTheta_O)) (neg.f32 sinTheta_O))
(* -1 (* sinTheta_O (+ (* -1 (/ sinTheta_i v)) (* -1 (/ (- (+ (* -1 (/ (- (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) sinTheta_i)) (/ 1 (* sinTheta_i v))))) (* sinTheta_O sinTheta_i)) (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) sinTheta_i)) (/ 1 (* sinTheta_i v)))) sinTheta_O)) (/ 1 v)) 6931/10000) sinTheta_O)))))
(.f32 (-.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (+.f32 (-.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 (-.f32 (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_i)) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))) sinTheta_i))) (.f32 sinTheta_O sinTheta_i)) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_i)) (/.f32 (*.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))) sinTheta_i))) sinTheta_O)) #s(literal -6931/10000 binary32)) sinTheta_O)) (neg.f32 sinTheta_O))
(/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))
(/.f32 #s(literal 1 binary32) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))
(+ (* sinTheta_i (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(fma.f32 sinTheta_i (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))
(+ (* sinTheta_i (- (+ (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (- (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(fma.f32 sinTheta_i (fma.f32 #s(literal 2 binary32) (/.f32 sinTheta_O (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (fma.f32 sinTheta_i (-.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (.f32 sinTheta_O (/.f32 (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32))))) (neg.f32 (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))))) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))
(+ (* sinTheta_i (- (+ (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (- (+ (* -1 (/ (* sinTheta_O (* sinTheta_i (- (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (* v (+ 6931/10000 (/ 1 v))))) (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(fma.f32 sinTheta_i (fma.f32 #s(literal 2 binary32) (/.f32 sinTheta_O (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (fma.f32 sinTheta_i (fma.f32 (neg.f32 sinTheta_O) (/.f32 (.f32 sinTheta_i (-.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (.f32 sinTheta_O (/.f32 (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)))))) (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32))) (-.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (.f32 sinTheta_O (/.f32 (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)))))) (neg.f32 (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))))) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))
(/ (* sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(* sinTheta_i (- (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)) (* 6931/10000 (/ 1 sinTheta_i))))
(.f32 sinTheta_i (+.f32 (+.f32 (/.f32 sinTheta_O v) (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_i))) (/.f32 #s(literal -6931/10000 binary32) sinTheta_i)))
(* sinTheta_i (- (+ (/ 1 (* sinTheta_O (* (pow sinTheta_i 2) v))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v))) (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) (* sinTheta_O (pow sinTheta_i 2))))))
(.f32 sinTheta_i (-.f32 (+.f32 (+.f32 (+.f32 (/.f32 sinTheta_O v) (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_i))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 sinTheta_O (.f32 sinTheta_i sinTheta_i)) v))) (/.f32 #s(literal -6931/10000 binary32) sinTheta_i)) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))) (.f32 sinTheta_O (.f32 sinTheta_i sinTheta_i)))))
(* sinTheta_i (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 (* sinTheta_O v)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) sinTheta_O)))) (* sinTheta_O (pow sinTheta_i 3)))) (+ (/ 1 (* sinTheta_O (* (pow sinTheta_i 2) v))) (+ (/ 1 (* sinTheta_i v)) (/ sinTheta_O v)))) (+ (* 6931/10000 (/ 1 sinTheta_i)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) (* sinTheta_O (pow sinTheta_i 2))))))
(.f32 sinTheta_i (-.f32 (-.f32 (+.f32 (+.f32 (/.f32 sinTheta_O v) (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_i))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 sinTheta_O (.f32 sinTheta_i sinTheta_i)) v))) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_O)) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))) sinTheta_O))) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_i sinTheta_i))))) (+.f32 (/.f32 #s(literal 6931/10000 binary32) sinTheta_i) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))) (.f32 sinTheta_O (.f32 sinTheta_i sinTheta_i))))))
(/ (* sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(* -1 (* sinTheta_i (+ (* -1 (/ sinTheta_O v)) (* -1 (/ (- (/ 1 v) 6931/10000) sinTheta_i)))))
(*.f32 (-.f32 (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32)) sinTheta_i) (/.f32 sinTheta_O v)) (neg.f32 sinTheta_i))
(* -1 (* sinTheta_i (+ (* -1 (/ sinTheta_O v)) (* -1 (/ (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) (* sinTheta_O sinTheta_i))) (+ (/ 1 v) (/ 1 (* sinTheta_O (* sinTheta_i v))))) 6931/10000) sinTheta_i)))))
(.f32 (-.f32 (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_O v)) (/.f32 (+.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 #s(literal 1 binary32) (.f32 sinTheta_O (.f32 v sinTheta_i)))) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))) (*.f32 sinTheta_O sinTheta_i))) #s(literal -6931/10000 binary32)) sinTheta_i)) (neg.f32 sinTheta_i))
(* -1 (* sinTheta_i (+ (* -1 (/ sinTheta_O v)) (* -1 (/ (- (+ (* -1 (/ (- (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) sinTheta_O)) (/ 1 (* sinTheta_O v))))) (* sinTheta_O sinTheta_i)) (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (- (/ 1 v) 6931/10000))) sinTheta_O)) (/ 1 (* sinTheta_O v)))) sinTheta_i)) (/ 1 v)) 6931/10000) sinTheta_i)))))
(.f32 (neg.f32 (+.f32 (/.f32 sinTheta_O v) (/.f32 (+.f32 (-.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 (-.f32 (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_O)) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))) sinTheta_O))) (.f32 sinTheta_O sinTheta_i)) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 v sinTheta_O)) (/.f32 (*.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))) sinTheta_O))) sinTheta_i)) #s(literal -6931/10000 binary32)) sinTheta_i))) (neg.f32 sinTheta_i))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/.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))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/.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))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/.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))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/.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))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/.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))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/.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))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/.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))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
(/.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))
(/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))
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(+ (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))))) (pow v 2))))))
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(+ (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))) (pow v 2))))))))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 #s(literal -1 binary32) v))))
(+ (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))))) v)))
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(+ (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))))) (pow v 2))))))
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(+ (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))) (pow v 2))))))))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v))))
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(fma.f32 cosTheta_O (/.f32 (*.f32 cosTheta_i (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v))))) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v)))))
(+ (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))) (* cosTheta_i (+ (* 1/2 (/ (* (pow cosTheta_O 2) (* cosTheta_i (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))))) (pow v 2))) (/ (* cosTheta_O (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v)))) v))))
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(+ (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))) (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ (* (pow cosTheta_O 3) (* cosTheta_i (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_O 2) (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v)))) (pow v 2))))) (/ (* cosTheta_O (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v)))) v))))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
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(exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v)))
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(+ (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))) (* cosTheta_O (+ (* 1/2 (/ (* cosTheta_O (* (pow cosTheta_i 2) (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))))) (pow v 2))) (/ (* cosTheta_i (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v)))) v))))
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(+ (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))) (* cosTheta_O (+ (* cosTheta_O (+ (* 1/6 (/ (* cosTheta_O (* (pow cosTheta_i 3) (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_i 2) (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v)))) (pow v 2))))) (/ (* cosTheta_i (exp (- (+ 6931/10000 (* -1 (/ (* sinTheta_O sinTheta_i) v))) (/ 1 v)))) v))))
(fma.f32 cosTheta_O (fma.f32 cosTheta_O (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v)))) (.f32 cosTheta_i cosTheta_i)) (.f32 v v)) (/.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 cosTheta_i cosTheta_i))) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v)))))) (.f32 v (.f32 v v)))) (/.f32 (*.f32 cosTheta_i (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v))))) v)) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 #s(literal -1 binary32) v)))))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp (- (+ 6931/10000 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (-.f32 #s(literal 0 binary32) (/.f32 sinTheta_i v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 #s(literal -1 binary32) v)))
(exp 6931/10000)
(exp.f32 #s(literal 6931/10000 binary32))
(+ (exp 6931/10000) (/ (* (exp 6931/10000) (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1)) v))
(fma.f32 (exp.f32 #s(literal 6931/10000 binary32)) (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))) v) (exp.f32 #s(literal 6931/10000 binary32)))
(+ (exp 6931/10000) (+ (* 1/2 (/ (* (exp 6931/10000) (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2)) (pow v 2))) (/ (* (exp 6931/10000) (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1)) v)))
(+.f32 (exp.f32 #s(literal 6931/10000 binary32)) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))))) (.f32 v v)) (/.f32 (.f32 (exp.f32 #s(literal 6931/10000 binary32)) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)))) v)))
(+ (exp 6931/10000) (+ (* 1/6 (/ (* (exp 6931/10000) (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 3)) (pow v 3))) (+ (* 1/2 (/ (* (exp 6931/10000) (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2)) (pow v 2))) (/ (* (exp 6931/10000) (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1)) v))))
(+.f32 (exp.f32 #s(literal 6931/10000 binary32)) (fma.f32 #s(literal 1/6 binary32) (/.f32 (.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))) (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)))))) (.f32 v (.f32 v v))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))))) (.f32 v v)) (/.f32 (*.f32 (exp.f32 #s(literal 6931/10000 binary32)) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)))) v))))
(exp 6931/10000)
(exp.f32 #s(literal 6931/10000 binary32))
(+ (exp 6931/10000) (* -1 (/ (* (exp 6931/10000) (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))))) v)))
(fma.f32 (exp.f32 #s(literal 6931/10000 binary32)) (-.f32 #s(literal 0 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i))) v)) (exp.f32 #s(literal 6931/10000 binary32)))
(+ (exp 6931/10000) (* -1 (/ (+ (* -1/2 (/ (* (exp 6931/10000) (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 2)) v)) (* (exp 6931/10000) (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))))) v)))
(-.f32 (exp.f32 #s(literal 6931/10000 binary32)) (/.f32 (fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_O cosTheta_i))) (-.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_O cosTheta_i))))) v) (.f32 (exp.f32 #s(literal 6931/10000 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_O cosTheta_i))))) v))
(+ (exp 6931/10000) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp 6931/10000) (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 3)) v)) (* 1/2 (* (exp 6931/10000) (pow (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))) 2)))) v)) (* (exp 6931/10000) (+ 1 (* -1 (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)))))) v)))
(-.f32 (exp.f32 #s(literal 6931/10000 binary32)) (/.f32 (fma.f32 (exp.f32 #s(literal 6931/10000 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_O cosTheta_i))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_O cosTheta_i))) (-.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_O cosTheta_i))))) (.f32 #s(literal -1/6 binary32) (/.f32 (.f32 (exp.f32 #s(literal 6931/10000 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_O cosTheta_i))) (.f32 (-.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_O cosTheta_i))) (-.f32 #s(literal 1 binary32) (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_O cosTheta_i)))))) v))) (neg.f32 v))) v))
(/ 1 v)
(/.f32 #s(literal 1 binary32) v)
(/ (+ 1 (* -6931/10000 v)) v)
(/.f32 (fma.f32 v #s(literal -6931/10000 binary32) #s(literal 1 binary32)) v)
(/ (+ 1 (* -6931/10000 v)) v)
(/.f32 (fma.f32 v #s(literal -6931/10000 binary32) #s(literal 1 binary32)) v)
(/ (+ 1 (* -6931/10000 v)) v)
(/.f32 (fma.f32 v #s(literal -6931/10000 binary32) #s(literal 1 binary32)) v)
-6931/10000
#s(literal -6931/10000 binary32)
(- (/ 1 v) 6931/10000)
(+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))
(- (/ 1 v) 6931/10000)
(+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))
(- (/ 1 v) 6931/10000)
(+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))
-6931/10000
#s(literal -6931/10000 binary32)
(- (/ 1 v) 6931/10000)
(+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))
(- (/ 1 v) 6931/10000)
(+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))
(- (/ 1 v) 6931/10000)
(+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))
(/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))
(/.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))
(+ (* -48038761/100000000 (/ (* sinTheta_O sinTheta_i) (* v (pow (+ 6931/10000 (/ 1 v)) 2)))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))
(fma.f32 #s(literal -48038761/100000000 binary32) (/.f32 (.f32 sinTheta_O sinTheta_i) (.f32 v (*.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))) (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))
(+ (* sinTheta_O (- (* 48038761/100000000 (/ (* sinTheta_O (pow sinTheta_i 2)) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 3)))) (* 48038761/100000000 (/ sinTheta_i (* v (pow (+ 6931/10000 (/ 1 v)) 2)))))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))
(fma.f32 sinTheta_O (.f32 #s(literal 48038761/100000000 binary32) (fma.f32 sinTheta_O (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (.f32 v v) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (neg.f32 (/.f32 sinTheta_i (.f32 v (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))))) (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))
(+ (* sinTheta_O (- (* sinTheta_O (- (* -48038761/100000000 (/ (* sinTheta_O (pow sinTheta_i 3)) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 4)))) (* -48038761/100000000 (/ (pow sinTheta_i 2) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 3)))))) (* 48038761/100000000 (/ sinTheta_i (* v (pow (+ 6931/10000 (/ 1 v)) 2)))))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))
(fma.f32 sinTheta_O (fma.f32 sinTheta_O (.f32 #s(literal -48038761/100000000 binary32) (-.f32 (/.f32 (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_i sinTheta_i))) (.f32 (.f32 v (.f32 v v)) (pow.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) #s(literal 4 binary32)))) (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (.f32 v v) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))))) (.f32 #s(literal -48038761/100000000 binary32) (/.f32 sinTheta_i (.f32 v (*.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))))) (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))
(* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))
(.f32 #s(literal 48038761/100000000 binary32) (/.f32 v (.f32 sinTheta_O sinTheta_i)))
(/ (+ (* -48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* sinTheta_O (pow sinTheta_i 2)))) (* 48038761/100000000 (/ v sinTheta_i))) sinTheta_O)
(/.f32 (fma.f32 #s(literal -48038761/100000000 binary32) (/.f32 (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))) (.f32 sinTheta_O (.f32 sinTheta_i sinTheta_i))) (/.f32 (*.f32 #s(literal 48038761/100000000 binary32) v) sinTheta_i)) sinTheta_O)
(/ (- (+ (* 48038761/100000000 (/ v sinTheta_i)) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 2) (pow sinTheta_i 3))))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* sinTheta_O (pow sinTheta_i 2))))) sinTheta_O)
(/.f32 (fma.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 v sinTheta_i) (.f32 (.f32 v (.f32 v v)) (/.f32 (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))) (.f32 (.f32 sinTheta_i (.f32 sinTheta_i sinTheta_i)) (.f32 sinTheta_O sinTheta_O))))) (.f32 #s(literal -48038761/100000000 binary32) (/.f32 (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))) (.f32 sinTheta_O (*.f32 sinTheta_i sinTheta_i))))) sinTheta_O)
(/ (- (+ (* -48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* (pow sinTheta_O 3) (pow sinTheta_i 4)))) (* 48038761/100000000 (/ v sinTheta_i))) (+ (* -48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 2) (pow sinTheta_i 3)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* sinTheta_O (pow sinTheta_i 2)))))) sinTheta_O)
(/.f32 (-.f32 (fma.f32 #s(literal -48038761/100000000 binary32) (.f32 (pow.f32 v #s(literal 4 binary32)) (/.f32 (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (.f32 (.f32 sinTheta_O (.f32 sinTheta_O sinTheta_O)) (pow.f32 sinTheta_i #s(literal 4 binary32))))) (/.f32 (.f32 #s(literal 48038761/100000000 binary32) v) sinTheta_i)) (fma.f32 #s(literal -48038761/100000000 binary32) (.f32 (.f32 v (.f32 v v)) (/.f32 (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))) (.f32 (.f32 sinTheta_i (.f32 sinTheta_i sinTheta_i)) (.f32 sinTheta_O sinTheta_O)))) (.f32 #s(literal 48038761/100000000 binary32) (/.f32 (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))) (.f32 sinTheta_O (.f32 sinTheta_i sinTheta_i)))))) sinTheta_O)
(* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))
(.f32 #s(literal 48038761/100000000 binary32) (/.f32 v (.f32 sinTheta_O sinTheta_i)))
(* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_i)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* sinTheta_O (pow sinTheta_i 2))))) sinTheta_O))
(/.f32 (fma.f32 #s(literal 48038761/100000000 binary32) (/.f32 (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))) (.f32 sinTheta_O (.f32 sinTheta_i sinTheta_i))) (/.f32 (*.f32 #s(literal -48038761/100000000 binary32) v) sinTheta_i)) (neg.f32 sinTheta_O))
(* -1 (/ (+ (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* sinTheta_O (pow sinTheta_i 3)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_i 2)))) sinTheta_O)) (* -48038761/100000000 (/ v sinTheta_i))) sinTheta_O))
(/.f32 (fma.f32 #s(literal -48038761/100000000 binary32) (/.f32 v sinTheta_i) (/.f32 (.f32 #s(literal 48038761/100000000 binary32) (fma.f32 (.f32 v (.f32 v v)) (/.f32 (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_i sinTheta_i)))) (neg.f32 (/.f32 (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))) (.f32 sinTheta_i sinTheta_i))))) (neg.f32 sinTheta_O))) (neg.f32 sinTheta_O))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* sinTheta_O (pow sinTheta_i 4)))) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (pow sinTheta_i 3)))) sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_i 2)))) sinTheta_O)) (* -48038761/100000000 (/ v sinTheta_i))) sinTheta_O))
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(/.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))
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(* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))
(.f32 #s(literal 48038761/100000000 binary32) (/.f32 v (.f32 sinTheta_O sinTheta_i)))
(/ (+ (* -48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i))) (* 48038761/100000000 (/ v sinTheta_O))) sinTheta_i)
(/.f32 (fma.f32 #s(literal -48038761/100000000 binary32) (/.f32 (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))) (.f32 sinTheta_i (.f32 sinTheta_O sinTheta_O))) (*.f32 #s(literal 48038761/100000000 binary32) (/.f32 v sinTheta_O))) sinTheta_i)
(/ (- (+ (* 48038761/100000000 (/ v sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) (pow sinTheta_i 2))))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i)))) sinTheta_i)
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(/ (- (+ (* -48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* (pow sinTheta_O 4) (pow sinTheta_i 3)))) (* 48038761/100000000 (/ v sinTheta_O))) (+ (* -48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) (pow sinTheta_i 2)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i))))) sinTheta_i)
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(* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))
(.f32 #s(literal 48038761/100000000 binary32) (/.f32 v (.f32 sinTheta_O sinTheta_i)))
(* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i)))) sinTheta_i))
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(* -1 (/ (+ (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) sinTheta_i))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_O 2)))) sinTheta_i)) (* -48038761/100000000 (/ v sinTheta_O))) sinTheta_i))
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6931/10000
#s(literal 6931/10000 binary32)
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#s(literal 6931/10000 binary32)
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1
#s(literal 1 binary32)
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(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (+ (* sinTheta_i (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (+ (* 1/2 (pow (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 2)) (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))))))
(fma.f32 sinTheta_i (fma.f32 (exp.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))) (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (.f32 (.f32 sinTheta_i (exp.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (fma.f32 #s(literal 1/2 binary32) (pow.f32 (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) #s(literal 2 binary32)) (-.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (.f32 sinTheta_O (/.f32 (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)))))))) (exp.f32 (/.f32 #s(literal 1 binary32) (.f32 (*.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (+ (* sinTheta_i (+ (* sinTheta_i (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* -1 (/ (* sinTheta_O (- (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))) (* v (+ 6931/10000 (/ 1 v))))) (+ (* 1/6 (pow (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 3)) (* (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (- (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v)))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (+ (* 1/2 (pow (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) 2)) (/ (pow sinTheta_O 2) (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ (* sinTheta_O (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* v (+ 6931/10000 (/ 1 v)))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (- (* 2 (/ sinTheta_O (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (/ sinTheta_O (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))))))
(fma.f32 sinTheta_i (fma.f32 sinTheta_i (fma.f32 (.f32 sinTheta_i (exp.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (fma.f32 (neg.f32 sinTheta_O) (/.f32 (-.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (.f32 sinTheta_O (/.f32 (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32))))) (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32))) (fma.f32 (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (-.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (.f32 sinTheta_O (/.f32 (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32))))) (.f32 #s(literal 1/6 binary32) (pow.f32 (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) #s(literal 3 binary32))))) (.f32 (exp.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))) (fma.f32 #s(literal 1/2 binary32) (pow.f32 (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) #s(literal 2 binary32)) (-.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (.f32 sinTheta_O (/.f32 (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))) (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)))))))) (.f32 (exp.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))) (-.f32 (/.f32 (.f32 #s(literal 2 binary32) sinTheta_O) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (/.f32 sinTheta_O (.f32 (.f32 v (.f32 v v)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))))))) (exp.f32 (/.f32 #s(literal 1 binary32) (.f32 (*.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 (*.f32 v v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 (*.f32 v v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 (*.f32 v v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 (*.f32 v v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 (*.f32 v v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 (*.f32 v v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 (*.f32 v v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))
(exp (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp.f32 (/.f32 (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) (.f32 (*.f32 v v) (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))

eval427.0ms (2.3%)

Memory: 22.1MiB live, 414.0MiB allocated
Compiler: Compiled 92 107 to 7 815 computations (91.5% saved)

prune573.0ms (3.2%)

Memory

-12.4MiB live, 396.4MiB allocated

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	2 338	13	2 351
Fresh	7	3	10
Picked	3	2	5
Done	0	0	0
Total	2 348	18	2 366

Accuracy

99.9%

Counts

2 366 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	93.5%	(/.f32 (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_O (neg.f32 sinTheta_i)) v)) (.f32 v #s(literal 2 binary32))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
▶	4.6%	(/.f32 (*.f32 (exp.f32 #s(literal 6931/10000 binary32)) #s(literal 1/2 binary32)) v)
	99.8%	(/.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)
	99.8%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 #s(literal 1 binary32) (exp.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)) (/.f32 (fma.f32 cosTheta_i cosTheta_O (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i))) v)))))))
	99.8%	(/.f32 #s(literal 1 binary32) (.f32 (.f32 v #s(literal 2 binary32)) (exp.f32 (neg.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (-.f32 #s(literal 0 binary32) (*.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) v) #s(literal 6931/10000 binary32))))))
	36.6%	(/.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) (+.f32 (/.f32 v (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 #s(literal -1 binary32) v))))) (/.f32 (.f32 sinTheta_O sinTheta_i) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 #s(literal -1 binary32) v))))))))
	47.8%	(.f32 (/.f32 #s(literal 1/2 binary32) v) (pow.f32 (exp.f32 (/.f32 (-.f32 #s(literal 48038761/100000000 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 v v)))) (-.f32 #s(literal 48038761/100000000 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (*.f32 v v)))))) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
	99.4%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (pow.f32 (exp.f32 #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
	99.4%	(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 v v)) (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal -6931/10000 binary32)))) (exp.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal -6931/10000 binary32))))))
▶	99.4%	(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 #s(literal 1 binary32) (.f32 v v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))))
	99.7%	(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 binary32) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))) (exp.f32 (/.f32 (.f32 (/.f32 #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 v (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))))))
▶	99.8%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
▶	99.4%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 #s(literal 1 binary32) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))))
	98.6%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))
	98.6%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
✓	99.4%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
✓	4.6%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 #s(literal 6931/10000 binary32)))
▶	99.8%	(.f32 (exp.f32 (neg.f32 (log.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)) v))))

Compiler

Compiled 862 to 581 computations (32.6% saved)

simplify348.0ms (1.9%)

Memory

3.9MiB live, 198.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 #s(literal 1/2 binary32) v)
✓	cost-diff	96	(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))
✓	cost-diff	160	(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 v v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))
✓	cost-diff	3456	(/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 #s(literal 1 binary32) (*.f32 v v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))))
✓	cost-diff	0	(exp.f32 #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) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
✓	cost-diff	3456	(/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
✓	cost-diff	0	(+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))
✓	cost-diff	0	(exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))
✓	cost-diff	0	(/.f32 #s(literal 1/2 binary32) v)
✓	cost-diff	352	(/.f32 #s(literal 1 binary32) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
✓	cost-diff	-32	(/.f32 (*.f32 (exp.f32 #s(literal 6931/10000 binary32)) #s(literal 1/2 binary32)) v)
✓	cost-diff	0	(exp.f32 #s(literal 6931/10000 binary32))
✓	cost-diff	0	(*.f32 (exp.f32 #s(literal 6931/10000 binary32)) #s(literal 1/2 binary32))
✓	cost-diff	0	(log.f32 (*.f32 v #s(literal 2 binary32)))
✓	cost-diff	0	(neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32))))
✓	cost-diff	0	(.f32 (exp.f32 (neg.f32 (log.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)) v))))
✓	cost-diff	6304	(exp.f32 (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))

Rules

3 008×	`-lowering-.f32`
3 008×	`-lowering-.f64`
2 836×	`/-lowering-/.f32`
2 836×	`/-lowering-/.f64`
1 968×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	356
1	91	342
2	175	329
3	433	328
4	1482	328
5	4285	328
6	7382	328
0	8505	308

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (exp (neg (log (* v 2)))) (exp (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) v))))
(exp (neg (log (* v 2))))
(neg (log (* v 2)))
(log (* v 2))
(* v 2)
v
2
(exp (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) v)))
(- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) v))
6931/10000
(/ (+ (* sinTheta_O sinTheta_i) 1) v)
(+ (* sinTheta_O sinTheta_i) 1)
sinTheta_O
sinTheta_i
1
(/ (* (exp 6931/10000) 1/2) v)
(* (exp 6931/10000) 1/2)
(exp 6931/10000)
6931/10000
1/2
v
(* (/ 1/2 v) (/ 1 (exp (+ (/ 1 v) -6931/10000))))
(/ 1/2 v)
1/2
v
(/ 1 (exp (+ (/ 1 v) -6931/10000)))
1
(exp (+ (/ 1 v) -6931/10000))
(+ (/ 1 v) -6931/10000)
(/ 1 v)
-6931/10000
(* (/ 1/2 v) (/ (exp 6931/10000) (exp (/ (+ (* sinTheta_O sinTheta_i) 1) v))))
(/ 1/2 v)
1/2
v
(/ (exp 6931/10000) (exp (/ (+ (* sinTheta_O sinTheta_i) 1) v)))
(exp 6931/10000)
6931/10000
(exp (/ (+ (* sinTheta_O sinTheta_i) 1) v))
(/ (+ (* sinTheta_O sinTheta_i) 1) v)
(+ (* sinTheta_O sinTheta_i) 1)
sinTheta_O
sinTheta_i
1
(* (/ 1/2 v) (/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))))))
(/ 1/2 v)
1/2
v
(/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))))
(exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))))
(/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))
48038761/100000000
(- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))
6931/10000
(/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))
(+ (* sinTheta_O sinTheta_i) 1)
sinTheta_O
sinTheta_i
1
(neg v)
(exp (/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))))
(/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))
(/ 1 (* v v))
(* v v)

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

localize277.0ms (1.5%)

Memory

-11.5MiB live, 263.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(exp.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 v v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))
✓	accuracy	99.5%	(/.f32 #s(literal 1 binary32) (*.f32 v v))
✓	accuracy	98.7%	(/.f32 #s(literal 48038761/100000000 binary32) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))
✓	accuracy	54.2%	(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 v v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))
✓	accuracy	100.0%	(/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)
✓	accuracy	100.0%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
✓	accuracy	100.0%	(/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
✓	accuracy	99.8%	(exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
✓	accuracy	100.0%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 #s(literal 1 binary32) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))))
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
✓	accuracy	99.9%	(+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))
✓	accuracy	99.8%	(exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))
✓	accuracy	100.0%	(*.f32 (exp.f32 #s(literal 6931/10000 binary32)) #s(literal 1/2 binary32))
✓	accuracy	100.0%	(exp.f32 #s(literal 6931/10000 binary32))
✓	accuracy	98.9%	(/.f32 (*.f32 (exp.f32 #s(literal 6931/10000 binary32)) #s(literal 1/2 binary32)) v)
✓	accuracy	100.0%	(.f32 (exp.f32 (neg.f32 (log.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)) v))))
✓	accuracy	99.9%	(-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))
✓	accuracy	99.8%	(exp.f32 (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)))
✓	accuracy	90.3%	(exp.f32 (neg.f32 (log.f32 (*.f32 v #s(literal 2 binary32)))))

Samples

166.0ms

256×

valid

Compiler

Compiled 333 to 46 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 145.0ms

ival-exp: 62.0ms (42.9% of total)

ival-div: 39.0ms (27% of total)

ival-mult: 23.0ms (15.9% of total)

const: 10.0ms (6.9% of total)

ival-log: 3.0ms (2.1% of total)

ival-add: 2.0ms (1.4% of total)

ival-sub: 2.0ms (1.4% of total)

ival-neg: 2.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series92.0ms (0.5%)

Memory

16.9MiB live, 149.3MiB allocated

Counts

24 → 552

Calls

Call 1

Inputs
#<alt (exp (neg (log (* v 2))))>
#<alt (* (exp (neg (log (* v 2)))) (exp (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) v))))>
#<alt (neg (log (* v 2)))>
#<alt (log (* v 2))>
#<alt (* (exp 6931/10000) 1/2)>
#<alt (exp 6931/10000)>
#<alt (/ (* (exp 6931/10000) 1/2) v)>
#<alt (/ 1 (exp (+ (/ 1 v) -6931/10000)))>
#<alt (/ 1/2 v)>
#<alt (exp (+ (/ 1 v) -6931/10000))>
#<alt (+ (/ 1 v) -6931/10000)>
#<alt (/ (exp 6931/10000) (exp (/ (+ (* sinTheta_O sinTheta_i) 1) v)))>
#<alt (* (/ 1/2 v) (/ (exp 6931/10000) (exp (/ (+ (* sinTheta_O sinTheta_i) 1) v))))>
#<alt (/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))))>
#<alt (/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))>
#<alt (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))>
#<alt (exp (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) v)))>
#<alt (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) v))>
#<alt (* (/ 1/2 v) (/ 1 (exp (+ (/ 1 v) -6931/10000))))>
#<alt (exp (/ (+ (* sinTheta_O sinTheta_i) 1) v))>
#<alt (/ (+ (* sinTheta_O sinTheta_i) 1) v)>
#<alt (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))>
#<alt (/ 1 (* v v))>
#<alt (exp (/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))))>

Outputs
#<alt (exp (neg (+ (log 2) (log v))))>
#<alt (exp (neg (+ (log 2) (log v))))>
#<alt (exp (neg (+ (log 2) (log v))))>
#<alt (exp (neg (+ (log 2) (log v))))>
#<alt (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))>
#<alt (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))>
#<alt (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))>
#<alt (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))>
#<alt (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))>
#<alt (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))>
#<alt (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))>
#<alt (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))>
#<alt (* (exp (neg (+ (log 2) (log v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt (* (exp (neg (+ (log 2) (log v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt (* (exp (neg (+ (log 2) (log v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt (* (exp (neg (+ (log 2) (log v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))))>
#<alt (+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))))>
#<alt (+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (+ (* 1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))))))>
#<alt (+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (+ (* -1/6 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) (pow v 3))) (+ (* 1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))))))>
#<alt (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))))>
#<alt (+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v)) (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) v)) (* 1/2 (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) v)) (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))>
#<alt (+ (* -1 (/ (* sinTheta_O (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) v)) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))>
#<alt (+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 2))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))>
#<alt (+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) (pow v 2))))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))>
#<alt (+ (* -1 (/ (* sinTheta_O (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) v)) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))>
#<alt (+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 2))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))>
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#<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)))>
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#<alt 6931/10000>
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#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
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#<alt (/ 1/2 (* v (exp (- (/ 1 v) 6931/10000))))>
#<alt (/ 1/2 (* v (exp (- (/ 1 v) 6931/10000))))>
#<alt (/ 1/2 (* v (exp (- (/ 1 v) 6931/10000))))>
#<alt (/ 1/2 (* v (exp -6931/10000)))>
#<alt (/ (- (* 1/2 (/ 1 (exp -6931/10000))) (* 1/2 (/ 1 (* v (exp -6931/10000))))) v)>
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#<alt (/ (- (+ (* 1/2 (/ 1 (exp -6931/10000))) (* 1/4 (/ 1 (* (pow v 2) (exp -6931/10000))))) (+ (/ 1/2 (* v (exp -6931/10000))) (* 1/12 (/ 1 (* (pow v 3) (exp -6931/10000)))))) v)>
#<alt (/ 1/2 (* v (exp -6931/10000)))>
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#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 (* v (exp -6931/10000)))) (* 1/4 (/ 1 (exp -6931/10000)))) v)) (* 1/2 (/ 1 (exp -6931/10000)))) v)) (* 1/2 (/ 1 (exp -6931/10000)))) v))>
#<alt (exp (/ 1 v))>
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#<alt (+ (exp (/ 1 v)) (* sinTheta_O (+ (* sinTheta_O (+ (* 1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (/ 1 v)))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (/ 1 v))) (pow v 2))))) (/ (* sinTheta_i (exp (/ 1 v))) v))))>
#<alt (exp (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
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#<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 v))>
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#<alt (+ (exp (/ 1 v)) (* sinTheta_i (+ (* sinTheta_i (+ (* 1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (/ 1 v)))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (/ 1 v))) (pow v 2))))) (/ (* sinTheta_O (exp (/ 1 v))) v))))>
#<alt (exp (/ (+ 1 (* sinTheta_O sinTheta_i)) v))>
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#<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 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (+ 1 (+ (* 1/2 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt (+ 1 (+ (* 1/6 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) (pow v 3))) (+ (* 1/2 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))>
#<alt 1>
#<alt (+ 1 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* -1/2 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) v))) v)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (+ 1 (* sinTheta_O sinTheta_i))) (* -1 (/ (+ (* 1/6 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) v)) (* 1/2 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v))) v)))>
#<alt (/ 1 v)>
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#<alt (* -1 (* sinTheta_O (- (* -1 (/ sinTheta_i v)) (/ 1 (* sinTheta_O v)))))>
#<alt (/ 1 v)>
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#<alt (/ (+ 1 (* sinTheta_O sinTheta_i)) v)>
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#<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 (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))>
#<alt (+ (* -48038761/100000000 (/ (* sinTheta_O sinTheta_i) (* v (pow (+ 6931/10000 (/ 1 v)) 2)))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))>
#<alt (+ (* sinTheta_O (- (* 48038761/100000000 (/ (* sinTheta_O (pow sinTheta_i 2)) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 3)))) (* 48038761/100000000 (/ sinTheta_i (* v (pow (+ 6931/10000 (/ 1 v)) 2)))))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))>
#<alt (+ (* sinTheta_O (- (* sinTheta_O (- (* -48038761/100000000 (/ (* sinTheta_O (pow sinTheta_i 3)) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 4)))) (* -48038761/100000000 (/ (pow sinTheta_i 2) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 3)))))) (* 48038761/100000000 (/ sinTheta_i (* v (pow (+ 6931/10000 (/ 1 v)) 2)))))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))>
#<alt (* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))>
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#<alt (/ (- (+ (* -48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* (pow sinTheta_O 3) (pow sinTheta_i 4)))) (* 48038761/100000000 (/ v sinTheta_i))) (+ (* -48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 2) (pow sinTheta_i 3)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* sinTheta_O (pow sinTheta_i 2)))))) sinTheta_O)>
#<alt (* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))>
#<alt (* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_i)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* sinTheta_O (pow sinTheta_i 2))))) sinTheta_O))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* sinTheta_O (pow sinTheta_i 3)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_i 2)))) sinTheta_O)) (* -48038761/100000000 (/ v sinTheta_i))) sinTheta_O))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* sinTheta_O (pow sinTheta_i 4)))) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (pow sinTheta_i 3)))) sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_i 2)))) sinTheta_O)) (* -48038761/100000000 (/ v sinTheta_i))) sinTheta_O))>
#<alt (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))>
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#<alt (+ (* sinTheta_i (- (* sinTheta_i (- (* -48038761/100000000 (/ (* (pow sinTheta_O 3) sinTheta_i) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 4)))) (* -48038761/100000000 (/ (pow sinTheta_O 2) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 3)))))) (* 48038761/100000000 (/ sinTheta_O (* v (pow (+ 6931/10000 (/ 1 v)) 2)))))) (* 48038761/100000000 (/ 1 (+ 6931/10000 (/ 1 v)))))>
#<alt (* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))>
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#<alt (/ (- (+ (* 48038761/100000000 (/ v sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) (pow sinTheta_i 2))))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i)))) sinTheta_i)>
#<alt (/ (- (+ (* -48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* (pow sinTheta_O 4) (pow sinTheta_i 3)))) (* 48038761/100000000 (/ v sinTheta_O))) (+ (* -48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) (pow sinTheta_i 2)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i))))) sinTheta_i)>
#<alt (* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))>
#<alt (* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i)))) sinTheta_i))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) sinTheta_i))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_O 2)))) sinTheta_i)) (* -48038761/100000000 (/ v sinTheta_O))) sinTheta_i))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* (pow sinTheta_O 4) sinTheta_i))) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (pow sinTheta_O 3)))) sinTheta_i)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_O 2)))) sinTheta_i)) (* -48038761/100000000 (/ v sinTheta_O))) sinTheta_i))>
#<alt (* 48038761/100000000 (/ v (+ 1 (* sinTheta_O sinTheta_i))))>
#<alt (* v (+ (* -332956652491/1000000000000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (* 48038761/100000000 (/ 1 (+ 1 (* sinTheta_O sinTheta_i))))))>
#<alt (* v (+ (* v (- (* 2307722558415121/10000000000000000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) (* 332956652491/1000000000000 (/ 1 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) (* 48038761/100000000 (/ 1 (+ 1 (* sinTheta_O sinTheta_i))))))>
#<alt (* v (+ (* v (- (* v (+ (* -15994825052375203651/100000000000000000000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 4))) (* 2307722558415121/10000000000000000 (/ 1 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))))) (* 332956652491/1000000000000 (/ 1 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) (* 48038761/100000000 (/ 1 (+ 1 (* sinTheta_O sinTheta_i))))))>
#<alt 6931/10000>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (- (+ 6931/10000 (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2)))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))>
#<alt (- (+ 6931/10000 (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) (pow v 3)))) (+ (* -10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))>
#<alt 6931/10000>
#<alt (+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))>
#<alt (+ 6931/10000 (* -1 (/ (- (* -10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) v)) (* -1 (+ 1 (* sinTheta_O sinTheta_i)))) v)))>
#<alt (+ 6931/10000 (* -1 (/ (- (* -1 (/ (- (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) v)) (* -10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v)) (* -1 (+ 1 (* sinTheta_O sinTheta_i)))) v)))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
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#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (/ 1 (pow v 2))>
#<alt (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))>
#<alt 1>
#<alt (+ 1 (* 10000/6931 (/ 1 (pow v 2))))>
#<alt (+ 1 (+ (* -100000000/48038761 (/ (+ 1 (* sinTheta_O sinTheta_i)) (pow v 3))) (* 10000/6931 (/ 1 (pow v 2)))))>
#<alt (+ 1 (+ (* -100000000/48038761 (/ (+ 1 (* sinTheta_O sinTheta_i)) (pow v 3))) (+ (* 1000000000000/332956652491 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 4))) (+ (* 10000/6931 (/ 1 (pow v 2))) (* 50000000/48038761 (/ 1 (pow v 4)))))))>
#<alt 1>
#<alt (+ 1 (* 10000/6931 (/ 1 (pow v 2))))>
#<alt (+ 1 (+ (* -100000000/48038761 (/ (+ 1 (* sinTheta_O sinTheta_i)) (pow v 3))) (* 10000/6931 (/ 1 (pow v 2)))))>
#<alt (+ 1 (+ (* -1 (/ (+ (* -1 (/ (+ 50000000/48038761 (* 1000000000000/332956652491 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v)) (* 100000000/48038761 (+ 1 (* sinTheta_O sinTheta_i)))) (pow v 3))) (* 10000/6931 (/ 1 (pow v 2)))))>
#<alt (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))>
#<alt (+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))))>
#<alt (+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (* sinTheta_O (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* 1/2 (/ (pow sinTheta_i 2) (* (pow v 6) (pow (+ 6931/10000 (/ 1 v)) 4)))) (/ (pow sinTheta_i 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)))))))))>
#<alt (+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (* sinTheta_O (+ (* sinTheta_O (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* -1 (/ (pow sinTheta_i 3) (* (pow v 5) (pow (+ 6931/10000 (/ 1 v)) 4)))) (+ (* -1 (/ (pow sinTheta_i 3) (* (pow v 7) (pow (+ 6931/10000 (/ 1 v)) 5)))) (* -1/6 (/ (pow sinTheta_i 3) (* (pow v 9) (pow (+ 6931/10000 (/ 1 v)) 6)))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* 1/2 (/ (pow sinTheta_i 2) (* (pow v 6) (pow (+ 6931/10000 (/ 1 v)) 4)))) (/ (pow sinTheta_i 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3))))))))))>
#<alt 1>
#<alt (+ 1 (/ 1 (* sinTheta_O (* sinTheta_i v))))>
#<alt (+ 1 (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))) (pow sinTheta_O 2))) (+ (/ 1 (* sinTheta_O (* sinTheta_i v))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (* (pow sinTheta_i 2) (pow v 2))))))))>
#<alt (+ 1 (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))) (* (pow sinTheta_O 3) (* sinTheta_i v)))) (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))) (pow sinTheta_O 2))) (+ (/ 1/6 (* (pow sinTheta_O 3) (* (pow sinTheta_i 3) (pow v 3)))) (+ (/ 1 (* sinTheta_O (* sinTheta_i v))) (+ (* 1/2 (/ 1 (* (pow sinTheta_O 2) (* (pow sinTheta_i 2) (pow v 2))))) (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))))) (* (pow sinTheta_O 3) sinTheta_i))))))))>
#<alt 1>
#<alt (+ 1 (/ 1 (* sinTheta_O (* sinTheta_i v))))>
#<alt (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1 (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2))))) (* 1/2 (/ 1 (* (pow sinTheta_i 2) (pow v 2))))) sinTheta_O)) (/ 1 (* sinTheta_i v))) sinTheta_O)))>
#<alt (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1 (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2))))) (+ (* -1 (/ (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))))) sinTheta_i)) (+ (* 6931/10000 (/ 1 (* (pow sinTheta_i 3) v))) (/ 1 (* (pow sinTheta_i 3) (pow v 2))))) (* 1/6 (/ 1 (* (pow sinTheta_i 3) (pow v 3))))) sinTheta_O)) (* 1/2 (/ 1 (* (pow sinTheta_i 2) (pow v 2)))))) sinTheta_O)) (/ 1 (* sinTheta_i v))) sinTheta_O)))>
#<alt (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))>
#<alt (+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))))>
#<alt (+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (* sinTheta_i (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* 1/2 (/ (pow sinTheta_O 2) (* (pow v 6) (pow (+ 6931/10000 (/ 1 v)) 4)))) (/ (pow sinTheta_O 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)))))))))>
#<alt (+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (* sinTheta_i (+ (* sinTheta_i (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* -1 (/ (pow sinTheta_O 3) (* (pow v 5) (pow (+ 6931/10000 (/ 1 v)) 4)))) (+ (* -1 (/ (pow sinTheta_O 3) (* (pow v 7) (pow (+ 6931/10000 (/ 1 v)) 5)))) (* -1/6 (/ (pow sinTheta_O 3) (* (pow v 9) (pow (+ 6931/10000 (/ 1 v)) 6)))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* 1/2 (/ (pow sinTheta_O 2) (* (pow v 6) (pow (+ 6931/10000 (/ 1 v)) 4)))) (/ (pow sinTheta_O 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3))))))))))>
#<alt 1>
#<alt (+ 1 (/ 1 (* sinTheta_O (* sinTheta_i v))))>
#<alt (+ 1 (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))) (pow sinTheta_i 2))) (+ (/ 1 (* sinTheta_O (* sinTheta_i v))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (* (pow sinTheta_i 2) (pow v 2))))))))>
#<alt (+ 1 (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))) (* sinTheta_O (* (pow sinTheta_i 3) v)))) (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))) (pow sinTheta_i 2))) (+ (/ 1/6 (* (pow sinTheta_O 3) (* (pow sinTheta_i 3) (pow v 3)))) (+ (/ 1 (* sinTheta_O (* sinTheta_i v))) (+ (* 1/2 (/ 1 (* (pow sinTheta_O 2) (* (pow sinTheta_i 2) (pow v 2))))) (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))))) (* sinTheta_O (pow sinTheta_i 3)))))))))>
#<alt 1>
#<alt (+ 1 (/ 1 (* sinTheta_O (* sinTheta_i v))))>
#<alt (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1 (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2))))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (pow v 2))))) sinTheta_i)) (/ 1 (* sinTheta_O v))) sinTheta_i)))>
#<alt (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1 (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2))))) (+ (* -1 (/ (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))))) sinTheta_O)) (+ (* 6931/10000 (/ 1 (* (pow sinTheta_O 3) v))) (/ 1 (* (pow sinTheta_O 3) (pow v 2))))) (* 1/6 (/ 1 (* (pow sinTheta_O 3) (pow v 3))))) sinTheta_i)) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (pow v 2)))))) sinTheta_i)) (/ 1 (* sinTheta_O v))) sinTheta_i)))>

Calls

138 calls:

Time	Variable		Point	Expression
27.0ms	sinTheta_i	@	0	(/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))))
4.0ms	sinTheta_O	@	0	(* (/ 1/2 v) (/ (exp 6931/10000) (exp (/ (+ (* sinTheta_O sinTheta_i) 1) v))))
3.0ms	sinTheta_i	@	inf	(/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))))
3.0ms	sinTheta_O	@	0	(/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))))
3.0ms	sinTheta_O	@	inf	(/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))))

rewrite486.0ms (2.7%)

Memory

-13.5MiB live, 901.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 904×	`/-lowering-/.f32`
4 904×	`/-lowering-/.f64`
4 498×	`-lowering-.f32`
4 498×	`-lowering-.f64`
3 756×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	227
1	214	191
2	1613	191
0	8562	179

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 953

Calls

Call 1

Inputs
(exp (neg (log (* v 2))))
(* (exp (neg (log (* v 2)))) (exp (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) v))))
(neg (log (* v 2)))
(log (* v 2))
(* (exp 6931/10000) 1/2)
(exp 6931/10000)
(/ (* (exp 6931/10000) 1/2) v)
(/ 1 (exp (+ (/ 1 v) -6931/10000)))
(/ 1/2 v)
(exp (+ (/ 1 v) -6931/10000))
(+ (/ 1 v) -6931/10000)
(/ (exp 6931/10000) (exp (/ (+ (* sinTheta_O sinTheta_i) 1) v)))
(* (/ 1/2 v) (/ (exp 6931/10000) (exp (/ (+ (* sinTheta_O sinTheta_i) 1) v))))
(/ (exp (/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))) (exp (/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))))
(/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))
(- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))
(exp (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) v)))
(- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) v))
(* (/ 1/2 v) (/ 1 (exp (+ (/ 1 v) -6931/10000))))
(exp (/ (+ (* sinTheta_O sinTheta_i) 1) v))
(/ (+ (* sinTheta_O sinTheta_i) 1) v)
(/ 48038761/100000000 (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v))))
(/ 1 (* v v))
(exp (/ (/ 1 (* v v)) (- 6931/10000 (/ (+ (* sinTheta_O sinTheta_i) 1) (neg v)))))

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

simplify460.0ms (2.5%)

Memory

27.0MiB live, 934.5MiB allocated

Algorithm

1×	egg-herbie

Rules

5 294×	`-lowering-.f32`
5 294×	`-lowering-.f64`
4 456×	`accelerator-lowering-fma.f32`
4 456×	`accelerator-lowering-fma.f64`
3 526×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1627	14233
1	5549	13903
0	8152	13304

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 552

Calls

Call 1

Inputs
(exp (neg (+ (log 2) (log v))))
(exp (neg (+ (log 2) (log v))))
(exp (neg (+ (log 2) (log v))))
(exp (neg (+ (log 2) (log v))))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(* (exp (neg (+ (log 2) (log v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (+ (log 2) (log v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (+ (log 2) (log v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (+ (log 2) (log v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))))
(+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))))
(+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (+ (* 1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))))))
(+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (+ (* -1/6 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) (pow v 3))) (+ (* 1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))))))
(* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))))
(+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))
(+ (* -1 (/ (+ (* -1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v)) (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) v)) (* 1/2 (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) v)) (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))
(+ (* -1 (/ (* sinTheta_O (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) v)) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))
(+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 2))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))
(+ (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) (pow v 2))))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))
(+ (* -1 (/ (* sinTheta_O (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) v)) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))
(+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 2))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))
(+ (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v))))) (pow v 2))))))) (* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (/ 1 v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* (exp (neg (log (* 2 v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(* -1 (+ (log 2) (log v)))
(* -1 (+ (log 2) (log v)))
(* -1 (+ (log 2) (log v)))
(* -1 (+ (log 2) (log v)))
(* -1 (+ (log 2) (* -1 (log (/ 1 v)))))
(* -1 (+ (log 2) (* -1 (log (/ 1 v)))))
(* -1 (+ (log 2) (* -1 (log (/ 1 v)))))
(* -1 (+ (log 2) (* -1 (log (/ 1 v)))))
(* -1 (+ (log -2) (* -1 (log (/ -1 v)))))
(* -1 (+ (log -2) (* -1 (log (/ -1 v)))))
(* -1 (+ (log -2) (* -1 (log (/ -1 v)))))
(* -1 (+ (log -2) (* -1 (log (/ -1 v)))))
(+ (log 2) (log v))
(+ (log 2) (log v))
(+ (log 2) (log v))
(+ (log 2) (log v))
(+ (log 2) (* -1 (log (/ 1 v))))
(+ (log 2) (* -1 (log (/ 1 v))))
(+ (log 2) (* -1 (log (/ 1 v))))
(+ (log 2) (* -1 (log (/ 1 v))))
(+ (log -2) (* -1 (log (/ -1 v))))
(+ (log -2) (* -1 (log (/ -1 v))))
(+ (log -2) (* -1 (log (/ -1 v))))
(+ (log -2) (* -1 (log (/ -1 v))))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(* 1/2 (/ (exp 6931/10000) v))
(/ 1 (exp (- (/ 1 v) 6931/10000)))
(/ 1 (exp (- (/ 1 v) 6931/10000)))
(/ 1 (exp (- (/ 1 v) 6931/10000)))
(/ 1 (exp (- (/ 1 v) 6931/10000)))
(/ 1 (exp -6931/10000))
(- (/ 1 (exp -6931/10000)) (/ 1 (* v (exp -6931/10000))))
(- (+ (/ 1/2 (* (pow v 2) (exp -6931/10000))) (/ 1 (exp -6931/10000))) (/ 1 (* v (exp -6931/10000))))
(- (+ (/ 1 (exp -6931/10000)) (* 1/2 (/ 1 (* (pow v 2) (exp -6931/10000))))) (+ (/ 1 (* v (exp -6931/10000))) (* 1/6 (/ 1 (* (pow v 3) (exp -6931/10000))))))
(/ 1 (exp -6931/10000))
(- (/ 1 (exp -6931/10000)) (/ 1 (* v (exp -6931/10000))))
(+ (* -1 (/ (- (/ 1 (exp -6931/10000)) (* 1/2 (/ 1 (* v (exp -6931/10000))))) v)) (/ 1 (exp -6931/10000)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 1/2 (/ 1 (exp -6931/10000))) (* 1/6 (/ 1 (* v (exp -6931/10000))))) v)) (/ 1 (exp -6931/10000))) v)) (/ 1 (exp -6931/10000)))
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(/ 1/2 v)
(exp (- (/ 1 v) 6931/10000))
(exp (- (/ 1 v) 6931/10000))
(exp (- (/ 1 v) 6931/10000))
(exp (- (/ 1 v) 6931/10000))
(exp -6931/10000)
(+ (exp -6931/10000) (/ (exp -6931/10000) v))
(+ (exp -6931/10000) (+ (* 1/2 (/ (exp -6931/10000) (pow v 2))) (/ (exp -6931/10000) v)))
(+ (exp -6931/10000) (+ (* 1/6 (/ (exp -6931/10000) (pow v 3))) (+ (* 1/2 (/ (exp -6931/10000) (pow v 2))) (/ (exp -6931/10000) v))))
(exp -6931/10000)
(+ (exp -6931/10000) (/ (exp -6931/10000) v))
(+ (exp -6931/10000) (* -1 (/ (+ (* -1 (exp -6931/10000)) (* -1/2 (/ (exp -6931/10000) v))) v)))
(+ (exp -6931/10000) (* -1 (/ (+ (* -1 (exp -6931/10000)) (* -1 (/ (+ (* 1/6 (/ (exp -6931/10000) v)) (* 1/2 (exp -6931/10000))) v))) v)))
(/ 1 v)
(/ (+ 1 (* -6931/10000 v)) v)
(/ (+ 1 (* -6931/10000 v)) v)
(/ (+ 1 (* -6931/10000 v)) v)
-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) 6931/10000)
(/ (exp 6931/10000) (exp (/ 1 v)))
(+ (* -1 (/ (* sinTheta_O (* sinTheta_i (exp 6931/10000))) (* v (exp (/ 1 v))))) (/ (exp 6931/10000) (exp (/ 1 v))))
(+ (* sinTheta_O (- (* -1 (* sinTheta_O (+ (* -1 (/ (* (pow sinTheta_i 2) (exp 6931/10000)) (* (pow v 2) (exp (/ 1 v))))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp 6931/10000)) (* (pow v 2) (exp (/ 1 v)))))))) (/ (* sinTheta_i (exp 6931/10000)) (* v (exp (/ 1 v)))))) (/ (exp 6931/10000) (exp (/ 1 v))))
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1
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1
(+ 1 (* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_i)) (/ 1 (* sinTheta_i v))) sinTheta_O)))
(+ 1 (* -1 (/ (+ (* -1 (/ (- (+ (* -48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_i 2))) (* 2307722558415121/20000000000000000 (/ (pow v 2) (pow sinTheta_i 2)))) (+ (* -1 (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2))))) (+ (* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_i)) (/ 1 (* sinTheta_i v))) (* sinTheta_i v))) (* 1/2 (/ 1 (* (pow sinTheta_i 2) (pow v 2))))))) sinTheta_O)) (+ (* -48038761/100000000 (/ v sinTheta_i)) (/ 1 (* sinTheta_i v)))) sinTheta_O)))
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(/ (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))) (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))))
(+ (* sinTheta_i (- (* -48038761/100000000 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* v (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* -1 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* (pow v 3) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))))) (/ (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))) (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))))
(+ (* sinTheta_i (- (+ (* -48038761/100000000 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* v (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* sinTheta_i (- (/ (* (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))) (+ (* 2307722558415121/20000000000000000 (/ (pow sinTheta_O 2) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 4)))) (* 48038761/100000000 (/ (pow sinTheta_O 2) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 3)))))) (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))) (+ (* -1 (/ (* sinTheta_O (- (* -48038761/100000000 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* v (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* -1 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* (pow v 3) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (/ (* (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))) (+ (* 1/2 (/ (pow sinTheta_O 2) (* (pow v 6) (pow (+ 6931/10000 (/ 1 v)) 4)))) (/ (pow sinTheta_O 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3))))) (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))))))) (* -1 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* (pow v 3) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))))) (/ (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))) (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))))
(+ (* sinTheta_i (- (+ (* -48038761/100000000 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* v (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* sinTheta_i (- (+ (* sinTheta_i (- (/ (* (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))) (+ (* -48038761/100000000 (/ (pow sinTheta_O 3) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 4)))) (+ (* -2307722558415121/10000000000000000 (/ (pow sinTheta_O 3) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 5)))) (* -110860132438012536505081/6000000000000000000000000 (/ (pow sinTheta_O 3) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 6))))))) (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))) (+ (* -1 (/ (* sinTheta_O (- (/ (* (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))) (+ (* 2307722558415121/20000000000000000 (/ (pow sinTheta_O 2) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 4)))) (* 48038761/100000000 (/ (pow sinTheta_O 2) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 3)))))) (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))) (+ (* -1 (/ (* sinTheta_O (- (* -48038761/100000000 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* v (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* -1 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* (pow v 3) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (/ (* (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))) (+ (* 1/2 (/ (pow sinTheta_O 2) (* (pow v 6) (pow (+ 6931/10000 (/ 1 v)) 4)))) (/ (pow sinTheta_O 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3))))) (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (+ (* (+ (* 1/2 (/ (pow sinTheta_O 2) (* (pow v 6) (pow (+ 6931/10000 (/ 1 v)) 4)))) (/ (pow sinTheta_O 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)))) (- (* -48038761/100000000 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* v (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* -1 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* (pow v 3) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))))) (/ (* (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))) (+ (* -1 (/ (pow sinTheta_O 3) (* (pow v 5) (pow (+ 6931/10000 (/ 1 v)) 4)))) (+ (* -1 (/ (pow sinTheta_O 3) (* (pow v 7) (pow (+ 6931/10000 (/ 1 v)) 5)))) (* -1/6 (/ (pow sinTheta_O 3) (* (pow v 9) (pow (+ 6931/10000 (/ 1 v)) 6))))))) (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))))))) (/ (* (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))) (+ (* 2307722558415121/20000000000000000 (/ (pow sinTheta_O 2) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 4)))) (* 48038761/100000000 (/ (pow sinTheta_O 2) (* (pow v 2) (pow (+ 6931/10000 (/ 1 v)) 3)))))) (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))))) (+ (* -1 (/ (* sinTheta_O (- (* -48038761/100000000 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* v (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))) (* -1 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* (pow v 3) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (/ (* (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))) (+ (* 1/2 (/ (pow sinTheta_O 2) (* (pow v 6) (pow (+ 6931/10000 (/ 1 v)) 4)))) (/ (pow sinTheta_O 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3))))) (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))))))) (* -1 (/ (* sinTheta_O (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v))))) (* (pow v 3) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (pow (+ 6931/10000 (/ 1 v)) 2))))))) (/ (exp (/ 48038761/100000000 (+ 6931/10000 (/ 1 v)))) (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))))
1
(- (+ 1 (* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))) (/ 1 (* sinTheta_O (* sinTheta_i v))))
(- (+ 1 (+ (* -48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) (pow sinTheta_i 2)))) (+ (* 2307722558415121/20000000000000000 (/ (pow v 2) (* (pow sinTheta_O 2) (pow sinTheta_i 2)))) (+ (* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (* (pow sinTheta_i 2) (pow v 2))))))))) (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))) (pow sinTheta_i 2))) (+ (/ 1 (* sinTheta_O (* sinTheta_i v))) (* 48038761/100000000 (/ 1 (* (pow sinTheta_O 2) (pow sinTheta_i 2)))))))
(- (+ 1 (+ (* -48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) (pow sinTheta_i 2)))) (+ (* -2307722558415121/10000000000000000 (/ (* (pow v 3) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 3) (pow sinTheta_i 3)))) (+ (* 110860132438012536505081/6000000000000000000000000 (/ (pow v 3) (* (pow sinTheta_O 3) (pow sinTheta_i 3)))) (+ (* 2307722558415121/20000000000000000 (/ (pow v 2) (* (pow sinTheta_O 2) (pow sinTheta_i 2)))) (+ (* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i))) (+ (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) (pow sinTheta_i 3)))) (+ (/ 48038761/100000000 (* (pow sinTheta_O 3) (* (pow sinTheta_i 3) v))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (* (pow sinTheta_i 2) (pow v 2))))))))))))) (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))) (pow sinTheta_i 2))) (+ (* -48038761/100000000 (/ (* v (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 3) (pow sinTheta_i 3)))) (+ (* 2307722558415121/20000000000000000 (/ v (* (pow sinTheta_O 3) (pow sinTheta_i 3)))) (+ (/ 2/3 (* (pow sinTheta_O 3) (* (pow sinTheta_i 3) (pow v 3)))) (+ (/ 1 (* sinTheta_O (* sinTheta_i v))) (+ (* 48038761/100000000 (/ 1 (* (pow sinTheta_O 2) (pow sinTheta_i 2)))) (+ (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))))) (* sinTheta_O (pow sinTheta_i 3))) (/ (* (+ (* -1 (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2))))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (pow v 2))))) (- (* 48038761/100000000 (/ v sinTheta_O)) (/ 1 (* sinTheta_O v)))) (pow sinTheta_i 3))))))))))
1
(+ 1 (* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_O)) (/ 1 (* sinTheta_O v))) sinTheta_i)))
(+ 1 (* -1 (/ (+ (* -1 (/ (- (+ (* -48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_O 2))) (* 2307722558415121/20000000000000000 (/ (pow v 2) (pow sinTheta_O 2)))) (+ (* -1 (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2))))) (+ (* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_O)) (/ 1 (* sinTheta_O v))) (* sinTheta_O v))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (pow v 2))))))) sinTheta_i)) (+ (* -48038761/100000000 (/ v sinTheta_O)) (/ 1 (* sinTheta_O v)))) sinTheta_i)))
(+ 1 (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (pow sinTheta_O 3))) (+ (* -110860132438012536505081/6000000000000000000000000 (/ (pow v 3) (pow sinTheta_O 3))) (+ (* 1/6 (/ 1 (* (pow sinTheta_O 3) (pow v 3)))) (* 2307722558415121/10000000000000000 (/ (* (pow v 3) (+ 6931/10000 (/ 1 v))) (pow sinTheta_O 3)))))) (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))))) sinTheta_O)) (+ (* -1 (/ (- (+ (* -48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_O 2))) (* 2307722558415121/20000000000000000 (/ (pow v 2) (pow sinTheta_O 2)))) (+ (* -1 (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2))))) (+ (* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_O)) (/ 1 (* sinTheta_O v))) (* sinTheta_O v))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (pow v 2))))))) (* sinTheta_O v))) (+ (* 6931/10000 (/ 1 (* (pow sinTheta_O 3) v))) (+ (* (+ (* -1 (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2))))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (pow v 2))))) (+ (* -48038761/100000000 (/ v sinTheta_O)) (/ 1 (* sinTheta_O v)))) (/ 1 (* (pow sinTheta_O 3) (pow v 2)))))))) sinTheta_i)) (+ (* -48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_O 2))) (* 2307722558415121/20000000000000000 (/ (pow v 2) (pow sinTheta_O 2))))) (+ (* -1 (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2))))) (+ (* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_O)) (/ 1 (* sinTheta_O v))) (* sinTheta_O v))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (pow v 2))))))) sinTheta_i)) (+ (* -48038761/100000000 (/ v sinTheta_O)) (/ 1 (* sinTheta_O v)))) sinTheta_i)))
(/ 1 (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))))
(+ (* 48038761/100000000 (/ v (* (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (+ 1 (* sinTheta_O sinTheta_i))))) (/ 1 (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))))
(+ (* v (+ (* -4351410491404879/20000000000000000 (/ v (* (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) (* 48038761/100000000 (/ 1 (* (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (+ 1 (* sinTheta_O sinTheta_i))))))) (/ 1 (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))))
(+ (* v (+ (* v (- (* 535804164344572917445081/6000000000000000000000000 (/ v (* (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)))) (* 4351410491404879/20000000000000000 (/ 1 (* (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))))) (* 48038761/100000000 (/ 1 (* (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (+ 1 (* sinTheta_O sinTheta_i))))))) (/ 1 (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))))
(exp 6931/10000)
(+ (exp 6931/10000) (* -1 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)))
(- (+ (exp 6931/10000) (+ (* -1 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)) (/ (* (exp 6931/10000) (+ (* 1/2 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) (pow v 2)))) (* 10000/6931 (/ (exp 6931/10000) (pow v 2))))
(- (+ (exp 6931/10000) (+ (* -1 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)) (+ (/ (* (exp 6931/10000) (+ (* -100000000/48038761 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (+ (* -10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (* -1/6 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))))) (pow v 3)) (/ (* (exp 6931/10000) (+ (* 1/2 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) (pow v 2))))) (+ (* -100000000/48038761 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) (pow v 3))) (+ (* -10000/6931 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) (pow v 3))) (* 10000/6931 (/ (exp 6931/10000) (pow v 2))))))
(exp 6931/10000)
(+ (exp 6931/10000) (* -1 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)))
(+ (exp 6931/10000) (* -1 (/ (+ (* -1 (/ (- (* (exp 6931/10000) (+ (* 1/2 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))) (* 10000/6931 (exp 6931/10000))) v)) (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(+ (exp 6931/10000) (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* (exp 6931/10000) (+ (* 1/6 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (+ (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)) (* 100000000/48038761 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))))) (+ (* 10000/6931 (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i)))) (* 100000000/48038761 (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i)))))) v)) (* (exp 6931/10000) (+ (* 1/2 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)) (* 10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) (* 10000/6931 (exp 6931/10000))) v)) (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(/ 1 (* v (+ 1 (* sinTheta_O sinTheta_i))))
(/ (+ (* -6931/10000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (/ 1 (+ 1 (* sinTheta_O sinTheta_i)))) v)
(/ (+ (* v (- (* 48038761/100000000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) (* 6931/10000 (/ 1 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) (/ 1 (+ 1 (* sinTheta_O sinTheta_i)))) v)
(/ (+ (* v (- (* v (+ (* -332956652491/1000000000000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 4))) (* 48038761/100000000 (/ 1 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))))) (* 6931/10000 (/ 1 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) (/ 1 (+ 1 (* sinTheta_O sinTheta_i)))) v)
(/ 10000/6931 (pow v 2))
(/ (+ 10000/6931 (* -100000000/48038761 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (pow v 2))
(/ (- (+ 10000/6931 (* 1000000000000/332956652491 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2)))) (* 100000000/48038761 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (pow v 2))
(/ (- (+ 10000/6931 (* -10000000000000000/2307722558415121 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) (pow v 3)))) (+ (* -1000000000000/332956652491 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))) (* 100000000/48038761 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))) (pow v 2))
(/ 10000/6931 (pow v 2))
(/ (+ 10000/6931 (* -100000000/48038761 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (pow v 2))
(/ (+ 10000/6931 (* -1 (/ (- (* -1000000000000/332956652491 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) v)) (* -100000000/48038761 (+ 1 (* sinTheta_O sinTheta_i)))) v))) (pow v 2))
(/ (+ 10000/6931 (* -1 (/ (- (* -1 (/ (- (* -10000000000000000/2307722558415121 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) v)) (* -1000000000000/332956652491 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v)) (* -100000000/48038761 (+ 1 (* sinTheta_O sinTheta_i)))) v))) (pow v 2))
(/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))
(+ (* -1 (/ (* sinTheta_O sinTheta_i) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(+ (* sinTheta_O (- (/ (* sinTheta_O (pow sinTheta_i 2)) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(+ (* sinTheta_O (- (* sinTheta_O (- (* -1 (/ (* sinTheta_O (pow sinTheta_i 3)) (* (pow v 5) (pow (+ 6931/10000 (/ 1 v)) 4)))) (* -1 (/ (pow sinTheta_i 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)))))) (/ sinTheta_i (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2))))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(/ 1 (* sinTheta_O (* sinTheta_i v)))
(/ (+ (* -1 (/ (+ (* 6931/10000 (/ 1 (pow sinTheta_i 2))) (/ 1 (* (pow sinTheta_i 2) v))) sinTheta_O)) (/ 1 (* sinTheta_i v))) sinTheta_O)
(/ (- (+ (/ 1 (* sinTheta_i v)) (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))))) (* (pow sinTheta_O 2) sinTheta_i))) (+ (/ 6931/10000 (* sinTheta_O (pow sinTheta_i 2))) (/ 1 (* sinTheta_O (* (pow sinTheta_i 2) v))))) sinTheta_O)
(/ (- (+ (* -1 (/ (* (pow v 2) (* (pow (+ 6931/10000 (/ 1 v)) 2) (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))))) (* (pow sinTheta_O 3) (pow sinTheta_i 2)))) (/ 1 (* sinTheta_i v))) (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))))) (* (pow sinTheta_O 2) sinTheta_i))) (+ (/ 6931/10000 (* sinTheta_O (pow sinTheta_i 2))) (/ 1 (* sinTheta_O (* (pow sinTheta_i 2) v)))))) sinTheta_O)
(/ 1 (* sinTheta_O (* sinTheta_i v)))
(* -1 (/ (- (+ (/ 6931/10000 (* sinTheta_O (pow sinTheta_i 2))) (/ 1 (* sinTheta_O (* (pow sinTheta_i 2) v)))) (/ 1 (* sinTheta_i v))) sinTheta_O))
(* -1 (/ (- (* -1 (/ (- (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))))) (* sinTheta_O sinTheta_i)) (+ (* 6931/10000 (/ 1 (pow sinTheta_i 2))) (/ 1 (* (pow sinTheta_i 2) v)))) sinTheta_O)) (/ 1 (* sinTheta_i v))) sinTheta_O))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (* (pow v 2) (* (pow (+ 6931/10000 (/ 1 v)) 2) (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))))) (* sinTheta_O (pow sinTheta_i 2))) (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))))) sinTheta_i)) sinTheta_O)) (+ (* 6931/10000 (/ 1 (pow sinTheta_i 2))) (/ 1 (* (pow sinTheta_i 2) v)))) sinTheta_O)) (/ 1 (* sinTheta_i v))) sinTheta_O))
(/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))
(+ (* -1 (/ (* sinTheta_O sinTheta_i) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
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1
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(/ (+ (* -48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i))) (* 48038761/100000000 (/ v sinTheta_O))) sinTheta_i)
(/ (- (+ (* 48038761/100000000 (/ v sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) (pow sinTheta_i 2))))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i)))) sinTheta_i)
(/ (- (+ (* -48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* (pow sinTheta_O 4) (pow sinTheta_i 3)))) (* 48038761/100000000 (/ v sinTheta_O))) (+ (* -48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) (pow sinTheta_i 2)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i))))) sinTheta_i)
(* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))
(* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i)))) sinTheta_i))
(* -1 (/ (+ (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) sinTheta_i))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_O 2)))) sinTheta_i)) (* -48038761/100000000 (/ v sinTheta_O))) sinTheta_i))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* (pow sinTheta_O 4) sinTheta_i))) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (pow sinTheta_O 3)))) sinTheta_i)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_O 2)))) sinTheta_i)) (* -48038761/100000000 (/ v sinTheta_O))) sinTheta_i))
(* 48038761/100000000 (/ v (+ 1 (* sinTheta_O sinTheta_i))))
(* v (+ (* -332956652491/1000000000000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (* 48038761/100000000 (/ 1 (+ 1 (* sinTheta_O sinTheta_i))))))
(* v (+ (* v (- (* 2307722558415121/10000000000000000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) (* 332956652491/1000000000000 (/ 1 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) (* 48038761/100000000 (/ 1 (+ 1 (* sinTheta_O sinTheta_i))))))
(* v (+ (* v (- (* v (+ (* -15994825052375203651/100000000000000000000 (/ v (pow (+ 1 (* sinTheta_O sinTheta_i)) 4))) (* 2307722558415121/10000000000000000 (/ 1 (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))))) (* 332956652491/1000000000000 (/ 1 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))))) (* 48038761/100000000 (/ 1 (+ 1 (* sinTheta_O sinTheta_i))))))
6931/10000
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(- (+ 6931/10000 (* 10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2)))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))
(- (+ 6931/10000 (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) (pow v 3)))) (+ (* -10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 2))) (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v))))
6931/10000
(+ 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))
(+ 6931/10000 (* -1 (/ (- (* -10000/6931 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) v)) (* -1 (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(+ 6931/10000 (* -1 (/ (- (* -1 (/ (- (* -100000000/48038761 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 3) v)) (* -10000/6931 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v)) (* -1 (+ 1 (* sinTheta_O sinTheta_i)))) v)))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(/ 1 (pow v 2))
(exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
(exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))
1
(+ 1 (* 10000/6931 (/ 1 (pow v 2))))
(+ 1 (+ (* -100000000/48038761 (/ (+ 1 (* sinTheta_O sinTheta_i)) (pow v 3))) (* 10000/6931 (/ 1 (pow v 2)))))
(+ 1 (+ (* -100000000/48038761 (/ (+ 1 (* sinTheta_O sinTheta_i)) (pow v 3))) (+ (* 1000000000000/332956652491 (/ (pow (+ 1 (* sinTheta_O sinTheta_i)) 2) (pow v 4))) (+ (* 10000/6931 (/ 1 (pow v 2))) (* 50000000/48038761 (/ 1 (pow v 4)))))))
1
(+ 1 (* 10000/6931 (/ 1 (pow v 2))))
(+ 1 (+ (* -100000000/48038761 (/ (+ 1 (* sinTheta_O sinTheta_i)) (pow v 3))) (* 10000/6931 (/ 1 (pow v 2)))))
(+ 1 (+ (* -1 (/ (+ (* -1 (/ (+ 50000000/48038761 (* 1000000000000/332956652491 (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v)) (* 100000000/48038761 (+ 1 (* sinTheta_O sinTheta_i)))) (pow v 3))) (* 10000/6931 (/ 1 (pow v 2)))))
(exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (* sinTheta_O (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* 1/2 (/ (pow sinTheta_i 2) (* (pow v 6) (pow (+ 6931/10000 (/ 1 v)) 4)))) (/ (pow sinTheta_i 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)))))))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (* sinTheta_O (+ (* sinTheta_O (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* -1 (/ (pow sinTheta_i 3) (* (pow v 5) (pow (+ 6931/10000 (/ 1 v)) 4)))) (+ (* -1 (/ (pow sinTheta_i 3) (* (pow v 7) (pow (+ 6931/10000 (/ 1 v)) 5)))) (* -1/6 (/ (pow sinTheta_i 3) (* (pow v 9) (pow (+ 6931/10000 (/ 1 v)) 6)))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* 1/2 (/ (pow sinTheta_i 2) (* (pow v 6) (pow (+ 6931/10000 (/ 1 v)) 4)))) (/ (pow sinTheta_i 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3))))))))))
1
(+ 1 (/ 1 (* sinTheta_O (* sinTheta_i v))))
(+ 1 (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))) (pow sinTheta_O 2))) (+ (/ 1 (* sinTheta_O (* sinTheta_i v))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (* (pow sinTheta_i 2) (pow v 2))))))))
(+ 1 (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))) (* (pow sinTheta_O 3) (* sinTheta_i v)))) (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))) (pow sinTheta_O 2))) (+ (/ 1/6 (* (pow sinTheta_O 3) (* (pow sinTheta_i 3) (pow v 3)))) (+ (/ 1 (* sinTheta_O (* sinTheta_i v))) (+ (* 1/2 (/ 1 (* (pow sinTheta_O 2) (* (pow sinTheta_i 2) (pow v 2))))) (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))))) (* (pow sinTheta_O 3) sinTheta_i))))))))
1
(+ 1 (/ 1 (* sinTheta_O (* sinTheta_i v))))
(+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1 (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2))))) (* 1/2 (/ 1 (* (pow sinTheta_i 2) (pow v 2))))) sinTheta_O)) (/ 1 (* sinTheta_i v))) sinTheta_O)))
(+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1 (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2))))) (+ (* -1 (/ (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_i 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_i 2)))))) sinTheta_i)) (+ (* 6931/10000 (/ 1 (* (pow sinTheta_i 3) v))) (/ 1 (* (pow sinTheta_i 3) (pow v 2))))) (* 1/6 (/ 1 (* (pow sinTheta_i 3) (pow v 3))))) sinTheta_O)) (* 1/2 (/ 1 (* (pow sinTheta_i 2) (pow v 2)))))) sinTheta_O)) (/ 1 (* sinTheta_i v))) sinTheta_O)))
(exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (* sinTheta_i (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* 1/2 (/ (pow sinTheta_O 2) (* (pow v 6) (pow (+ 6931/10000 (/ 1 v)) 4)))) (/ (pow sinTheta_O 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)))))))))
(+ (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v)))))) (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)))) (* sinTheta_i (+ (* sinTheta_i (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* -1 (/ (pow sinTheta_O 3) (* (pow v 5) (pow (+ 6931/10000 (/ 1 v)) 4)))) (+ (* -1 (/ (pow sinTheta_O 3) (* (pow v 7) (pow (+ 6931/10000 (/ 1 v)) 5)))) (* -1/6 (/ (pow sinTheta_O 3) (* (pow v 9) (pow (+ 6931/10000 (/ 1 v)) 6)))))))) (* (exp (/ 1 (* (pow v 2) (+ 6931/10000 (/ 1 v))))) (+ (* 1/2 (/ (pow sinTheta_O 2) (* (pow v 6) (pow (+ 6931/10000 (/ 1 v)) 4)))) (/ (pow sinTheta_O 2) (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3))))))))))
1
(+ 1 (/ 1 (* sinTheta_O (* sinTheta_i v))))
(+ 1 (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))) (pow sinTheta_i 2))) (+ (/ 1 (* sinTheta_O (* sinTheta_i v))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (* (pow sinTheta_i 2) (pow v 2))))))))
(+ 1 (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))) (* sinTheta_O (* (pow sinTheta_i 3) v)))) (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))) (pow sinTheta_i 2))) (+ (/ 1/6 (* (pow sinTheta_O 3) (* (pow sinTheta_i 3) (pow v 3)))) (+ (/ 1 (* sinTheta_O (* sinTheta_i v))) (+ (* 1/2 (/ 1 (* (pow sinTheta_O 2) (* (pow sinTheta_i 2) (pow v 2))))) (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))))) (* sinTheta_O (pow sinTheta_i 3)))))))))
1
(+ 1 (/ 1 (* sinTheta_O (* sinTheta_i v))))
(+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1 (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2))))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (pow v 2))))) sinTheta_i)) (/ 1 (* sinTheta_O v))) sinTheta_i)))
(+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1 (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2))))) (+ (* -1 (/ (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))))) sinTheta_O)) (+ (* 6931/10000 (/ 1 (* (pow sinTheta_O 3) v))) (/ 1 (* (pow sinTheta_O 3) (pow v 2))))) (* 1/6 (/ 1 (* (pow sinTheta_O 3) (pow v 3))))) sinTheta_i)) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (pow v 2)))))) sinTheta_i)) (/ 1 (* sinTheta_O v))) sinTheta_i)))

Outputs
(exp (neg (+ (log 2) (log v))))
(exp.f32 (-.f32 (-.f32 #s(literal 0 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)))
(exp (neg (+ (log 2) (log v))))
(exp.f32 (-.f32 (-.f32 #s(literal 0 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)))
(exp (neg (+ (log 2) (log v))))
(exp.f32 (-.f32 (-.f32 #s(literal 0 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)))
(exp (neg (+ (log 2) (log v))))
(exp.f32 (-.f32 (-.f32 #s(literal 0 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp.f32 (-.f32 (-.f32 #s(literal 0 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp.f32 (-.f32 (-.f32 #s(literal 0 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp.f32 (-.f32 (-.f32 #s(literal 0 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)))
(exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))
(exp.f32 (-.f32 (-.f32 #s(literal 0 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) v)) (-.f32 #s(literal 0 binary32) (log.f32 #s(literal -2 binary32)))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) v)) (-.f32 #s(literal 0 binary32) (log.f32 #s(literal -2 binary32)))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) v)) (-.f32 #s(literal 0 binary32) (log.f32 #s(literal -2 binary32)))))
(exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) v)) (-.f32 #s(literal 0 binary32) (log.f32 #s(literal -2 binary32)))))
(* (exp (neg (+ (log 2) (log v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(exp.f32 (+.f32 (-.f32 (-.f32 #s(literal 0 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)) (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(* (exp (neg (+ (log 2) (log v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(exp.f32 (+.f32 (-.f32 (-.f32 #s(literal 0 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)) (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(* (exp (neg (+ (log 2) (log v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(exp.f32 (+.f32 (-.f32 (-.f32 #s(literal 0 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)) (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(* (exp (neg (+ (log 2) (log v)))) (exp (- 6931/10000 (+ (/ 1 v) (/ (* sinTheta_O sinTheta_i) v)))))
(exp.f32 (+.f32 (-.f32 (-.f32 #s(literal 0 binary32) (log.f32 #s(literal 2 binary32))) (log.f32 v)) (-.f32 #s(literal 6931/10000 binary32) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 #s(literal 1 binary32) v)))))
(* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))))
(exp.f32 (-.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v))))
(+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))))
(-.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)))) (/.f32 (*.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)))) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) v))
(+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (+ (* 1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))))))
(-.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)))) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (.f32 v v)) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v))))) (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)))) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) v))
(+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (+ (* -1/6 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3))) (pow v 3))) (+ (* 1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) (pow v 2))) (* (exp 6931/10000) (exp (neg (+ (log 2) (* -1 (log (/ 1 v))))))))))
(-.f32 (fma.f32 #s(literal -1/6 binary32) (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)))) (.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 #s(literal 1/2 binary32) (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)))) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)))) (.f32 v v)) (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)))))) (/.f32 (*.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)))) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) v))
(* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))))
(exp.f32 (-.f32 #s(literal 6931/10000 binary32) (-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) v)))))
(+ (* -1 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i)))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))
(-.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) v))))) (/.f32 (*.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) v))))) (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32))) v))
(+ (* -1 (/ (+ (* -1/2 (/ (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2))) v)) (* (exp 6931/10000) (* (exp (neg (+ (log -2) (* -1 (log (/ -1 v)))))) (+ 1 (* sinTheta_O sinTheta_i))))) v)) (* (exp 6931/10000) (exp (neg (+ (log -2) (* -1 (log (/ -1 v))))))))
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(exp.f32 #s(literal 6931/10000 binary32))
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(+ (* v (+ (* v (- (* 535804164344572917445081/6000000000000000000000000 (/ v (* (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 3)))) (* 4351410491404879/20000000000000000 (/ 1 (* (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (pow (+ 1 (* sinTheta_O sinTheta_i)) 2)))))) (* 48038761/100000000 (/ 1 (* (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v)))))) (+ 1 (* sinTheta_O sinTheta_i))))))) (/ 1 (exp (/ 1 (* (pow v 2) (- 6931/10000 (* -1 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))))))
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(exp.f32 #s(literal 6931/10000 binary32))
(+ (exp 6931/10000) (* -1 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)))
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(exp 6931/10000)
(exp.f32 #s(literal 6931/10000 binary32))
(+ (exp 6931/10000) (* -1 (/ (* (exp 6931/10000) (+ 1 (* sinTheta_O sinTheta_i))) v)))
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(/ 1 (* v (+ 1 (* sinTheta_O sinTheta_i))))
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(/ (+ 10000/6931 (* -100000000/48038761 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))) (pow v 2))
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(/ 1 (* sinTheta_O (* sinTheta_i v)))
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(/ (+ (* -1 (/ (+ (* 6931/10000 (/ 1 (pow sinTheta_i 2))) (/ 1 (* (pow sinTheta_i 2) v))) sinTheta_O)) (/ 1 (* sinTheta_i v))) sinTheta_O)
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6931/10000
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(/ (- (+ (* -48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* (pow sinTheta_O 3) (pow sinTheta_i 4)))) (* 48038761/100000000 (/ v sinTheta_i))) (+ (* -48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 2) (pow sinTheta_i 3)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* sinTheta_O (pow sinTheta_i 2)))))) sinTheta_O)
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(* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))
(/.f32 (.f32 #s(literal 48038761/100000000 binary32) v) (.f32 sinTheta_O sinTheta_i))
(* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_i)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* sinTheta_O (pow sinTheta_i 2))))) sinTheta_O))
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(* -1 (/ (+ (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* sinTheta_O (pow sinTheta_i 3)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_i 2)))) sinTheta_O)) (* -48038761/100000000 (/ v sinTheta_i))) sinTheta_O))
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(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* sinTheta_O (pow sinTheta_i 4)))) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (pow sinTheta_i 3)))) sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_i 2)))) sinTheta_O)) (* -48038761/100000000 (/ v sinTheta_i))) sinTheta_O))
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(/.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))
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(* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))
(/.f32 (.f32 #s(literal 48038761/100000000 binary32) v) (.f32 sinTheta_O sinTheta_i))
(/ (+ (* -48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i))) (* 48038761/100000000 (/ v sinTheta_O))) sinTheta_i)
(/.f32 (fma.f32 #s(literal 48038761/100000000 binary32) (/.f32 v sinTheta_O) (/.f32 (.f32 #s(literal -48038761/100000000 binary32) (.f32 (.f32 v v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32)))) (.f32 sinTheta_i (*.f32 sinTheta_O sinTheta_O)))) sinTheta_i)
(/ (- (+ (* 48038761/100000000 (/ v sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) (pow sinTheta_i 2))))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i)))) sinTheta_i)
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(/ (- (+ (* -48038761/100000000 (/ (* (pow v 4) (pow (+ 6931/10000 (/ 1 v)) 3)) (* (pow sinTheta_O 4) (pow sinTheta_i 3)))) (* 48038761/100000000 (/ v sinTheta_O))) (+ (* -48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) (pow sinTheta_i 2)))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i))))) sinTheta_i)
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(* 48038761/100000000 (/ v (* sinTheta_O sinTheta_i)))
(/.f32 (.f32 #s(literal 48038761/100000000 binary32) v) (.f32 sinTheta_O sinTheta_i))
(* -1 (/ (+ (* -48038761/100000000 (/ v sinTheta_O)) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (* (pow sinTheta_O 2) sinTheta_i)))) sinTheta_i))
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(* -1 (/ (+ (* -1 (/ (- (* 48038761/100000000 (/ (* (pow v 3) (pow (+ 6931/10000 (/ 1 v)) 2)) (* (pow sinTheta_O 3) sinTheta_i))) (* 48038761/100000000 (/ (* (pow v 2) (+ 6931/10000 (/ 1 v))) (pow sinTheta_O 2)))) sinTheta_i)) (* -48038761/100000000 (/ v sinTheta_O))) sinTheta_i))
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#s(literal 6931/10000 binary32)
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(+ 1 (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))) (pow sinTheta_i 2))) (+ (/ 1 (* sinTheta_O (* sinTheta_i v))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (* (pow sinTheta_i 2) (pow v 2))))))))
(+.f32 #s(literal 1 binary32) (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 sinTheta_O (.f32 v sinTheta_i))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 sinTheta_O sinTheta_O) (.f32 (.f32 v v) (.f32 sinTheta_i sinTheta_i))))) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 v (.f32 sinTheta_O sinTheta_O))) (/.f32 #s(literal 6931/10000 binary32) (.f32 sinTheta_O sinTheta_O))) (*.f32 sinTheta_i sinTheta_i))))
(+ 1 (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))) (* sinTheta_O (* (pow sinTheta_i 3) v)))) (+ (* -1 (/ (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))) (pow sinTheta_i 2))) (+ (/ 1/6 (* (pow sinTheta_O 3) (* (pow sinTheta_i 3) (pow v 3)))) (+ (/ 1 (* sinTheta_O (* sinTheta_i v))) (+ (* 1/2 (/ 1 (* (pow sinTheta_O 2) (* (pow sinTheta_i 2) (pow v 2))))) (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))))) (* sinTheta_O (pow sinTheta_i 3)))))))))
(+.f32 (-.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 v (.f32 sinTheta_O sinTheta_O))) (/.f32 #s(literal 6931/10000 binary32) (.f32 sinTheta_O sinTheta_O))) (.f32 sinTheta_O (.f32 v (.f32 sinTheta_i (.f32 sinTheta_i sinTheta_i)))))) (-.f32 (+.f32 (+.f32 (/.f32 #s(literal 1/6 binary32) (.f32 (.f32 sinTheta_O (.f32 sinTheta_O sinTheta_O)) (.f32 (.f32 v (.f32 v v)) (.f32 sinTheta_i (.f32 sinTheta_i sinTheta_i))))) (/.f32 #s(literal 1 binary32) (.f32 sinTheta_O (.f32 v sinTheta_i)))) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 sinTheta_O sinTheta_O) (.f32 (.f32 v v) (.f32 sinTheta_i sinTheta_i)))) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 v (.f32 sinTheta_O sinTheta_O))) (/.f32 #s(literal 6931/10000 binary32) (.f32 sinTheta_O sinTheta_O)))) (.f32 sinTheta_O (.f32 sinTheta_i (.f32 sinTheta_i sinTheta_i)))))) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 v (.f32 sinTheta_O sinTheta_O))) (/.f32 #s(literal 6931/10000 binary32) (.f32 sinTheta_O sinTheta_O))) (*.f32 sinTheta_i sinTheta_i))))
1
#s(literal 1 binary32)
(+ 1 (/ 1 (* sinTheta_O (* sinTheta_i v))))
(+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 sinTheta_O (.f32 v sinTheta_i))))
(+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1 (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2))))) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (pow v 2))))) sinTheta_i)) (/ 1 (* sinTheta_O v))) sinTheta_i)))
(-.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (+.f32 (/.f32 (-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 v v) (.f32 sinTheta_O sinTheta_O))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 v (.f32 sinTheta_O sinTheta_O))) (/.f32 #s(literal 6931/10000 binary32) (.f32 sinTheta_O sinTheta_O)))) sinTheta_i) (/.f32 #s(literal 1 binary32) (*.f32 v sinTheta_O)))) sinTheta_i))
(+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1 (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2))))) (+ (* -1 (/ (- (+ (* -1 (/ (* v (* (+ 6931/10000 (/ 1 v)) (+ (/ 1 (* (pow sinTheta_O 2) v)) (* 6931/10000 (/ 1 (pow sinTheta_O 2)))))) sinTheta_O)) (+ (* 6931/10000 (/ 1 (* (pow sinTheta_O 3) v))) (/ 1 (* (pow sinTheta_O 3) (pow v 2))))) (* 1/6 (/ 1 (* (pow sinTheta_O 3) (pow v 3))))) sinTheta_i)) (* 1/2 (/ 1 (* (pow sinTheta_O 2) (pow v 2)))))) sinTheta_i)) (/ 1 (* sinTheta_O v))) sinTheta_i)))
(-.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 (-.f32 (-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 v v) (.f32 sinTheta_O sinTheta_O))) (/.f32 (+.f32 (-.f32 (+.f32 (/.f32 #s(literal 6931/10000 binary32) (.f32 v (.f32 sinTheta_O (.f32 sinTheta_O sinTheta_O)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 v v) (.f32 sinTheta_O (.f32 sinTheta_O sinTheta_O))))) (/.f32 (.f32 (fma.f32 v #s(literal 6931/10000 binary32) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 v (.f32 sinTheta_O sinTheta_O))) (/.f32 #s(literal 6931/10000 binary32) (.f32 sinTheta_O sinTheta_O)))) sinTheta_O)) (/.f32 #s(literal -1/6 binary32) (.f32 (.f32 v (.f32 v v)) (.f32 sinTheta_O (.f32 sinTheta_O sinTheta_O))))) sinTheta_i)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 v (.f32 sinTheta_O sinTheta_O))) (/.f32 #s(literal 6931/10000 binary32) (.f32 sinTheta_O sinTheta_O)))) (neg.f32 sinTheta_i)) (/.f32 #s(literal -1 binary32) (*.f32 v sinTheta_O))) sinTheta_i))

eval192.0ms (1.1%)

Memory: 8.1MiB live, 364.6MiB allocated
Compiler: Compiled 51 547 to 4 917 computations (90.5% saved)

prune248.0ms (1.4%)

Memory

-13.6MiB live, 430.6MiB allocated

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	1 759	7	1 766
Fresh	3	8	11
Picked	3	2	5
Done	2	0	2
Total	1 767	17	1 784

Accuracy

99.9%

Counts

1 784 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	93.5%	(/.f32 (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_O (neg.f32 sinTheta_i)) v)) (.f32 v #s(literal 2 binary32))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
	99.4%	(/.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
	99.8%	(/.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)
	99.8%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 #s(literal 1 binary32) (exp.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)) (/.f32 (fma.f32 cosTheta_i cosTheta_O (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i))) v)))))))
	36.6%	(/.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) (+.f32 (/.f32 v (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 #s(literal -1 binary32) v))))) (/.f32 (.f32 sinTheta_O sinTheta_i) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 #s(literal -1 binary32) v))))))))
	99.4%	(/.f32 #s(literal 1/2 binary32) (*.f32 v (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))))
	99.4%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (pow.f32 (exp.f32 #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
	99.4%	(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 v v)) (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal -6931/10000 binary32)))) (exp.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal -6931/10000 binary32))))))
	99.4%	(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 #s(literal 1 binary32) (.f32 v v)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))))
	99.4%	(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 #s(literal 1 binary32) v) (.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v)) v)))))
	99.8%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (pow.f32 (E.f32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
✓	99.8%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
	99.4%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (/.f32 #s(literal 1 binary32) v))))
	98.6%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))
	98.6%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
	4.6%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) #s(literal 1 binary32))
✓	99.8%	(.f32 (exp.f32 (neg.f32 (log.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)) v))))

Compiler

Compiled 1 140 to 482 computations (57.7% saved)

regimes103.0ms (0.6%)

Memory

12.9MiB live, 207.4MiB allocated

Counts

39 → 1

Calls

Call 1

Inputs
(*.f32 (/.f32 #s(literal 1/2 binary32) v) #s(literal 1 binary32))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 #s(literal 6931/10000 binary32)))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v)
(/.f32 (*.f32 (exp.f32 #s(literal 6931/10000 binary32)) #s(literal 1/2 binary32)) v)
(.f32 (/.f32 #s(literal 1 binary32) v) (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(/.f32 #s(literal 1 binary32) (*.f32 (/.f32 v (exp.f32 #s(literal 6931/10000 binary32))) #s(literal 2 binary32)))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(/.f32 #s(literal 1/2 binary32) (*.f32 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 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 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 (/.f32 #s(literal 1/2 binary32) 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 #s(literal 6931/10000 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v)))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 #s(literal 1 binary32) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))))
(/.f32 #s(literal 1 binary32) (.f32 (.f32 v #s(literal 2 binary32)) (exp.f32 (neg.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (-.f32 #s(literal 0 binary32) (*.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) v) #s(literal 6931/10000 binary32))))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 #s(literal 1 binary32) (exp.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)) (/.f32 (fma.f32 cosTheta_i cosTheta_O (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i))) v)))))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (pow.f32 (exp.f32 #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (/.f32 #s(literal 1 binary32) v))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (pow.f32 (E.f32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(/.f32 (/.f32 (exp.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (.f32 v #s(literal 2 binary32))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
(/.f32 (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_O (neg.f32 sinTheta_i)) v)) (.f32 v #s(literal 2 binary32))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 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 (/.f32 #s(literal 1 binary32) (.f32 v v)) (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal -6931/10000 binary32)))) (exp.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal -6931/10000 binary32))))))
(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 #s(literal 1 binary32) (.f32 v v)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))))
(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 #s(literal 1 binary32) v) (.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 #s(literal 2 binary32) (+.f32 (/.f32 v (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 #s(literal -1 binary32) v))))) (/.f32 (.f32 sinTheta_O sinTheta_i) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 #s(literal -1 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 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))) (exp.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 v v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))))
(.f32 (/.f32 #s(literal 1/2 binary32) v) (pow.f32 (exp.f32 (/.f32 (-.f32 #s(literal 48038761/100000000 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 v v)))) (-.f32 #s(literal 48038761/100000000 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (*.f32 v v)))))) (-.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) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 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 v (+.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) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 1 binary32) (.f32 v 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 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))))
(.f32 (exp.f32 (neg.f32 (log.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)) v))))
(.f32 (exp.f32 (neg.f32 (log.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)) (/.f32 #s(literal -1 binary32) v)))))
(/.f32 (exp.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (.f32 v #s(literal 2 binary32))))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
(/.f32 (exp.f32 (-.f32 (-.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) v) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal -6931/10000 binary32))) (exp.f32 (/.f32 #s(literal 1 binary32) v)))
(/.f32 (exp.f32 (+.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_O (neg.f32 sinTheta_i))) v))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
(/.f32 (exp.f32 (.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (neg.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (log.f32 (.f32 v #s(literal 2 binary32))))) cosTheta_O)))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
(/.f32 (exp.f32 (/.f32 (fma.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) (+.f32 #s(literal 0 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) (.f32 v (-.f32 #s(literal 0 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))))) (.f32 v (+.f32 #s(literal 0 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))

Outputs
(.f32 (exp.f32 (neg.f32 (log.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)) v))))

Calls

9 calls:

14.0ms	cosTheta_i
13.0ms	(*.f32 sinTheta_i sinTheta_O)
12.0ms	(+.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))))
11.0ms	sinTheta_i
11.0ms	v

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)

regimes86.0ms (0.5%)

Memory

-11.1MiB live, 145.3MiB allocated

Counts

32 → 1

Calls

Call 1

Inputs
(*.f32 (/.f32 #s(literal 1/2 binary32) v) #s(literal 1 binary32))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 #s(literal 6931/10000 binary32)))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v)
(/.f32 (*.f32 (exp.f32 #s(literal 6931/10000 binary32)) #s(literal 1/2 binary32)) v)
(.f32 (/.f32 #s(literal 1 binary32) v) (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(/.f32 #s(literal 1 binary32) (*.f32 (/.f32 v (exp.f32 #s(literal 6931/10000 binary32))) #s(literal 2 binary32)))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal 6931/10000 binary32))))
(/.f32 #s(literal 1/2 binary32) (*.f32 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 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 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 (/.f32 #s(literal 1/2 binary32) 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 #s(literal 6931/10000 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v)))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 #s(literal 1 binary32) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))))
(/.f32 #s(literal 1 binary32) (.f32 (.f32 v #s(literal 2 binary32)) (exp.f32 (neg.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (-.f32 #s(literal 0 binary32) (*.f32 sinTheta_O sinTheta_i))) #s(literal 1 binary32)) v) #s(literal 6931/10000 binary32))))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (-.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (.f32 cosTheta_i cosTheta_O)) v) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)))))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 #s(literal 1 binary32) (exp.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32)) (/.f32 (fma.f32 cosTheta_i cosTheta_O (-.f32 #s(literal 0 binary32) (.f32 sinTheta_O sinTheta_i))) v)))))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (pow.f32 (exp.f32 #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (/.f32 #s(literal 1 binary32) v))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (exp.f32 (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (pow.f32 (E.f32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) v))))
(/.f32 (/.f32 (exp.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (.f32 v #s(literal 2 binary32))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 binary32))))
(/.f32 (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_O (neg.f32 sinTheta_i)) v)) (.f32 v #s(literal 2 binary32))) (exp.f32 (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal -6931/10000 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 (/.f32 #s(literal 1 binary32) (.f32 v v)) (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal -6931/10000 binary32)))) (exp.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 (/.f32 #s(literal -1 binary32) v) #s(literal -6931/10000 binary32))))))
(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 #s(literal 1 binary32) (.f32 v v)) (+.f32 (/.f32 #s(literal 1 binary32) v) #s(literal 6931/10000 binary32))))))
(.f32 (/.f32 #s(literal 1/2 binary32) v) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 #s(literal 1 binary32) v) (.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 #s(literal 2 binary32) (+.f32 (/.f32 v (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 #s(literal -1 binary32) v))))) (/.f32 (.f32 sinTheta_O sinTheta_i) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 #s(literal -1 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 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v))))) (exp.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 v v)) (-.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))))
(.f32 (/.f32 #s(literal 1/2 binary32) v) (pow.f32 (exp.f32 (/.f32 (-.f32 #s(literal 48038761/100000000 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (.f32 v v)))) (-.f32 #s(literal 48038761/100000000 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (*.f32 v v)))))) (-.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) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 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 v (+.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) (/.f32 (exp.f32 (/.f32 #s(literal 48038761/100000000 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 1 binary32) (.f32 v 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 6931/10000 binary32) (/.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (neg.f32 v)))))))

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

Calls

9 calls:

15.0ms	cosTheta_i
10.0ms	(+.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))))
9.0ms	(*.f32 sinTheta_i sinTheta_O)
9.0ms	v
9.0ms	sinTheta_O

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)

regimes55.0ms (0.3%)

Memory

19.2MiB live, 58.1MiB allocated

Counts

19 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

25.0ms	sinTheta_i
6.0ms	cosTheta_i
6.0ms	sinTheta_O
6.0ms	cosTheta_O
5.0ms	v

Results

Accuracy	Segments	Branch
99.8%	1	`cosTheta_i`
99.8%	1	`cosTheta_O`
99.8%	1	`sinTheta_O`
99.8%	1	`sinTheta_i`
99.8%	1	`v`
99.8%	1	`(*.f32 cosTheta_i cosTheta_O)`

Compiler

Compiled 38 to 31 computations (18.4% saved)

regimes27.0ms (0.1%)

Memory

-24.8MiB live, 52.0MiB allocated

Counts

15 → 1

Calls

Call 1

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

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

Calls

5 calls:

6.0ms	cosTheta_i
6.0ms	v
5.0ms	sinTheta_i
5.0ms	cosTheta_O
5.0ms	sinTheta_O

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`

Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes27.0ms (0.1%)

Memory

-4.4MiB live, 41.2MiB allocated

Counts

12 → 1

Calls

Call 1

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

Outputs
(/.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)

Calls

5 calls:

10.0ms	cosTheta_i
4.0ms	sinTheta_O
4.0ms	sinTheta_i
4.0ms	cosTheta_O
4.0ms	v

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`

Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes18.0ms (0.1%)

Memory

30.6MiB live, 30.6MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

5 calls:

4.0ms	cosTheta_i
3.0ms	cosTheta_O
3.0ms	sinTheta_i
3.0ms	sinTheta_O
3.0ms	v

Results

Accuracy	Segments	Branch
99.4%	1	`cosTheta_i`
99.4%	1	`cosTheta_O`
99.4%	1	`sinTheta_i`
99.4%	1	`sinTheta_O`
99.4%	1	`v`

Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes17.0ms (0.1%)

Memory

-3.8MiB live, 35.0MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

5 calls:

4.0ms	v
3.0ms	cosTheta_O
3.0ms	sinTheta_O
3.0ms	cosTheta_i
3.0ms	sinTheta_i

Results

Accuracy	Segments	Branch
99.4%	1	`cosTheta_i`
99.4%	1	`cosTheta_O`
99.4%	1	`sinTheta_i`
99.4%	1	`sinTheta_O`
99.4%	1	`v`

Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes17.0ms (0.1%)

Memory

-3.1MiB live, 32.8MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

5 calls:

6.0ms	sinTheta_O
3.0ms	cosTheta_i
3.0ms	v
3.0ms	sinTheta_i
3.0ms	cosTheta_O

Results

Accuracy	Segments	Branch
98.6%	1	`cosTheta_i`
98.6%	1	`cosTheta_O`
98.6%	1	`sinTheta_i`
98.6%	1	`sinTheta_O`
98.6%	1	`v`

Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes12.0ms (0.1%)

Memory

-8.6MiB live, 30.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

5 calls:

3.0ms	sinTheta_i
2.0ms	sinTheta_O
2.0ms	v
2.0ms	cosTheta_O
2.0ms	cosTheta_i

Results

Accuracy	Segments	Branch
4.6%	1	`cosTheta_i`
4.6%	1	`cosTheta_O`
4.6%	1	`sinTheta_i`
4.6%	1	`sinTheta_O`
4.6%	1	`v`

Compiler

Compiled 30 to 25 computations (16.7% saved)

simplify15.0ms (0.1%)

Memory

-15.5MiB live, 27.4MiB allocated

Algorithm

1×	egg-herbie

Rules

46×	`*-commutative_binary32`
28×	`+-commutative_binary32`
24×	`sub-neg_binary32`
22×	`neg-sub0_binary32`
22×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	113
1	78	113
2	96	113
3	115	113
4	127	113
5	139	113
6	144	113
7	152	113
8	154	113
9	155	113

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.5s (8.3%)

Memory

40.5MiB live, 1 666.4MiB allocated

Rules

11 284×	`accelerator-lowering-fma.f32`
11 284×	`accelerator-lowering-fma.f64`
9 370×	`accelerator-lowering-fma.f32`
9 370×	`accelerator-lowering-fma.f64`
9 354×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	357
1	280	258
2	2439	255
0	9299	243
0	278	4128
1	891	3918
2	3129	3629
0	8250	3465
0	1627	14233
1	5549	13903
0	8152	13304
0	41	227
1	214	191
2	1613	191
0	8562	179
0	1730	23906
1	5696	23039
0	9322	22155
0	665	8987
1	2242	8313
0	8211	8054
0	21	60
1	134	55
2	1494	55
0	8235	55
0	36	142
1	173	127
2	1324	126
0	8111	122

Stop Event

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

Compiler

Compiled 383 to 275 computations (28.2% saved)

preprocess90.0ms (0.5%)

Memory

-25.0MiB live, 194.2MiB allocated

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 716 to 486 computations (32.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	52	113
1	78	113
2	96	113
3	115	113
4	127	113
5	139	113
6	144	113
7	152	113
8	154	113
9	155	113

Iter	Nodes	Cost
0	52	113
1	78	113
2	96	113
3	115	113
4	127	113
5	139	113
6	144	113
7	152	113
8	154	113
9	155	113

analyze1.1s (5.8%)

sample6.0s (32.7%)

preprocess328.0ms (1.8%)

explain268.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify376.0ms (2.1%)

localize67.0ms (0.4%)

series82.0ms (0.5%)

rewrite492.0ms (2.7%)

simplify466.0ms (2.6%)

eval85.0ms (0.5%)

prune100.0ms (0.6%)

simplify257.0ms (1.4%)

localize110.0ms (0.6%)

series87.0ms (0.5%)

rewrite603.0ms (3.3%)

simplify489.0ms (2.7%)

eval103.0ms (0.6%)

prune176.0ms (1%)

simplify276.0ms (1.5%)

localize237.0ms (1.3%)

series185.0ms (1%)

rewrite478.0ms (2.6%)

simplify824.0ms (4.5%)

eval427.0ms (2.3%)

prune573.0ms (3.2%)

simplify348.0ms (1.9%)

localize277.0ms (1.5%)

series92.0ms (0.5%)

rewrite486.0ms (2.7%)

simplify460.0ms (2.5%)

eval192.0ms (1.1%)

prune248.0ms (1.4%)

regimes103.0ms (0.6%)

regimes86.0ms (0.5%)

regimes55.0ms (0.3%)

regimes27.0ms (0.1%)

regimes27.0ms (0.1%)

regimes18.0ms (0.1%)

regimes17.0ms (0.1%)

regimes17.0ms (0.1%)

regimes12.0ms (0.1%)

simplify15.0ms (0.1%)

soundness1.5s (8.3%)

preprocess90.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	52	113
1	78	113
2	96	113
3	115	113
4	127	113
5	139	113
6	144	113
7	152	113
8	154	113
9	155	113