Metrics for HairBSDF, Mp, lower

analyze405.0ms (2.8%)

Memory

26.6MiB live, 966.3MiB 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 (41.7%)

Memory

13.9MiB live, 3 891.1MiB allocated

Samples

4.1s	8 256×	0	valid
233.0ms	137×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 3.5s

const: 1.0s (29.9% of total)

ival-<=: 750.0ms (21.5% of total)

ival-div: 624.0ms (17.9% of total)

ival-mult: 557.0ms (16% of total)

ival-log: 211.0ms (6% of total)

ival-exp: 92.0ms (2.6% of total)

ival-add: 73.0ms (2.1% of total)

ival-sub: 70.0ms (2% of total)

ival-and: 52.0ms (1.5% of total)

exact: 16.0ms (0.5% of total)

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

Bogosity

preprocess320.0ms (2.2%)

Memory

-3.6MiB live, 480.4MiB 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)))))

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

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)

explain251.0ms (1.8%)

Memory

28.6MiB live, 503.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
88	4	(-1.4267898799198806e-19 3.4587471994022067e-35 -0.0004458891344256699 -7.982112469527632e-28 1.3787234687256955e-9)	19	(-7.0575003334114865e-19 8.58710778963081e-26 4.0288595604186957e-22 0.003017882350832224 3.4486362210373045e-7)	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`
85	4	(2.3875044462376147e-30 9.772385204939578e-28 1.0557072147325028e-35 1.1188818489137608e-19 1.8876457341665542e-10)	24	(-7.625037113377218e-29 4.238448195392676e-30 -2.623048489153369e-35 2.3063133625100818e-9 1.3604545298333358e-33)	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`
3	4	(-4.9693672574955546e-27 6.149358895479229e-32 -4.109242865979468e-7 -8.508743043478262e-9 0.0018757825018838048)	3	(-1.2107899127755672e-9 1.9712709686814378e-8 -2.0069981787607105e-10 1.4672363022327772e-6 0.025411022827029228)	`(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 cosTheta_i cosTheta_O) v)`	u/n	10	0
↳	`(*.f32 cosTheta_i cosTheta_O)`	underflow	95
`/.f32`	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`	u/n	9	0
↳	`(*.f32 sinTheta_i sinTheta_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	4	3

Confusion

	Predicted +	Predicted -
+	0	3
-	22	231

Precision

0.0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	3	0
-	22	0	231

Precision?

0.12

Recall?

1.0

Freqs

test

number	freq
0	234
1	21
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

89.0ms

512×

valid

Compiler

Compiled 330 to 88 computations (73.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-div: 14.0ms (21.8% of total)

ival-add: 12.0ms (18.7% of total)

ival-mult: 11.0ms (17.1% of total)

const: 11.0ms (17.1% of total)

ival-log: 6.0ms (9.3% of total)

ival-exp: 4.0ms (6.2% of total)

ival-sub: 4.0ms (6.2% of total)

exact: 1.0ms (1.6% of total)

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

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

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 5 to 5 computations (0% saved)

prune1.0ms (0%)

Memory

2.9MiB live, 2.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	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)))))

Status

Accuracy

Program

▶

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)))))

Compiler

Compiled 30 to 21 computations (30% saved)

simplify269.0ms (1.9%)

Memory

-11.1MiB live, 431.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

6 404×	`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)))))
(/.f32 (exp.f32 (fma.f32 (/.f32 #s(literal -1 binary32) v) (fma.f32 sinTheta_i sinTheta_O #s(literal 1 binary32)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) #s(literal 6931/10000 binary32)))) (*.f32 v #s(literal 2 binary32)))
(+ (+ (- (- (/ (* 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)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v))
(fma.f32 sinTheta_i (/.f32 sinTheta_O (neg.f32 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(/ (* cosTheta_i cosTheta_O) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(* cosTheta_i cosTheta_O)
(*.f32 cosTheta_i cosTheta_O)
cosTheta_i
cosTheta_O
v
(/ (* sinTheta_i sinTheta_O) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(* 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)

localize64.0ms (0.4%)

Memory

-7.1MiB live, 151.3MiB 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	76.5%	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	accuracy	76.1%	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Samples

41.0ms

256×

valid

Compiler

Compiled 135 to 23 computations (83% saved)

Precisions

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

ival-div: 8.0ms (30.5% of total)

ival-mult: 5.0ms (19% of total)

const: 4.0ms (15.2% of total)

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

ival-exp: 2.0ms (7.6% 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)

series81.0ms (0.6%)

Memory

20.1MiB live, 173.5MiB 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 (/ (* cosTheta_i cosTheta_O) v)>
#<alt (/ (* sinTheta_i sinTheta_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 (/ (* 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 (/ (* 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 (* -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)))
20.0ms	v	@	-inf	(log (/ 1 (* 2 v)))
8.0ms	v	@	inf	(log (/ 1 (* 2 v)))
3.0ms	v	@	inf	(- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v))
1.0ms	v	@	-inf	(exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1 v)) 6931/10000) (log (/ 1 (* 2 v)))))

rewrite397.0ms (2.8%)

Memory

12.4MiB live, 895.4MiB 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)))
(/ (* cosTheta_i cosTheta_O) v)
(/ (* sinTheta_i sinTheta_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))) (neg.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 (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 (.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 (neg.f32 (.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 (neg.f32 (.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 (neg.f32 (.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)))
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(.f32 (neg.f32 (-.f32 (.f32 (.f32 cosTheta_i cosTheta_O) v) (.f32 v (.f32 sinTheta_i sinTheta_O)))) (/.f32 #s(literal 1 binary32) (neg.f32 (.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 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.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 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_O (neg.f32 sinTheta_i))) v))))
(.f32 (/.f32 (-.f32 (.f32 (.f32 cosTheta_i cosTheta_O) v) (.f32 v (*.f32 sinTheta_i sinTheta_O))) v) (/.f32 #s(literal 1 binary32) v))

simplify374.0ms (2.6%)

Memory

8.7MiB live, 833.7MiB 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)))
(/ (* 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)
(/ (* 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)
(* -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))))
(fma.f32 cosTheta_O (fma.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 cosTheta_O (fma.f32 #s(literal 1/6 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 (.f32 cosTheta_O cosTheta_i) (.f32 cosTheta_i cosTheta_i))) (.f32 v (.f32 v v))) (/.f32 (.f32 #s(literal 1/2 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 cosTheta_i))) (.f32 v v))))) (.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.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))))
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(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/ (* sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(* cosTheta_i (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))) (/ cosTheta_O v)))
(.f32 cosTheta_i (fma.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v (neg.f32 cosTheta_i))) (/.f32 cosTheta_O v)))
(* cosTheta_i (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))) (/ cosTheta_O v)))
(.f32 cosTheta_i (fma.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v (neg.f32 cosTheta_i))) (/.f32 cosTheta_O v)))
(* cosTheta_i (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v))) (/ cosTheta_O v)))
(.f32 cosTheta_i (fma.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v (neg.f32 cosTheta_i))) (/.f32 cosTheta_O v)))
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(.f32 cosTheta_i (fma.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v (neg.f32 cosTheta_i))) (/.f32 cosTheta_O v)))
(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(.f32 cosTheta_i (fma.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v (neg.f32 cosTheta_i))) (/.f32 cosTheta_O v)))
(* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_i v)))))
(.f32 cosTheta_i (fma.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v (neg.f32 cosTheta_i))) (/.f32 cosTheta_O v)))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(- (/ (* cosTheta_O cosTheta_i) v) (/ (* sinTheta_O sinTheta_i) v))
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (* 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)))
(.f32 cosTheta_O (fma.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v (neg.f32 cosTheta_O))) (/.f32 cosTheta_i v)))
(* cosTheta_O (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))) (/ cosTheta_i v)))
(.f32 cosTheta_O (fma.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v (neg.f32 cosTheta_O))) (/.f32 cosTheta_i v)))
(* cosTheta_O (+ (* -1 (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v))) (/ cosTheta_i v)))
(.f32 cosTheta_O (fma.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v (neg.f32 cosTheta_O))) (/.f32 cosTheta_i v)))
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(.f32 cosTheta_O (fma.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v (neg.f32 cosTheta_O))) (/.f32 cosTheta_i v)))
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(.f32 cosTheta_O (fma.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v (neg.f32 cosTheta_O))) (/.f32 cosTheta_i v)))
(* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ (* sinTheta_O sinTheta_i) (* cosTheta_O v)))))
(.f32 cosTheta_O (fma.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v (neg.f32 cosTheta_O))) (/.f32 cosTheta_i v)))
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (- (* cosTheta_O cosTheta_i) (* sinTheta_O sinTheta_i)) v)
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(* -1 (/ (- (* -1 (* cosTheta_O cosTheta_i)) (* -1 (* sinTheta_O sinTheta_i))) v))
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(* -1 (/ (- (* -1 (* cosTheta_O cosTheta_i)) (* -1 (* sinTheta_O sinTheta_i))) v))
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(* -1 (/ (- (* -1 (* cosTheta_O cosTheta_i)) (* -1 (* sinTheta_O sinTheta_i))) v))
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(* -1 (/ (- (* -1 (* cosTheta_O cosTheta_i)) (* -1 (* sinTheta_O sinTheta_i))) v))
(/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) (*.f32 cosTheta_O cosTheta_i)) v)
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* 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) v)) (/ (* 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) v)) (/ (* 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) v))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (/ sinTheta_O v)))
(.f32 sinTheta_i (fma.f32 cosTheta_O (/.f32 cosTheta_i (.f32 v sinTheta_i)) (/.f32 sinTheta_O (neg.f32 v))))
(* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (/ sinTheta_O v)))
(.f32 sinTheta_i (fma.f32 cosTheta_O (/.f32 cosTheta_i (.f32 v sinTheta_i)) (/.f32 sinTheta_O (neg.f32 v))))
(* sinTheta_i (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v)) (/ sinTheta_O v)))
(.f32 sinTheta_i (fma.f32 cosTheta_O (/.f32 cosTheta_i (.f32 v sinTheta_i)) (/.f32 sinTheta_O (neg.f32 v))))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(* -1 (* sinTheta_i (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (* -1 (/ sinTheta_O v)))))
(.f32 sinTheta_i (fma.f32 cosTheta_O (/.f32 cosTheta_i (.f32 v sinTheta_i)) (/.f32 sinTheta_O (neg.f32 v))))
(* -1 (* sinTheta_i (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (* -1 (/ sinTheta_O v)))))
(.f32 sinTheta_i (fma.f32 cosTheta_O (/.f32 cosTheta_i (.f32 v sinTheta_i)) (/.f32 sinTheta_O (neg.f32 v))))
(* -1 (* sinTheta_i (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_i v))) (* -1 (/ sinTheta_O v)))))
(.f32 sinTheta_i (fma.f32 cosTheta_O (/.f32 cosTheta_i (.f32 v sinTheta_i)) (/.f32 sinTheta_O (neg.f32 v))))
(/ (* cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* 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) v)) (/ (* 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) v)) (/ (* 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) v))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (/ sinTheta_i v)))
(.f32 sinTheta_O (fma.f32 cosTheta_O (/.f32 cosTheta_i (.f32 v sinTheta_O)) (/.f32 (neg.f32 sinTheta_i) v)))
(* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (/ sinTheta_i v)))
(.f32 sinTheta_O (fma.f32 cosTheta_O (/.f32 cosTheta_i (.f32 v sinTheta_O)) (/.f32 (neg.f32 sinTheta_i) v)))
(* sinTheta_O (- (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v)) (/ sinTheta_i v)))
(.f32 sinTheta_O (fma.f32 cosTheta_O (/.f32 cosTheta_i (.f32 v sinTheta_O)) (/.f32 (neg.f32 sinTheta_i) v)))
(* -1 (/ (* sinTheta_O sinTheta_i) v))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(* -1 (* sinTheta_O (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (* -1 (/ sinTheta_i v)))))
(.f32 sinTheta_O (fma.f32 cosTheta_O (/.f32 cosTheta_i (.f32 v sinTheta_O)) (/.f32 (neg.f32 sinTheta_i) v)))
(* -1 (* sinTheta_O (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (* -1 (/ sinTheta_i v)))))
(.f32 sinTheta_O (fma.f32 cosTheta_O (/.f32 cosTheta_i (.f32 v sinTheta_O)) (/.f32 (neg.f32 sinTheta_i) v)))
(* -1 (* sinTheta_O (- (* -1 (/ (* cosTheta_O cosTheta_i) (* sinTheta_O v))) (* -1 (/ sinTheta_i v)))))
(.f32 sinTheta_O (fma.f32 cosTheta_O (/.f32 cosTheta_i (.f32 v sinTheta_O)) (/.f32 (neg.f32 sinTheta_i) v)))

eval79.0ms (0.5%)

Memory: 6.4MiB live, 196.5MiB allocated
Compiler: Compiled 25 794 to 2 903 computations (88.7% saved)

prune85.0ms (0.6%)

Memory

5.6MiB live, 205.8MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	745	4	749
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	746	4	750

Accuracy

99.9%

Counts

750 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(.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)))
▶	4.5%	(.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)))))
▶	99.8%	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))))

Compiler

Compiled 76 to 61 computations (19.7% saved)

simplify291.0ms (2%)

Memory

-0.5MiB live, 517.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(exp.f32 #s(literal 6931/10000 binary32))
✓	cost-diff	0	(/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (*.f32 v #s(literal 2 binary32)))
✓	cost-diff	64	(+.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O (neg.f32 sinTheta_i))) #s(literal -1 binary32))
✓	cost-diff	3264	(.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)))
✓	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))
✓	cost-diff	0	(+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
✓	cost-diff	64	(+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
✓	cost-diff	128	(log.f32 (/.f32 #s(literal 1/2 binary32) v))
✓	cost-diff	2944	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))))

Rules

8 388×	`accelerator-lowering-fma.f32`
8 388×	`accelerator-lowering-fma.f64`
3 376×	`-lowering-.f32`
3 376×	`-lowering-.f64`
2 498×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	243
1	81	233
2	169	224
3	338	224
4	697	224
5	1423	224
6	2081	224
7	3577	224
8	6901	224
0	8124	211

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize208.0ms (1.5%)

Memory

-59.0MiB live, 255.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
✓	accuracy	99.9%	(.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)))
✓	accuracy	99.9%	(exp.f32 (/.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O (neg.f32 sinTheta_i))) #s(literal -1 binary32)) v))
✓	accuracy	99.0%	(/.f32 (exp.f32 #s(literal 6931/10000 binary32)) (*.f32 v #s(literal 2 binary32)))
✓	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 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v))
✓	accuracy	100.0%	(+.f32 #s(literal 6931/10000 binary32) (*.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v)))
✓	accuracy	99.9%	(.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	99.9%	(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%	(log.f32 (/.f32 #s(literal 1/2 binary32) v))
✓	accuracy	99.9%	(+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
✓	accuracy	99.8%	(+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
✓	accuracy	99.8%	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))))

Samples

131.0ms

256×

valid

Compiler

Compiled 228 to 41 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 79.0ms

ival-div: 39.0ms (49.6% of total)

ival-mult: 13.0ms (16.5% of total)

ival-add: 8.0ms (10.2% of total)

ival-exp: 7.0ms (8.9% of total)

const: 7.0ms (8.9% of total)

ival-log: 3.0ms (3.8% of total)

exact: 1.0ms (1.3% of total)

ival-neg: 1.0ms (1.3% of total)

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

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

series58.0ms (0.4%)

Memory

27.8MiB live, 105.8MiB allocated

Counts

18 → 528

Calls

Call 1

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

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

Calls

132 calls:

Time	Variable		Point	Expression
3.0ms	sinTheta_O	@	0	(* (/ 1/2 v) (exp (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v)))))
3.0ms	cosTheta_O	@	0	(+ (log (/ 1/2 v)) (/ (+ (* cosTheta_O cosTheta_i) -1) v))
2.0ms	cosTheta_i	@	-inf	(+ (+ (* cosTheta_i cosTheta_O) (* sinTheta_O (neg sinTheta_i))) -1)
2.0ms	v	@	inf	(exp (/ (+ (+ (* cosTheta_i cosTheta_O) (* sinTheta_O (neg sinTheta_i))) -1) v))
1.0ms	v	@	inf	(* (/ 1/2 v) (exp (+ 6931/10000 (* (+ (* sinTheta_O sinTheta_i) 1) (/ -1 v)))))

rewrite334.0ms (2.3%)

Memory

1.1MiB live, 597.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 040×	`accelerator-lowering-fma.f32`
5 040×	`accelerator-lowering-fma.f64`
4 168×	`-lowering-.f32`
4 168×	`-lowering-.f64`
4 036×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	172
1	207	159
2	1632	158
0	8197	148

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 690

Calls

Call 1

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

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

simplify425.0ms (3%)

Memory

-15.1MiB live, 618.6MiB allocated

Algorithm

1×	egg-herbie

Rules

8 022×	`-lowering-.f32`
8 022×	`-lowering-.f64`
7 858×	`accelerator-lowering-fma.f32`
7 858×	`accelerator-lowering-fma.f64`
3 520×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	744	8384
1	2345	7949
0	8064	7513

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 528

Calls

Call 1

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

Outputs
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))))
(exp (- (+ 6931/10000 (+ (log (/ 1/2 v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v)))
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))))
(exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v)))))
(exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 1/2 binary32))) (log.f32 v)))
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(fma.f32 (exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 1/2 binary32))) (log.f32 v))) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v) (exp.f32 (-.f32 (+.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 1/2 binary32))) (log.f32 v))))
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(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
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(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
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(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
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(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
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(+ (* -1/2 (/ (* sinTheta_O (* sinTheta_i (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))))) (pow v 2))) (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v)))
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(+ (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v)) (* sinTheta_O (+ (* -1/2 (/ (* sinTheta_i (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))) (pow v 2))) (* 1/4 (/ (* sinTheta_O (* (pow sinTheta_i 2) (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))))) (pow v 3))))))
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(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
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(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
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(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
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(+ (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v)) (* sinTheta_i (+ (* -1/2 (/ (* sinTheta_O (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))) (pow v 2))) (* 1/4 (/ (* (pow sinTheta_O 2) (* sinTheta_i (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))))) (pow v 3))))))
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(+ (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v)) (* sinTheta_i (+ (* -1/2 (/ (* sinTheta_O (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))) (pow v 2))) (* sinTheta_i (+ (* -1/12 (/ (* (pow sinTheta_O 3) (* sinTheta_i (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))))) (pow v 4))) (* 1/4 (/ (* (pow sinTheta_O 2) (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))) (pow v 3))))))))
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(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
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(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
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(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))) v))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.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)))) v)
(- (* -1 (* sinTheta_O sinTheta_i)) 1)
(fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))
(- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1)
(fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))
(- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1)
(fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))
(- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1)
(fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))
(* cosTheta_O cosTheta_i)
(*.f32 cosTheta_O cosTheta_i)
(* cosTheta_i (- (+ cosTheta_O (* -1 (/ (* sinTheta_O sinTheta_i) cosTheta_i))) (/ 1 cosTheta_i)))
(*.f32 cosTheta_i (+.f32 cosTheta_O (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) cosTheta_i)))
(* cosTheta_i (- (+ cosTheta_O (* -1 (/ (* sinTheta_O sinTheta_i) cosTheta_i))) (/ 1 cosTheta_i)))
(*.f32 cosTheta_i (+.f32 cosTheta_O (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) cosTheta_i)))
(* cosTheta_i (- (+ cosTheta_O (* -1 (/ (* sinTheta_O sinTheta_i) cosTheta_i))) (/ 1 cosTheta_i)))
(*.f32 cosTheta_i (+.f32 cosTheta_O (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) cosTheta_i)))
(* cosTheta_O cosTheta_i)
(*.f32 cosTheta_O cosTheta_i)
(* -1 (* cosTheta_i (+ (* -1 cosTheta_O) (* -1 (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) cosTheta_i)))))
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(* -1 (* cosTheta_i (+ (* -1 cosTheta_O) (* -1 (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) cosTheta_i)))))
(*.f32 (-.f32 (neg.f32 cosTheta_O) (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) cosTheta_i)) (neg.f32 cosTheta_i))
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(* cosTheta_O cosTheta_i)
(*.f32 cosTheta_O cosTheta_i)
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(*.f32 cosTheta_O (+.f32 cosTheta_i (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) cosTheta_O)))
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(* cosTheta_O cosTheta_i)
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(* -1 (* sinTheta_O sinTheta_i))
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(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 (/ (+ 1 (* sinTheta_O sinTheta_i)) v))))
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(exp (- 6931/10000 (/ 1 v)))
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))
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(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)
(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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(exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v))
(+ (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v)) (/ (* cosTheta_O (* cosTheta_i (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v)))) v))
(fma.f32 cosTheta_O (*.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v)) (/.f32 cosTheta_i v)) (exp.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v)))
(+ (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v)) (* cosTheta_i (+ (* 1/2 (/ (* (pow cosTheta_O 2) (* cosTheta_i (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v)))) (pow v 2))) (/ (* cosTheta_O (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v))) v))))
(fma.f32 cosTheta_i (fma.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta_O cosTheta_O) (.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v)) (/.f32 cosTheta_i (.f32 v v)))) (*.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v)) (/.f32 cosTheta_O v))) (exp.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v)))
(+ (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v)) (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ (* (pow cosTheta_O 3) (* cosTheta_i (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v)))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_O 2) (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v))) (pow v 2))))) (/ (* cosTheta_O (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v))) v))))
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(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v))
(+ (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v)) (/ (* cosTheta_O (* cosTheta_i (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v)))) v))
(fma.f32 cosTheta_O (*.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v)) (/.f32 cosTheta_i v)) (exp.f32 (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v)))
(+ (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v)) (* cosTheta_O (+ (* 1/2 (/ (* cosTheta_O (* (pow cosTheta_i 2) (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v)))) (pow v 2))) (/ (* cosTheta_i (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v))) v))))
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(+ (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v)) (* cosTheta_O (+ (* cosTheta_O (+ (* 1/6 (/ (* cosTheta_O (* (pow cosTheta_i 3) (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v)))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_i 2) (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v))) (pow v 2))))) (/ (* cosTheta_i (exp (/ (- (* -1 (* sinTheta_O sinTheta_i)) 1) v))) v))))
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(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(+ (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))) v)))
(fma.f32 (neg.f32 sinTheta_O) (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (/.f32 sinTheta_i v)) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
(+ (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v)) (* 1/2 (/ (* sinTheta_O (* (pow sinTheta_i 2) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))) (pow v 2))))))
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(+ (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)) (* sinTheta_O (+ (* -1 (/ (* sinTheta_i (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v)) (* sinTheta_O (+ (* -1/6 (/ (* sinTheta_O (* (pow sinTheta_i 3) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_i 2) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) (pow v 2))))))))
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(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
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(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
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(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
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(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(+ (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)) (* -1 (/ (* sinTheta_O (* sinTheta_i (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))) v)))
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(+ (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v)) (* 1/2 (/ (* (pow sinTheta_O 2) (* sinTheta_i (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))) (pow v 2))))))
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(+ (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)) (* sinTheta_i (+ (* -1 (/ (* sinTheta_O (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v)) (* sinTheta_i (+ (* -1/6 (/ (* (pow sinTheta_O 3) (* sinTheta_i (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))) (pow v 3))) (* 1/2 (/ (* (pow sinTheta_O 2) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) (pow v 2))))))))
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(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
(exp (/ (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v))
1
#s(literal 1 binary32)
(- (+ 1 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))
(+.f32 #s(literal 1 binary32) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v)))
(- (+ 1 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (+ (* 1/2 (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))
(+.f32 #s(literal 1 binary32) (+.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))) (.f32 v v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v)))
(- (+ 1 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (+ (* 1/6 (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 3) (pow v 3))) (+ (* 1/2 (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v))))) (/ 1 v))
(+.f32 #s(literal 1 binary32) (+.f32 (fma.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) (/.f32 (.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))) (.f32 v (.f32 v v)))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))) (.f32 v v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v)))
1
#s(literal 1 binary32)
(- (+ 1 (+ (* -1 (/ (* sinTheta_O sinTheta_i) v)) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))
(+.f32 #s(literal 1 binary32) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)) v)))
(+ 1 (* -1 (/ (+ (* -1 (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1)) (* -1/2 (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2) v))) v)))
(-.f32 #s(literal 1 binary32) (/.f32 (fma.f32 #s(literal -1/2 binary32) (/.f32 (*.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))) v) (neg.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))))) v))
(+ 1 (* -1 (/ (+ (* -1 (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1)) (* -1 (/ (+ (* 1/6 (/ (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 3) v)) (* 1/2 (pow (- (+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i)) 1) 2))) v))) v)))
(-.f32 #s(literal 1 binary32) (/.f32 (-.f32 (neg.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))) (.f32 #s(literal 1/6 binary32) (.f32 (.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32)))) (/.f32 (fma.f32 cosTheta_O cosTheta_i (fma.f32 sinTheta_O (neg.f32 sinTheta_i) #s(literal -1 binary32))) v)))) v)) v))
(* -1 (* sinTheta_O sinTheta_i))
(*.f32 sinTheta_i (neg.f32 sinTheta_O))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
(* 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 (neg.f32 cosTheta_i) (fma.f32 sinTheta_O (/.f32 sinTheta_i cosTheta_i) (neg.f32 cosTheta_O)))
(* -1 (* cosTheta_i (+ (* -1 cosTheta_O) (/ (* sinTheta_O sinTheta_i) cosTheta_i))))
(*.f32 (neg.f32 cosTheta_i) (fma.f32 sinTheta_O (/.f32 sinTheta_i cosTheta_i) (neg.f32 cosTheta_O)))
(* -1 (* cosTheta_i (+ (* -1 cosTheta_O) (/ (* sinTheta_O sinTheta_i) cosTheta_i))))
(*.f32 (neg.f32 cosTheta_i) (fma.f32 sinTheta_O (/.f32 sinTheta_i cosTheta_i) (neg.f32 cosTheta_O)))
(* -1 (* sinTheta_O sinTheta_i))
(*.f32 sinTheta_i (neg.f32 sinTheta_O))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
(* 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))))
(*.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))))
(*.f32 (neg.f32 cosTheta_O) (fma.f32 sinTheta_O (/.f32 sinTheta_i cosTheta_O) (neg.f32 cosTheta_i)))
(* cosTheta_O cosTheta_i)
(*.f32 cosTheta_O cosTheta_i)
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
(* -1 (* sinTheta_O sinTheta_i))
(*.f32 sinTheta_i (neg.f32 sinTheta_O))
(* 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)))
(*.f32 sinTheta_O (fma.f32 cosTheta_O (/.f32 cosTheta_i sinTheta_O) (neg.f32 sinTheta_i)))
(* -1 (* sinTheta_O sinTheta_i))
(*.f32 sinTheta_i (neg.f32 sinTheta_O))
(* -1 (* sinTheta_O (+ sinTheta_i (* -1 (/ (* cosTheta_O cosTheta_i) sinTheta_O)))))
(*.f32 (neg.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 (neg.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 (neg.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 cosTheta_O cosTheta_i (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
(+ (* -1 (* sinTheta_O sinTheta_i)) (* cosTheta_O cosTheta_i))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
(* -1 (* sinTheta_O sinTheta_i))
(*.f32 sinTheta_i (neg.f32 sinTheta_O))
(* sinTheta_i (+ (* -1 sinTheta_O) (/ (* cosTheta_O cosTheta_i) sinTheta_i)))
(*.f32 sinTheta_i (fma.f32 cosTheta_O (/.f32 cosTheta_i sinTheta_i) (neg.f32 sinTheta_O)))
(* sinTheta_i (+ (* -1 sinTheta_O) (/ (* cosTheta_O cosTheta_i) sinTheta_i)))
(*.f32 sinTheta_i (fma.f32 cosTheta_O (/.f32 cosTheta_i sinTheta_i) (neg.f32 sinTheta_O)))
(* sinTheta_i (+ (* -1 sinTheta_O) (/ (* cosTheta_O cosTheta_i) sinTheta_i)))
(*.f32 sinTheta_i (fma.f32 cosTheta_O (/.f32 cosTheta_i sinTheta_i) (neg.f32 sinTheta_O)))
(* -1 (* sinTheta_O sinTheta_i))
(*.f32 sinTheta_i (neg.f32 sinTheta_O))
(* -1 (* sinTheta_i (+ sinTheta_O (* -1 (/ (* cosTheta_O cosTheta_i) sinTheta_i)))))
(*.f32 (neg.f32 sinTheta_i) (fma.f32 (neg.f32 cosTheta_O) (/.f32 cosTheta_i sinTheta_i) sinTheta_O))
(* -1 (* sinTheta_i (+ sinTheta_O (* -1 (/ (* cosTheta_O cosTheta_i) sinTheta_i)))))
(*.f32 (neg.f32 sinTheta_i) (fma.f32 (neg.f32 cosTheta_O) (/.f32 cosTheta_i sinTheta_i) sinTheta_O))
(* -1 (* sinTheta_i (+ sinTheta_O (* -1 (/ (* cosTheta_O cosTheta_i) sinTheta_i)))))
(*.f32 (neg.f32 sinTheta_i) (fma.f32 (neg.f32 cosTheta_O) (/.f32 cosTheta_i sinTheta_i) sinTheta_O))

eval155.0ms (1.1%)

Memory: 41.3MiB live, 226.7MiB allocated
Compiler: Compiled 33 821 to 3 468 computations (89.7% saved)

prune151.0ms (1.1%)

Memory

-38.3MiB live, 330.0MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	1 246	9	1 255
Fresh	0	0	0
Picked	4	0	4
Done	0	0	0
Total	1 250	9	1 259

Accuracy

99.9%

Counts

1 259 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
▶	4.5%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v)
▶	99.8%	(.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
	4.5%	(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 #s(literal 6931/10000 binary32)))
	99.8%	(.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (.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)))
	98.7%	(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
▶	14.9%	(exp.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
▶	98.7%	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
▶	99.8%	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 #s(literal -1 binary32) v))))

Compiler

Compiled 270 to 220 computations (18.5% saved)

simplify10.0ms (0.1%)

Memory

22.2MiB live, 22.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log.f32 (/.f32 #s(literal 1/2 binary32) v))
✓	cost-diff	0	(+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 #s(literal -1 binary32) v))
✓	cost-diff	0	(+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 #s(literal -1 binary32) v)))
✓	cost-diff	3136	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 #s(literal -1 binary32) v))))
✓	cost-diff	0	(fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))
✓	cost-diff	0	(/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)
✓	cost-diff	0	(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
✓	cost-diff	0	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
✓	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 (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v)
✓	cost-diff	0	(*.f32 cosTheta_O cosTheta_i)
✓	cost-diff	0	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	cost-diff	0	(exp.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	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 (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v)
✓	cost-diff	3264	(.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))

Rules

144×	`-lowering-.f32`
144×	`-lowering-.f64`
48×	`+-lowering-+.f64`
48×	`+-lowering-+.f32`
44×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	164
1	42	163
2	75	162
3	117	162
4	154	162
5	175	162
6	181	162
7	182	162
0	182	154

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize91.0ms (0.6%)

Memory

13.5MiB live, 209.2MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(log.f32 (/.f32 #s(literal 1/2 binary32) v))
✓	accuracy	99.9%	(+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 #s(literal -1 binary32) v)))
✓	accuracy	99.8%	(+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 #s(literal -1 binary32) v))
✓	accuracy	99.8%	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 #s(literal -1 binary32) v))))
✓	accuracy	100.0%	(fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))
✓	accuracy	100.0%	(/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)
✓	accuracy	100.0%	(+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
✓	accuracy	99.9%	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #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	99.0%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v)
✓	accuracy	100.0%	(*.f32 cosTheta_O cosTheta_i)
✓	accuracy	99.8%	(exp.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	accuracy	76.1%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	accuracy	100.0%	(exp.f32 #s(literal 6931/10000 binary32))
✓	accuracy	99.9%	(.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
✓	accuracy	99.9%	(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
✓	accuracy	99.0%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v)

Samples

53.0ms

256×

valid

Compiler

Compiled 158 to 28 computations (82.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-exp: 11.0ms (30.5% of total)

ival-div: 8.0ms (22.2% of total)

ival-mult: 5.0ms (13.8% of total)

ival-add: 4.0ms (11.1% of total)

const: 4.0ms (11.1% of total)

ival-log: 3.0ms (8.3% of total)

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

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

exact: 0.0ms (0% of total)

series74.0ms (0.5%)

Memory

-28.1MiB live, 50.1MiB allocated

Counts

16 → 360

Calls

Call 1

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

Outputs
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (/ (+ (* 1/2 (exp 6931/10000)) (* 1/2 (/ (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)) v))) v)>
#<alt (/ (+ (* 1/4 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 2)) (pow v 2))) (+ (* 1/2 (exp 6931/10000)) (* 1/2 (/ (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)) v)))) v)>
#<alt (/ (+ (* 1/12 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 3)) (pow v 3))) (+ (* 1/4 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 2)) (pow v 2))) (+ (* 1/2 (exp 6931/10000)) (* 1/2 (/ (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)) v))))) v)>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* -1 (/ (+ (* -1/2 (exp 6931/10000)) (* -1/2 (/ (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)) v))) v))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 2)) v)) (* 1/2 (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)))) v)) (* -1/2 (exp 6931/10000))) v))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 2))) (* -1/12 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 3)) v))) v)) (* 1/2 (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)))) v)) (* -1/2 (exp 6931/10000))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v))>
#<alt (+ (* 1/2 (/ (* cosTheta_O (* cosTheta_i (* (exp 6931/10000) (exp (/ -1 v))))) (pow v 2))) (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v)))>
#<alt (+ (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v)) (* cosTheta_O (+ (* 1/4 (/ (* cosTheta_O (* (pow cosTheta_i 2) (* (exp 6931/10000) (exp (/ -1 v))))) (pow v 3))) (* 1/2 (/ (* cosTheta_i (* (exp 6931/10000) (exp (/ -1 v)))) (pow v 2))))))>
#<alt (+ (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v)) (* cosTheta_O (+ (* 1/2 (/ (* cosTheta_i (* (exp 6931/10000) (exp (/ -1 v)))) (pow v 2))) (* cosTheta_O (+ (* 1/12 (/ (* cosTheta_O (* (pow cosTheta_i 3) (* (exp 6931/10000) (exp (/ -1 v))))) (pow v 4))) (* 1/4 (/ (* (pow cosTheta_i 2) (* (exp 6931/10000) (exp (/ -1 v)))) (pow v 3))))))))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v))>
#<alt (+ (* 1/2 (/ (* cosTheta_O (* cosTheta_i (* (exp 6931/10000) (exp (/ -1 v))))) (pow v 2))) (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v)))>
#<alt (+ (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v)) (* cosTheta_i (+ (* 1/4 (/ (* (pow cosTheta_O 2) (* cosTheta_i (* (exp 6931/10000) (exp (/ -1 v))))) (pow v 3))) (* 1/2 (/ (* cosTheta_O (* (exp 6931/10000) (exp (/ -1 v)))) (pow v 2))))))>
#<alt (+ (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v)) (* cosTheta_i (+ (* 1/2 (/ (* cosTheta_O (* (exp 6931/10000) (exp (/ -1 v)))) (pow v 2))) (* cosTheta_i (+ (* 1/12 (/ (* (pow cosTheta_O 3) (* cosTheta_i (* (exp 6931/10000) (exp (/ -1 v))))) (pow v 4))) (* 1/4 (/ (* (pow cosTheta_O 2) (* (exp 6931/10000) (exp (/ -1 v)))) (pow v 3))))))))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) 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))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt 1>
#<alt (+ 1 (/ (* cosTheta_O cosTheta_i) v))>
#<alt (+ 1 (* cosTheta_O (+ (* 1/2 (/ (* cosTheta_O (pow cosTheta_i 2)) (pow v 2))) (/ cosTheta_i v))))>
#<alt (+ 1 (* cosTheta_O (+ (* cosTheta_O (+ (* 1/6 (/ (* cosTheta_O (pow cosTheta_i 3)) (pow v 3))) (* 1/2 (/ (pow cosTheta_i 2) (pow v 2))))) (/ cosTheta_i v))))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt 1>
#<alt (+ 1 (/ (* cosTheta_O cosTheta_i) v))>
#<alt (+ 1 (* cosTheta_i (+ (* 1/2 (/ (* (pow cosTheta_O 2) cosTheta_i) (pow v 2))) (/ cosTheta_O v))))>
#<alt (+ 1 (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ (* (pow cosTheta_O 3) cosTheta_i) (pow v 3))) (* 1/2 (/ (pow cosTheta_O 2) (pow v 2))))) (/ cosTheta_O v))))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt (exp (/ (* cosTheta_O cosTheta_i) v))>
#<alt 1>
#<alt (+ 1 (/ (* cosTheta_O cosTheta_i) v))>
#<alt (+ 1 (+ (* 1/2 (/ (* (pow cosTheta_O 2) (pow cosTheta_i 2)) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v)))>
#<alt (+ 1 (+ (* 1/6 (/ (* (pow cosTheta_O 3) (pow cosTheta_i 3)) (pow v 3))) (+ (* 1/2 (/ (* (pow cosTheta_O 2) (pow cosTheta_i 2)) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v))))>
#<alt 1>
#<alt (+ 1 (/ (* cosTheta_O cosTheta_i) v))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (* cosTheta_O cosTheta_i)) (* -1/2 (/ (* (pow cosTheta_O 2) (pow cosTheta_i 2)) v))) v)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (* cosTheta_O cosTheta_i)) (* -1 (/ (+ (* 1/6 (/ (* (pow cosTheta_O 3) (pow cosTheta_i 3)) v)) (* 1/2 (* (pow cosTheta_O 2) (pow cosTheta_i 2)))) v))) 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 (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (exp (- 6931/10000 (/ 1 v)))>
#<alt (+ (exp (- 6931/10000 (/ 1 v))) (/ (* cosTheta_O (* cosTheta_i (exp (- 6931/10000 (/ 1 v))))) v))>
#<alt (+ (exp (- 6931/10000 (/ 1 v))) (* cosTheta_O (+ (* 1/2 (/ (* cosTheta_O (* (pow cosTheta_i 2) (exp (- 6931/10000 (/ 1 v))))) (pow v 2))) (/ (* cosTheta_i (exp (- 6931/10000 (/ 1 v)))) v))))>
#<alt (+ (exp (- 6931/10000 (/ 1 v))) (* cosTheta_O (+ (* cosTheta_O (+ (* 1/6 (/ (* cosTheta_O (* (pow cosTheta_i 3) (exp (- 6931/10000 (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_i 2) (exp (- 6931/10000 (/ 1 v)))) (pow v 2))))) (/ (* cosTheta_i (exp (- 6931/10000 (/ 1 v)))) v))))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- 6931/10000 (/ 1 v)))>
#<alt (+ (exp (- 6931/10000 (/ 1 v))) (/ (* cosTheta_O (* cosTheta_i (exp (- 6931/10000 (/ 1 v))))) v))>
#<alt (+ (exp (- 6931/10000 (/ 1 v))) (* cosTheta_i (+ (* 1/2 (/ (* (pow cosTheta_O 2) (* cosTheta_i (exp (- 6931/10000 (/ 1 v))))) (pow v 2))) (/ (* cosTheta_O (exp (- 6931/10000 (/ 1 v)))) v))))>
#<alt (+ (exp (- 6931/10000 (/ 1 v))) (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ (* (pow cosTheta_O 3) (* cosTheta_i (exp (- 6931/10000 (/ 1 v))))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_O 2) (exp (- 6931/10000 (/ 1 v)))) (pow v 2))))) (/ (* cosTheta_O (exp (- 6931/10000 (/ 1 v)))) v))))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v)))>
#<alt (exp 6931/10000)>
#<alt (+ (exp 6931/10000) (/ (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)) v))>
#<alt (+ (exp 6931/10000) (+ (* 1/2 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 2)) (pow v 2))) (/ (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)) v)))>
#<alt (+ (exp 6931/10000) (+ (* 1/6 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 3)) (pow v 3))) (+ (* 1/2 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 2)) (pow v 2))) (/ (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)) v))))>
#<alt (exp 6931/10000)>
#<alt (+ (exp 6931/10000) (/ (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)) v))>
#<alt (+ (exp 6931/10000) (* -1 (/ (+ (* -1 (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1))) (* -1/2 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 2)) v))) v)))>
#<alt (+ (exp 6931/10000) (* -1 (/ (+ (* -1 (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1))) (* -1 (/ (+ (* 1/6 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 3)) v)) (* 1/2 (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 2)))) v))) v)))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (/ cosTheta_i v)) (/ 1 (* cosTheta_O v))))>
#<alt (* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (/ cosTheta_i v)) (/ 1 (* cosTheta_O v))))>
#<alt (* cosTheta_O (- (+ (* 6931/10000 (/ 1 cosTheta_O)) (/ cosTheta_i v)) (/ 1 (* cosTheta_O v))))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_O)))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_O)))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_O)))))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (/ cosTheta_O v)) (/ 1 (* cosTheta_i v))))>
#<alt (* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (/ cosTheta_O v)) (/ 1 (* cosTheta_i v))))>
#<alt (* cosTheta_i (- (+ (* 6931/10000 (/ 1 cosTheta_i)) (/ cosTheta_O v)) (/ 1 (* cosTheta_i v))))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_i)))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_i)))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (* -1 (/ (- 6931/10000 (/ 1 v)) cosTheta_i)))))>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) 1) v)>
#<alt (/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) 1) v)>
#<alt (/ (- (+ (* 6931/10000 v) (* cosTheta_O cosTheta_i)) 1) v)>
#<alt 6931/10000>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt 6931/10000>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 6931/10000 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (/ -1 v)>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_O (- (/ cosTheta_i v) (/ 1 (* cosTheta_O v))))>
#<alt (* cosTheta_O (- (/ cosTheta_i v) (/ 1 (* cosTheta_O v))))>
#<alt (* cosTheta_O (- (/ cosTheta_i v) (/ 1 (* cosTheta_O v))))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ 1 (* cosTheta_O v)))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ 1 (* cosTheta_O v)))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 (/ cosTheta_i v)) (/ 1 (* cosTheta_O v)))))>
#<alt (/ -1 v)>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (- (/ (* cosTheta_O cosTheta_i) v) (/ 1 v))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* cosTheta_i (- (/ cosTheta_O v) (/ 1 (* cosTheta_i v))))>
#<alt (* cosTheta_i (- (/ cosTheta_O v) (/ 1 (* cosTheta_i v))))>
#<alt (* cosTheta_i (- (/ cosTheta_O v) (/ 1 (* cosTheta_i v))))>
#<alt (/ (* cosTheta_O cosTheta_i) v)>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ 1 (* cosTheta_i v)))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ 1 (* cosTheta_i v)))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 (/ cosTheta_O v)) (/ 1 (* cosTheta_i v)))))>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt (/ (- (* cosTheta_O cosTheta_i) 1) v)>
#<alt -1>
#<alt (- (* cosTheta_O cosTheta_i) 1)>
#<alt (- (* cosTheta_O cosTheta_i) 1)>
#<alt (- (* cosTheta_O cosTheta_i) 1)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_O (- cosTheta_i (/ 1 cosTheta_O)))>
#<alt (* cosTheta_O (- cosTheta_i (/ 1 cosTheta_O)))>
#<alt (* cosTheta_O (- cosTheta_i (/ 1 cosTheta_O)))>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* -1 (* cosTheta_O (+ (* -1 cosTheta_i) (/ 1 cosTheta_O))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 cosTheta_i) (/ 1 cosTheta_O))))>
#<alt (* -1 (* cosTheta_O (+ (* -1 cosTheta_i) (/ 1 cosTheta_O))))>
#<alt -1>
#<alt (- (* cosTheta_O cosTheta_i) 1)>
#<alt (- (* cosTheta_O cosTheta_i) 1)>
#<alt (- (* cosTheta_O cosTheta_i) 1)>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* cosTheta_i (- cosTheta_O (/ 1 cosTheta_i)))>
#<alt (* cosTheta_i (- cosTheta_O (/ 1 cosTheta_i)))>
#<alt (* cosTheta_i (- cosTheta_O (/ 1 cosTheta_i)))>
#<alt (* cosTheta_O cosTheta_i)>
#<alt (* -1 (* cosTheta_i (+ (* -1 cosTheta_O) (/ 1 cosTheta_i))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 cosTheta_O) (/ 1 cosTheta_i))))>
#<alt (* -1 (* cosTheta_i (+ (* -1 cosTheta_O) (/ 1 cosTheta_i))))>
#<alt (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 v)))>
#<alt (exp (- (+ 6931/10000 (log (/ 1/2 v))) (/ 1 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))))) v)))>
#<alt (+ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ (* -1 (/ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) v)) (* 1/2 (/ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (pow v 2)))))>
#<alt (+ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (+ (* -1 (/ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) v)) (+ (* -1/6 (/ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (pow v 3))) (* 1/2 (/ (exp (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))) (pow v 2))))))>
#<alt (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v)))))>
#<alt (+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) v)))>
#<alt (+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1/2 (/ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) v))) v)))>
#<alt (+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (+ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) (* -1 (/ (+ (* -1/6 (/ (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))) v)) (* 1/2 (exp (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))))) v))) v)))>
#<alt (/ -1 v)>
#<alt (/ (- (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v))))) 1) v)>
#<alt (/ (- (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v))))) 1) v)>
#<alt (/ (- (* v (+ 6931/10000 (+ (log 1/2) (* -1 (log v))))) 1) v)>
#<alt (+ 6931/10000 (+ (log 1/2) (log (/ 1 v))))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (log (/ 1 v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (log (/ 1 v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log 1/2) (log (/ 1 v)))) (/ 1 v))>
#<alt (+ 6931/10000 (+ (log -1/2) (log (/ -1 v))))>
#<alt (- (+ 6931/10000 (+ (log -1/2) (log (/ -1 v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log -1/2) (log (/ -1 v)))) (/ 1 v))>
#<alt (- (+ 6931/10000 (+ (log -1/2) (log (/ -1 v)))) (/ 1 v))>
#<alt (/ -1 v)>
#<alt (/ (- (* v (+ (log 1/2) (* -1 (log v)))) 1) v)>
#<alt (/ (- (* v (+ (log 1/2) (* -1 (log v)))) 1) v)>
#<alt (/ (- (* v (+ (log 1/2) (* -1 (log v)))) 1) v)>
#<alt (+ (log 1/2) (log (/ 1 v)))>
#<alt (- (+ (log 1/2) (log (/ 1 v))) (/ 1 v))>
#<alt (- (+ (log 1/2) (log (/ 1 v))) (/ 1 v))>
#<alt (- (+ (log 1/2) (log (/ 1 v))) (/ 1 v))>
#<alt (+ (log -1/2) (log (/ -1 v)))>
#<alt (- (+ (log -1/2) (log (/ -1 v))) (/ 1 v))>
#<alt (- (+ (log -1/2) (log (/ -1 v))) (/ 1 v))>
#<alt (- (+ (log -1/2) (log (/ -1 v))) (/ 1 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 (exp (/ -1 v))>
#<alt (+ (exp (/ -1 v)) (/ (* cosTheta_O (* cosTheta_i (exp (/ -1 v)))) v))>
#<alt (+ (exp (/ -1 v)) (* cosTheta_O (+ (* 1/2 (/ (* cosTheta_O (* (pow cosTheta_i 2) (exp (/ -1 v)))) (pow v 2))) (/ (* cosTheta_i (exp (/ -1 v))) v))))>
#<alt (+ (exp (/ -1 v)) (* cosTheta_O (+ (* cosTheta_O (+ (* 1/6 (/ (* cosTheta_O (* (pow cosTheta_i 3) (exp (/ -1 v)))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_i 2) (exp (/ -1 v))) (pow v 2))))) (/ (* cosTheta_i (exp (/ -1 v))) v))))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ -1 v))>
#<alt (+ (exp (/ -1 v)) (/ (* cosTheta_O (* cosTheta_i (exp (/ -1 v)))) v))>
#<alt (+ (exp (/ -1 v)) (* cosTheta_i (+ (* 1/2 (/ (* (pow cosTheta_O 2) (* cosTheta_i (exp (/ -1 v)))) (pow v 2))) (/ (* cosTheta_O (exp (/ -1 v))) v))))>
#<alt (+ (exp (/ -1 v)) (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ (* (pow cosTheta_O 3) (* cosTheta_i (exp (/ -1 v)))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_O 2) (exp (/ -1 v))) (pow v 2))))) (/ (* cosTheta_O (exp (/ -1 v))) v))))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt 1>
#<alt (- (+ 1 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 1 (+ (* 1/2 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 2) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))>
#<alt (- (+ 1 (+ (* 1/6 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 3) (pow v 3))) (+ (* 1/2 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 2) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt 1>
#<alt (- (+ 1 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (- (* cosTheta_O cosTheta_i) 1)) (* -1/2 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 2) v))) v)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (- (* cosTheta_O cosTheta_i) 1)) (* -1 (/ (+ (* 1/6 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 3) v)) (* 1/2 (pow (- (* cosTheta_O cosTheta_i) 1) 2))) v))) v)))>

Calls

90 calls:

Time	Variable		Point	Expression
18.0ms	cosTheta_O	@	-inf	(* (/ (* 1/2 (exp 6931/10000)) v) (exp (/ (+ (* cosTheta_O cosTheta_i) -1) v)))
4.0ms	cosTheta_O	@	inf	(* (/ (* 1/2 (exp 6931/10000)) v) (exp (/ (+ (* cosTheta_O cosTheta_i) -1) v)))
1.0ms	cosTheta_i	@	-inf	(* (/ (* 1/2 (exp 6931/10000)) v) (exp (/ (+ (* cosTheta_O cosTheta_i) -1) v)))
1.0ms	v	@	0	(* (/ (* 1/2 (exp 6931/10000)) v) (exp (/ (+ (* cosTheta_O cosTheta_i) -1) v)))
1.0ms	cosTheta_O	@	0	(* (/ (* 1/2 (exp 6931/10000)) v) (exp (/ (+ (* cosTheta_O cosTheta_i) -1) v)))

rewrite385.0ms (2.7%)

Memory

11.4MiB live, 495.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 756×	`accelerator-lowering-fma.f32`
5 756×	`accelerator-lowering-fma.f64`
3 962×	`-lowering-.f32`
3 962×	`-lowering-.f64`
3 426×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	113
1	123	112
2	951	111
0	8595	105

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 573

Calls

Call 1

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

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

simplify645.0ms (4.5%)

Memory

9.1MiB live, 638.1MiB allocated

Algorithm

1×	egg-herbie

Rules

13 096×	`accelerator-lowering-fma.f32`
13 096×	`accelerator-lowering-fma.f64`
7 226×	`-lowering-.f32`
7 226×	`-lowering-.f64`
3 890×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	443	3925
1	1319	3841
2	4394	3697
0	9023	3424

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

Inputs
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (exp 6931/10000) v))
(/ (+ (* 1/2 (exp 6931/10000)) (* 1/2 (/ (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)) v))) v)
(/ (+ (* 1/4 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 2)) (pow v 2))) (+ (* 1/2 (exp 6931/10000)) (* 1/2 (/ (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)) v)))) v)
(/ (+ (* 1/12 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 3)) (pow v 3))) (+ (* 1/4 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 2)) (pow v 2))) (+ (* 1/2 (exp 6931/10000)) (* 1/2 (/ (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)) v))))) v)
(* 1/2 (/ (exp 6931/10000) v))
(* -1 (/ (+ (* -1/2 (exp 6931/10000)) (* -1/2 (/ (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)) v))) v))
(* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 2)) v)) (* 1/2 (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)))) v)) (* -1/2 (exp 6931/10000))) v))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 2))) (* -1/12 (/ (* (exp 6931/10000) (pow (- (* cosTheta_O cosTheta_i) 1) 3)) v))) v)) (* 1/2 (* (exp 6931/10000) (- (* cosTheta_O cosTheta_i) 1)))) v)) (* -1/2 (exp 6931/10000))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v))
(+ (* 1/2 (/ (* cosTheta_O (* cosTheta_i (* (exp 6931/10000) (exp (/ -1 v))))) (pow v 2))) (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v)))
(+ (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v)) (* cosTheta_O (+ (* 1/4 (/ (* cosTheta_O (* (pow cosTheta_i 2) (* (exp 6931/10000) (exp (/ -1 v))))) (pow v 3))) (* 1/2 (/ (* cosTheta_i (* (exp 6931/10000) (exp (/ -1 v)))) (pow v 2))))))
(+ (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v)) (* cosTheta_O (+ (* 1/2 (/ (* cosTheta_i (* (exp 6931/10000) (exp (/ -1 v)))) (pow v 2))) (* cosTheta_O (+ (* 1/12 (/ (* cosTheta_O (* (pow cosTheta_i 3) (* (exp 6931/10000) (exp (/ -1 v))))) (pow v 4))) (* 1/4 (/ (* (pow cosTheta_i 2) (* (exp 6931/10000) (exp (/ -1 v)))) (pow v 3))))))))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v))
(+ (* 1/2 (/ (* cosTheta_O (* cosTheta_i (* (exp 6931/10000) (exp (/ -1 v))))) (pow v 2))) (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v)))
(+ (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v)) (* cosTheta_i (+ (* 1/4 (/ (* (pow cosTheta_O 2) (* cosTheta_i (* (exp 6931/10000) (exp (/ -1 v))))) (pow v 3))) (* 1/2 (/ (* cosTheta_O (* (exp 6931/10000) (exp (/ -1 v)))) (pow v 2))))))
(+ (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v)) (* cosTheta_i (+ (* 1/2 (/ (* cosTheta_O (* (exp 6931/10000) (exp (/ -1 v)))) (pow v 2))) (* cosTheta_i (+ (* 1/12 (/ (* (pow cosTheta_O 3) (* cosTheta_i (* (exp 6931/10000) (exp (/ -1 v))))) (pow v 4))) (* 1/4 (/ (* (pow cosTheta_O 2) (* (exp 6931/10000) (exp (/ -1 v)))) (pow v 3))))))))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ (- (* cosTheta_O cosTheta_i) 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))
(* 1/2 (/ (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
(+ 1 (/ (* cosTheta_O cosTheta_i) v))
(+ 1 (* cosTheta_O (+ (* 1/2 (/ (* cosTheta_O (pow cosTheta_i 2)) (pow v 2))) (/ cosTheta_i v))))
(+ 1 (* cosTheta_O (+ (* cosTheta_O (+ (* 1/6 (/ (* cosTheta_O (pow cosTheta_i 3)) (pow v 3))) (* 1/2 (/ (pow cosTheta_i 2) (pow v 2))))) (/ cosTheta_i v))))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
1
(+ 1 (/ (* cosTheta_O cosTheta_i) v))
(+ 1 (* cosTheta_i (+ (* 1/2 (/ (* (pow cosTheta_O 2) cosTheta_i) (pow v 2))) (/ cosTheta_O v))))
(+ 1 (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ (* (pow cosTheta_O 3) cosTheta_i) (pow v 3))) (* 1/2 (/ (pow cosTheta_O 2) (pow v 2))))) (/ cosTheta_O v))))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
(exp (/ (* cosTheta_O cosTheta_i) v))
1
(+ 1 (/ (* cosTheta_O cosTheta_i) v))
(+ 1 (+ (* 1/2 (/ (* (pow cosTheta_O 2) (pow cosTheta_i 2)) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v)))
(+ 1 (+ (* 1/6 (/ (* (pow cosTheta_O 3) (pow cosTheta_i 3)) (pow v 3))) (+ (* 1/2 (/ (* (pow cosTheta_O 2) (pow cosTheta_i 2)) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v))))
1
(+ 1 (/ (* cosTheta_O cosTheta_i) v))
(+ 1 (* -1 (/ (+ (* -1 (* cosTheta_O cosTheta_i)) (* -1/2 (/ (* (pow cosTheta_O 2) (pow cosTheta_i 2)) v))) v)))
(+ 1 (* -1 (/ (+ (* -1 (* cosTheta_O cosTheta_i)) (* -1 (/ (+ (* 1/6 (/ (* (pow cosTheta_O 3) (pow cosTheta_i 3)) v)) (* 1/2 (* (pow cosTheta_O 2) (pow cosTheta_i 2)))) v))) 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)
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6931/10000
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-1
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Outputs
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(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ -1 v))
(exp.f32 (/.f32 #s(literal -1 binary32) v))
(+ (exp (/ -1 v)) (/ (* cosTheta_O (* cosTheta_i (exp (/ -1 v)))) v))
(fma.f32 cosTheta_O (*.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v)) (/.f32 cosTheta_i v)) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(+ (exp (/ -1 v)) (* cosTheta_i (+ (* 1/2 (/ (* (pow cosTheta_O 2) (* cosTheta_i (exp (/ -1 v)))) (pow v 2))) (/ (* cosTheta_O (exp (/ -1 v))) v))))
(fma.f32 cosTheta_i (fma.f32 (/.f32 (.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v)) (.f32 cosTheta_O cosTheta_O)) (.f32 v v)) (.f32 #s(literal 1/2 binary32) cosTheta_i) (*.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v)) (/.f32 cosTheta_O v))) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(+ (exp (/ -1 v)) (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ (* (pow cosTheta_O 3) (* cosTheta_i (exp (/ -1 v)))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_O 2) (exp (/ -1 v))) (pow v 2))))) (/ (* cosTheta_O (exp (/ -1 v))) v))))
(fma.f32 cosTheta_i (fma.f32 cosTheta_i (fma.f32 (.f32 #s(literal 1/2 binary32) (.f32 cosTheta_O cosTheta_O)) (/.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v)) (.f32 v v)) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 cosTheta_O (.f32 cosTheta_O cosTheta_O))) (.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v)) (/.f32 cosTheta_i (.f32 v (.f32 v v)))))) (*.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v)) (/.f32 cosTheta_O v))) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp (/ (- (* cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
1
#s(literal 1 binary32)
(- (+ 1 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
(+.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(- (+ 1 (+ (* 1/2 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 2) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))
(+.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))) (.f32 v v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
(- (+ 1 (+ (* 1/6 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 3) (pow v 3))) (+ (* 1/2 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 2) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))
(+.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))) (.f32 v v)) (fma.f32 #s(literal 1/6 binary32) (/.f32 (.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) (.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)))) (.f32 v (.f32 v v))) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))))
1
#s(literal 1 binary32)
(- (+ 1 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))
(+.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(+ 1 (* -1 (/ (+ (* -1 (- (* cosTheta_O cosTheta_i) 1)) (* -1/2 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 2) v))) v)))
(-.f32 #s(literal 1 binary32) (/.f32 (fma.f32 #s(literal -1/2 binary32) (*.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)) (fma.f32 cosTheta_O (neg.f32 cosTheta_i) #s(literal 1 binary32))) v))
(+ 1 (* -1 (/ (+ (* -1 (- (* cosTheta_O cosTheta_i) 1)) (* -1 (/ (+ (* 1/6 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 3) v)) (* 1/2 (pow (- (* cosTheta_O cosTheta_i) 1) 2))) v))) v)))
(+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) (/.f32 (fma.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) (.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))) (.f32 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))))) v)) v))

eval162.0ms (1.1%)

Memory: 18.8MiB live, 162.0MiB allocated
Compiler: Compiled 21 349 to 2 568 computations (88% saved)

prune490.0ms (3.4%)

Memory

-136.5MiB live, 230.8MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	1 187	8	1 195
Fresh	3	1	4
Picked	5	0	5
Done	0	0	0
Total	1 195	9	1 204

Accuracy

99.9%

Counts

1 204 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.1%	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) #s(literal 1 binary32))
▶	99.8%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
▶	99.8%	(.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
	99.8%	(*.f32 (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 1/2 binary32)))) (exp.f32 (log.f32 v))) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
▶	99.8%	(.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
▶	98.7%	(exp.f32 (/.f32 #s(literal -1 binary32) v))
	99.8%	(exp.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) v)))
	98.7%	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))
▶	6.3%	#s(literal 1 binary32)

Compiler

Compiled 252 to 214 computations (15.1% saved)

simplify277.0ms (1.9%)

Memory

3.9MiB live, 408.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log.f32 (*.f32 v #s(literal 2 binary32)))
✓	cost-diff	0	(-.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32))))
✓	cost-diff	2944	(exp.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))))
✓	cost-diff	3264	(.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
✓	cost-diff	0	(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
✓	cost-diff	0	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))
✓	cost-diff	0	(*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
✓	cost-diff	0	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
✓	cost-diff	0	(/.f32 #s(literal -1 binary32) v)
✓	cost-diff	0	(exp.f32 (/.f32 #s(literal -1 binary32) v))
✓	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 (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v)
✓	cost-diff	3264	(.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))

Rules

7 292×	`accelerator-lowering-fma.f32`
7 292×	`accelerator-lowering-fma.f64`
2 500×	`-lowering-.f32`
2 500×	`-lowering-.f64`
2 198×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	141
1	50	139
2	84	138
3	156	138
4	253	138
5	449	138
6	913	138
7	1891	138
8	4070	138
9	7155	138
0	8126	134

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize92.0ms (0.6%)

Memory

23.0MiB live, 184.4MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
✓	accuracy	99.9%	(-.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32))))
✓	accuracy	99.9%	(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
✓	accuracy	90.1%	(exp.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))))
✓	accuracy	100.0%	(*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))
✓	accuracy	100.0%	(+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))
✓	accuracy	99.9%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
✓	accuracy	99.9%	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))
✓	accuracy	100.0%	(/.f32 #s(literal -1 binary32) v)
✓	accuracy	99.9%	(exp.f32 (/.f32 #s(literal -1 binary32) v))
✓	accuracy	100.0%	(exp.f32 #s(literal 6931/10000 binary32))
✓	accuracy	99.9%	(.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
✓	accuracy	99.9%	(exp.f32 (/.f32 #s(literal -1 binary32) v))
✓	accuracy	99.0%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v)

Samples

57.0ms

256×

valid

Compiler

Compiled 140 to 31 computations (77.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-exp: 10.0ms (24.8% of total)

ival-mult: 8.0ms (19.9% of total)

ival-div: 7.0ms (17.4% of total)

const: 7.0ms (17.4% of total)

ival-log: 4.0ms (9.9% of total)

ival-add: 2.0ms (5% of total)

ival-sub: 1.0ms (2.5% of total)

exact: 1.0ms (2.5% of total)

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

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

series103.0ms (0.7%)

Memory

-21.4MiB live, 101.0MiB allocated

Counts

15 → 204

Calls

Call 1

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

Outputs
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v))>
#<alt (* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (/ (+ (* -1/2 (/ (exp 6931/10000) v)) (* 1/2 (exp 6931/10000))) v)>
#<alt (/ (+ (* -1/2 (/ (exp 6931/10000) v)) (+ (* 1/4 (/ (exp 6931/10000) (pow v 2))) (* 1/2 (exp 6931/10000)))) v)>
#<alt (/ (+ (* -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)>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* -1 (/ (+ (* -1/2 (exp 6931/10000)) (* 1/2 (/ (exp 6931/10000) v))) v))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (exp 6931/10000)) (* 1/4 (/ (exp 6931/10000) v))) v)) (* -1/2 (exp 6931/10000))) v))>
#<alt (* -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))>
#<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))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (exp (/ -1 v))>
#<alt (exp (/ -1 v))>
#<alt (exp (/ -1 v))>
#<alt (exp (/ -1 v))>
#<alt 1>
#<alt (- 1 (/ 1 v))>
#<alt (- (+ 1 (/ 1/2 (pow v 2))) (/ 1 v))>
#<alt (- (+ 1 (/ 1/2 (pow v 2))) (+ (/ 1 v) (* 1/6 (/ 1 (pow v 3)))))>
#<alt 1>
#<alt (- 1 (/ 1 v))>
#<alt (+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 v))) v)))>
#<alt (+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1/2 (* 1/6 (/ 1 v))) v))) v)))>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (/ -1 v)>
#<alt (* 1/2 (/ (exp (- 6931/10000 (/ 1 v))) v))>
#<alt (* 1/2 (/ (exp (- 6931/10000 (/ 1 v))) v))>
#<alt (* 1/2 (/ (exp (- 6931/10000 (/ 1 v))) v))>
#<alt (* 1/2 (/ (exp (- 6931/10000 (/ 1 v))) v))>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (/ (+ (* -1/2 (/ (exp 6931/10000) v)) (* 1/2 (exp 6931/10000))) v)>
#<alt (/ (+ (* -1/2 (/ (exp 6931/10000) v)) (+ (* 1/4 (/ (exp 6931/10000) (pow v 2))) (* 1/2 (exp 6931/10000)))) v)>
#<alt (/ (+ (* -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)>
#<alt (* 1/2 (/ (exp 6931/10000) v))>
#<alt (* -1 (/ (+ (* -1/2 (exp 6931/10000)) (* 1/2 (/ (exp 6931/10000) v))) v))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (exp 6931/10000)) (* 1/4 (/ (exp 6931/10000) v))) v)) (* -1/2 (exp 6931/10000))) v))>
#<alt (* -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))>
#<alt (* 1/2 (exp (- 6931/10000 (/ 1 v))))>
#<alt (* 1/2 (exp (- 6931/10000 (/ 1 v))))>
#<alt (* 1/2 (exp (- 6931/10000 (/ 1 v))))>
#<alt (* 1/2 (exp (- 6931/10000 (/ 1 v))))>
#<alt (* 1/2 (exp 6931/10000))>
#<alt (+ (* -1/2 (/ (exp 6931/10000) v)) (* 1/2 (exp 6931/10000)))>
#<alt (+ (* -1/2 (/ (exp 6931/10000) v)) (+ (* 1/4 (/ (exp 6931/10000) (pow v 2))) (* 1/2 (exp 6931/10000))))>
#<alt (+ (* -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)))))>
#<alt (* 1/2 (exp 6931/10000))>
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#<alt (exp (- 6931/10000 (/ 1 v)))>
#<alt (exp (- 6931/10000 (/ 1 v)))>
#<alt (exp (- 6931/10000 (/ 1 v)))>
#<alt (exp (- 6931/10000 (/ 1 v)))>
#<alt (exp 6931/10000)>
#<alt (+ (exp 6931/10000) (* -1 (/ (exp 6931/10000) v)))>
#<alt (+ (exp 6931/10000) (+ (* -1 (/ (exp 6931/10000) v)) (* 1/2 (/ (exp 6931/10000) (pow v 2)))))>
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#<alt (exp 6931/10000)>
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#<alt (+ (exp 6931/10000) (* -1 (/ (+ (exp 6931/10000) (* -1/2 (/ (exp 6931/10000) v))) v)))>
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#<alt (/ -1 v)>
#<alt (/ (- (* 6931/10000 v) 1) v)>
#<alt (/ (- (* 6931/10000 v) 1) v)>
#<alt (/ (- (* 6931/10000 v) 1) v)>
#<alt 6931/10000>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt 6931/10000>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (- 6931/10000 (/ 1 v))>
#<alt (* (exp (- 6931/10000 (+ (log 2) (log v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (* (exp (- 6931/10000 (+ (log 2) (log v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (* (exp (- 6931/10000 (+ (log 2) (log v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (* (exp (- 6931/10000 (+ (log 2) (log v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v))))))>
#<alt (+ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (/ (* (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (- (* cosTheta_O cosTheta_i) 1)) v))>
#<alt (+ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (+ (* 1/2 (/ (* (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (- (* cosTheta_O cosTheta_i) 1) 2)) (pow v 2))) (/ (* (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (- (* cosTheta_O cosTheta_i) 1)) v)))>
#<alt (+ (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (+ (* 1/6 (/ (* (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (- (* cosTheta_O cosTheta_i) 1) 3)) (pow v 3))) (+ (* 1/2 (/ (* (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (pow (- (* cosTheta_O cosTheta_i) 1) 2)) (pow v 2))) (/ (* (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))) (- (* cosTheta_O cosTheta_i) 1)) v))))>
#<alt (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v))))))>
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#<alt (+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (+ (* -1 (* (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (- (* cosTheta_O cosTheta_i) 1))) (* -1/2 (/ (* (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (- (* cosTheta_O cosTheta_i) 1) 2)) v))) v)))>
#<alt (+ (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (* -1 (/ (+ (* -1 (* (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (- (* cosTheta_O cosTheta_i) 1))) (* -1 (/ (+ (* 1/6 (/ (* (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (- (* cosTheta_O cosTheta_i) 1) 3)) v)) (* 1/2 (* (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))) (pow (- (* cosTheta_O cosTheta_i) 1) 2)))) v))) v)))>
#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ -1 v)))>
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#<alt (+ (* cosTheta_O (+ (* cosTheta_O (+ (* 1/6 (/ (* cosTheta_O (* (pow cosTheta_i 3) (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ -1 v))))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_i 2) (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ -1 v)))) (pow v 2))))) (/ (* cosTheta_i (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ -1 v)))) v))) (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ -1 v))))>
#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
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#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
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#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
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#<alt (+ (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ (* (pow cosTheta_O 3) (* cosTheta_i (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ -1 v))))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_O 2) (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ -1 v)))) (pow v 2))))) (/ (* cosTheta_O (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ -1 v)))) v))) (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ -1 v))))>
#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (* (exp (- 6931/10000 (log (* 2 v)))) (exp (/ (- (* cosTheta_O cosTheta_i) 1) v)))>
#<alt (exp (- 6931/10000 (+ (log 2) (log v))))>
#<alt (exp (- 6931/10000 (+ (log 2) (log v))))>
#<alt (exp (- 6931/10000 (+ (log 2) (log v))))>
#<alt (exp (- 6931/10000 (+ (log 2) (log v))))>
#<alt (exp (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v))))))>
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#<alt (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v))))))>
#<alt (exp (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v))))))>
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#<alt (- 6931/10000 (+ (log 2) (log v)))>
#<alt (- 6931/10000 (+ (log 2) (log v)))>
#<alt (- 6931/10000 (+ (log 2) (log v)))>
#<alt (- 6931/10000 (+ (log 2) (log v)))>
#<alt (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))>
#<alt (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))>
#<alt (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))>
#<alt (- 6931/10000 (+ (log 2) (* -1 (log (/ 1 v)))))>
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#<alt (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))>
#<alt (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))>
#<alt (- 6931/10000 (+ (log -2) (* -1 (log (/ -1 v)))))>
#<alt (+ (log 2) (log v))>
#<alt (+ (log 2) (log v))>
#<alt (+ (log 2) (log v))>
#<alt (+ (log 2) (log v))>
#<alt (+ (log 2) (* -1 (log (/ 1 v))))>
#<alt (+ (log 2) (* -1 (log (/ 1 v))))>
#<alt (+ (log 2) (* -1 (log (/ 1 v))))>
#<alt (+ (log 2) (* -1 (log (/ 1 v))))>
#<alt (+ (log -2) (* -1 (log (/ -1 v))))>
#<alt (+ (log -2) (* -1 (log (/ -1 v))))>
#<alt (+ (log -2) (* -1 (log (/ -1 v))))>
#<alt (+ (log -2) (* -1 (log (/ -1 v))))>
#<alt (exp (/ -1 v))>
#<alt (+ (exp (/ -1 v)) (/ (* cosTheta_O (* cosTheta_i (exp (/ -1 v)))) v))>
#<alt (+ (exp (/ -1 v)) (* cosTheta_O (+ (* 1/2 (/ (* cosTheta_O (* (pow cosTheta_i 2) (exp (/ -1 v)))) (pow v 2))) (/ (* cosTheta_i (exp (/ -1 v))) v))))>
#<alt (+ (exp (/ -1 v)) (* cosTheta_O (+ (* cosTheta_O (+ (* 1/6 (/ (* cosTheta_O (* (pow cosTheta_i 3) (exp (/ -1 v)))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_i 2) (exp (/ -1 v))) (pow v 2))))) (/ (* cosTheta_i (exp (/ -1 v))) v))))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ -1 v))>
#<alt (+ (exp (/ -1 v)) (/ (* cosTheta_O (* cosTheta_i (exp (/ -1 v)))) v))>
#<alt (+ (exp (/ -1 v)) (* cosTheta_i (+ (* 1/2 (/ (* (pow cosTheta_O 2) (* cosTheta_i (exp (/ -1 v)))) (pow v 2))) (/ (* cosTheta_O (exp (/ -1 v))) v))))>
#<alt (+ (exp (/ -1 v)) (* cosTheta_i (+ (* cosTheta_i (+ (* 1/6 (/ (* (pow cosTheta_O 3) (* cosTheta_i (exp (/ -1 v)))) (pow v 3))) (* 1/2 (/ (* (pow cosTheta_O 2) (exp (/ -1 v))) (pow v 2))))) (/ (* cosTheta_O (exp (/ -1 v))) v))))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt (exp (/ (- (* cosTheta_O cosTheta_i) 1) v))>
#<alt 1>
#<alt (- (+ 1 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (- (+ 1 (+ (* 1/2 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 2) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v))) (/ 1 v))>
#<alt (- (+ 1 (+ (* 1/6 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 3) (pow v 3))) (+ (* 1/2 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 2) (pow v 2))) (/ (* cosTheta_O cosTheta_i) v)))) (/ 1 v))>
#<alt 1>
#<alt (- (+ 1 (/ (* cosTheta_O cosTheta_i) v)) (/ 1 v))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (- (* cosTheta_O cosTheta_i) 1)) (* -1/2 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 2) v))) v)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (- (* cosTheta_O cosTheta_i) 1)) (* -1 (/ (+ (* 1/6 (/ (pow (- (* cosTheta_O cosTheta_i) 1) 3) v)) (* 1/2 (pow (- (* cosTheta_O cosTheta_i) 1) 2))) v))) v)))>

Calls

51 calls:

Time	Variable		Point	Expression
40.0ms	v	@	inf	(exp (- 6931/10000 (log (* v 2))))
18.0ms	cosTheta_O	@	inf	(* (exp (- 6931/10000 (log (* v 2)))) (exp (/ (+ (* cosTheta_O cosTheta_i) -1) v)))
13.0ms	v	@	-inf	(exp (- 6931/10000 (log (* v 2))))
12.0ms	v	@	0	(* (exp (- 6931/10000 (log (* v 2)))) (exp (/ (+ (* cosTheta_O cosTheta_i) -1) v)))
6.0ms	cosTheta_i	@	inf	(* (exp (- 6931/10000 (log (* v 2)))) (exp (/ (+ (* cosTheta_O cosTheta_i) -1) v)))

rewrite303.0ms (2.1%)

Memory

30.7MiB live, 418.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 678×	`accelerator-lowering-fma.f32`
4 678×	`accelerator-lowering-fma.f64`
4 240×	`-lowering-.f32`
4 240×	`-lowering-.f64`
3 400×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	99
1	110	97
2	749	96
0	8443	94

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 491

Calls

Call 1

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

Outputs
(neg.f32 (*.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) (/.f32 #s(literal -1/2 binary32) v)))
(neg.f32 (.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (exp.f32 #s(literal 6931/10000 binary32)) v)) (exp.f32 (/.f32 #s(literal -1 binary32) v))))
(neg.f32 (.f32 #s(literal 1 binary32) (.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) (/.f32 #s(literal -1/2 binary32) v))))
(neg.f32 (/.f32 #s(literal -1 binary32) (/.f32 (*.f32 v #s(literal 2 binary32)) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 v #s(literal 2 binary32)) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))))) #s(literal -1 binary32)))
(pow.f32 (/.f32 (*.f32 v #s(literal 2 binary32)) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) #s(literal -1 binary32))
(-.f32 #s(literal 0 binary32) (*.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) (/.f32 #s(literal -1/2 binary32) v)))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 v)) (*.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) (/.f32 #s(literal -1/2 binary32) v)))
(/.f32 #s(literal 1/2 binary32) (/.f32 v (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
(/.f32 #s(literal -1 binary32) (/.f32 (*.f32 v #s(literal -2 binary32)) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
(/.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v)) (/.f32 v (*.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32)))))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
(/.f32 (*.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v))) #s(literal -1/2 binary32)) (neg.f32 v))
(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 v #s(literal 2 binary32)) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
(/.f32 (/.f32 #s(literal 1 binary32) v) (/.f32 #s(literal 2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))))
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (/.f32 #s(literal -1 binary32) v))) (/.f32 v (exp.f32 #s(literal 6931/10000 binary32))))
(/.f32 (/.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v)) v) (/.f32 #s(literal 2 binary32) (exp.f32 #s(literal 6931/10000 binary32))))
(/.f32 (neg.f32 (exp.f32 (/.f32 #s(literal -1 binary32) v))) (/.f32 v (*.f32 (exp.f32 #s(literal 6931/10000 binary32)) #s(literal -1/2 binary32))))
(/.f32 (.f32 #s(literal -1 binary32) (exp.f32 (/.f32 #s(literal -1 binary32) v))) (/.f32 v (.f32 (exp.f32 #s(literal 6931/10000 binary32)) #s(literal -1/2 binary32))))
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(/.f32 (-.f32 (pow.f32 (/.f32 #s(literal 332956652491/1000000000000 binary32) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32)) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 #s(literal 332956652491/1000000000000 binary32) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))) (/.f32 #s(literal 332956652491/1000000000000 binary32) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))) (fma.f32 (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32)) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))) (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32)) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))) (.f32 (/.f32 #s(literal 332956652491/1000000000000 binary32) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))) (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32)) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32)))))))
(/.f32 (-.f32 (pow.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) #s(literal 3 binary32)) (pow.f32 (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) #s(literal 3 binary32))) (fma.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (fma.f32 (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))))))))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 v)) #s(literal 3 binary32)) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32))) (fma.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 v)) (-.f32 #s(literal 6931/10000 binary32) (log.f32 v)) (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (*.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 v)) (log.f32 #s(literal 2 binary32))))))
(/.f32 (-.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) #s(literal 48038761/100000000 binary32)) (-.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 6931/10000 binary32)))
(/.f32 (-.f32 (.f32 (/.f32 #s(literal 332956652491/1000000000000 binary32) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))) (/.f32 #s(literal 332956652491/1000000000000 binary32) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32)))) (.f32 (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32)) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))) (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32)) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))))) (+.f32 (/.f32 #s(literal 332956652491/1000000000000 binary32) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))) (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32)) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32)))))
(/.f32 (-.f32 (.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))))) (.f32 (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))))) (+.f32 (/.f32 #s(literal 48038761/100000000 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (/.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))))))
(/.f32 (-.f32 (*.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 v)) (-.f32 #s(literal 6931/10000 binary32) (log.f32 v))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))) (+.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 v)) (log.f32 #s(literal 2 binary32))))
(/.f32 (.f32 (-.f32 #s(literal 332956652491/1000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32))) #s(literal 1 binary32)) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32)))
(/.f32 (.f32 (-.f32 #s(literal 48038761/100000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))) #s(literal 1 binary32)) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))))
(/.f32 (.f32 (-.f32 #s(literal 36911618591269576715823706172806771/1000000000000000000000000000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 9 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32)))) (+.f32 (fma.f32 #s(literal 332956652491/1000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32)) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 6 binary32))) #s(literal 110860132438012536505081/1000000000000000000000000 binary32)))
(/.f32 (.f32 (-.f32 #s(literal 110860132438012536505081/1000000000000000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 6 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32)))) (+.f32 #s(literal 332956652491/1000000000000 binary32) (pow.f32 (log.f32 (*.f32 v #s(literal 2 binary32))) #s(literal 3 binary32))))
(/.f32 (.f32 (-.f32 #s(literal 110860132438012536505081/1000000000000000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 6 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))))) (fma.f32 (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)) (+.f32 #s(literal 48038761/100000000 binary32) (pow.f32 (log.f32 (*.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))) #s(literal 2307722558415121/10000000000000000 binary32)))
(/.f32 (.f32 (-.f32 #s(literal 2307722558415121/10000000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 4 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))))) (+.f32 #s(literal 48038761/100000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))))
(.f32 #s(literal 1 binary32) (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))))
(.f32 (-.f32 #s(literal 332956652491/1000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))))
(.f32 (-.f32 #s(literal 332956652491/1000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) (-.f32 (neg.f32 (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 6931/10000 binary32)) #s(literal 48038761/100000000 binary32))))
(.f32 (-.f32 #s(literal 48038761/100000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32))))))
(.f32 (neg.f32 (-.f32 #s(literal 332956652491/1000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32)))) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32)))))
(.f32 (+.f32 #s(literal -48038761/100000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (neg.f32 (+.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))))))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32))) (-.f32 #s(literal 332956652491/1000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (-.f32 #s(literal 48038761/100000000 binary32) (pow.f32 (log.f32 (*.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))))
(.f32 (/.f32 (-.f32 #s(literal 48038761/100000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))) (-.f32 #s(literal 48038761/100000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32)))) (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))))
(.f32 (/.f32 (-.f32 #s(literal 332956652491/1000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32))) (+.f32 #s(literal 110860132438012536505081/1000000000000000000000000 binary32) (pow.f32 (.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) #s(literal 3 binary32)))) (fma.f32 (.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (-.f32 (.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32))))) #s(literal 48038761/100000000 binary32)) #s(literal 2307722558415121/10000000000000000 binary32)))
(.f32 (/.f32 (-.f32 #s(literal 332956652491/1000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32))) (-.f32 #s(literal 2307722558415121/10000000000000000 binary32) (pow.f32 (.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) #s(literal 2 binary32)))) (-.f32 #s(literal 48038761/100000000 binary32) (.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))))))
(.f32 (/.f32 (-.f32 #s(literal 48038761/100000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))) (+.f32 #s(literal 332956652491/1000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32)))) (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (-.f32 (log.f32 (*.f32 v #s(literal 2 binary32))) #s(literal 6931/10000 binary32)) #s(literal 48038761/100000000 binary32)))
(+.f32 (log.f32 v) (log.f32 #s(literal 2 binary32)))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v))
(-.f32 (/.f32 (pow.f32 (log.f32 v) #s(literal 2 binary32)) (log.f32 (/.f32 v #s(literal 2 binary32)))) (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 v #s(literal 2 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (log.f32 #s(literal 2 binary32)) (-.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)) (pow.f32 (log.f32 v) #s(literal 2 binary32))) (+.f32 (pow.f32 (log.f32 v) #s(literal 3 binary32)) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (log.f32 (/.f32 v #s(literal 2 binary32))) (.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (log.f32 (/.f32 v #s(literal 2 binary32))))))
(/.f32 (+.f32 (pow.f32 (log.f32 v) #s(literal 3 binary32)) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32))) (fma.f32 (log.f32 #s(literal 2 binary32)) (-.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)) (pow.f32 (log.f32 v) #s(literal 2 binary32))))
(/.f32 (+.f32 (pow.f32 (log.f32 v) #s(literal 3 binary32)) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32))) (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (-.f32 (pow.f32 (log.f32 v) #s(literal 2 binary32)) (*.f32 (log.f32 v) (log.f32 #s(literal 2 binary32))))))
(/.f32 (.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (log.f32 (/.f32 v #s(literal 2 binary32)))) (log.f32 (/.f32 v #s(literal 2 binary32))))
(/.f32 (neg.f32 (+.f32 (pow.f32 (log.f32 v) #s(literal 3 binary32)) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)))) (neg.f32 (fma.f32 (log.f32 #s(literal 2 binary32)) (-.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)) (pow.f32 (log.f32 v) #s(literal 2 binary32)))))
(/.f32 (neg.f32 (.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (log.f32 (/.f32 v #s(literal 2 binary32))))) (neg.f32 (log.f32 (/.f32 v #s(literal 2 binary32)))))
(/.f32 (-.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (pow.f32 (log.f32 v) #s(literal 2 binary32))) (-.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)))
(*.f32 (+.f32 (pow.f32 (log.f32 v) #s(literal 3 binary32)) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (log.f32 #s(literal 2 binary32)) (-.f32 (log.f32 #s(literal 2 binary32)) (log.f32 v)) (pow.f32 (log.f32 v) #s(literal 2 binary32)))))
(.f32 (.f32 (log.f32 (*.f32 v #s(literal 2 binary32))) (log.f32 (/.f32 v #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (log.f32 (/.f32 v #s(literal 2 binary32)))))
(log.f32 (*.f32 v #s(literal 2 binary32)))
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp.f32 (*.f32 (log.f32 (exp.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) v)))
(pow.f32 (exp.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) v))
(pow.f32 (pow.f32 (exp.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) v))
(pow.f32 (exp.f32 #s(literal 1 binary32)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(pow.f32 (exp.f32 (/.f32 #s(literal 1 binary32) v)) (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)))
(pow.f32 (exp.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta_O cosTheta_i))) (/.f32 #s(literal -1 binary32) v))
(/.f32 #s(literal 1 binary32) (exp.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta_O cosTheta_i)) v)))
(*.f32 (pow.f32 (exp.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))) (/.f32 #s(literal 1/2 binary32) v)) (pow.f32 (exp.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32))) (/.f32 #s(literal 1/2 binary32) v)))

simplify358.0ms (2.5%)

Memory

-27.6MiB live, 734.4MiB allocated

Algorithm

1×	egg-herbie

Rules

6 658×	`accelerator-lowering-fma.f32`
6 658×	`accelerator-lowering-fma.f64`
6 246×	`-lowering-.f32`
6 246×	`-lowering-.f64`
3 302×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	310	2678
1	873	2590
2	2642	2358
3	7407	2312
0	8495	2199

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ -1 v))) v))
(* 1/2 (/ (* (exp 6931/10000) (exp (/ -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))
(* 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))
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Outputs
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1
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1
#s(literal 1 binary32)
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eval117.0ms (0.8%)

Memory: -1.5MiB live, 124.5MiB allocated
Compiler: Compiled 13 126 to 1 563 computations (88.1% saved)

prune99.0ms (0.7%)

Memory

24.4MiB live, 221.5MiB allocated

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	761	4	765
Fresh	0	4	4
Picked	1	4	5
Done	0	0	0
Total	762	12	774

Accuracy

99.9%

Counts

774 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.1%	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) #s(literal 1 binary32))
	98.8%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (/.f32 #s(literal -1 binary32) v))) v)
✓	99.8%	(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
✓	99.8%	(.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
	99.8%	(*.f32 (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 1/2 binary32)))) (exp.f32 (log.f32 v))) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
	99.8%	(.f32 (exp.f32 (/.f32 (-.f32 #s(literal 110860132438012536505081/1000000000000000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 6 binary32))) (.f32 (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32)) (+.f32 #s(literal 332956652491/1000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32)))))) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
	99.8%	(.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
	99.8%	(.f32 (exp.f32 (.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (-.f32 #s(literal 48038761/100000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))))) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
✓	98.7%	(exp.f32 (/.f32 #s(literal -1 binary32) v))
	99.8%	(exp.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) v)))
	98.7%	(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))
✓	6.3%	#s(literal 1 binary32)

Compiler

Compiled 543 to 276 computations (49.2% saved)

regimes90.0ms (0.6%)

Memory

-35.8MiB live, 124.2MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) #s(literal 1 binary32))
(exp.f32 (/.f32 #s(literal -1 binary32) v))
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))
(exp.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(*.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)
(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 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) (exp.f32 (/.f32 #s(literal -1 binary32) v))) v)
(/.f32 (*.f32 #s(literal 1/2 binary32) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (/.f32 #s(literal -1 binary32) v)))) v)
(.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v)))))
(exp.f32 (-.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (*.f32 v #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) v)))
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 #s(literal -1 binary32) v))))
(.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(exp.f32 (+.f32 #s(literal 6931/10000 binary32) (+.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v))))
(.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (exp.f32 #s(literal 6931/10000 binary32))) v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
(.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)))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))
(.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (exp.f32 (/.f32 #s(literal -1 binary32) v)))
(.f32 (exp.f32 (-.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
(.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (neg.f32 (log.f32 (.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 (/.f32 (exp.f32 (+.f32 #s(literal 6931/10000 binary32) (log.f32 #s(literal 1/2 binary32)))) (exp.f32 (log.f32 v))) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
(.f32 (exp.f32 (.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32))))) (-.f32 #s(literal 48038761/100000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 2 binary32))))) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))
(.f32 (exp.f32 (/.f32 (-.f32 #s(literal 110860132438012536505081/1000000000000000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 6 binary32))) (.f32 (fma.f32 (log.f32 (.f32 v #s(literal 2 binary32))) (+.f32 #s(literal 6931/10000 binary32) (log.f32 (.f32 v #s(literal 2 binary32)))) #s(literal 48038761/100000000 binary32)) (+.f32 #s(literal 332956652491/1000000000000 binary32) (pow.f32 (log.f32 (.f32 v #s(literal 2 binary32))) #s(literal 3 binary32)))))) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i #s(literal -1 binary32)) v)))

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

Calls

9 calls:

11.0ms	sinTheta_O
8.0ms	(*.f32 sinTheta_i sinTheta_O)
8.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))
7.0ms	sinTheta_i
7.0ms	cosTheta_i

Results

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

Compiler

Compiled 105 to 78 computations (25.7% saved)

regimes43.0ms (0.3%)

Memory

21.2MiB live, 98.9MiB allocated

Counts

15 → 1

Calls

Call 1

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

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

Calls

9 calls:

6.0ms	cosTheta_O
5.0ms	(+.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))))
5.0ms	sinTheta_i
5.0ms	sinTheta_O
5.0ms	cosTheta_i

Results

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

Compiler

Compiled 105 to 78 computations (25.7% saved)

regimes37.0ms (0.3%)

Memory

9.6MiB live, 88.9MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

9 calls:

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

Results

Accuracy	Segments	Branch
98.8%	1	`cosTheta_i`
98.8%	1	`cosTheta_O`
98.8%	1	`sinTheta_i`
98.8%	1	`sinTheta_O`
98.8%	1	`v`
98.8%	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)))))`
98.8%	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))))`
98.8%	1	`(*.f32 cosTheta_i cosTheta_O)`
98.8%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 105 to 78 computations (25.7% saved)

regimes34.0ms (0.2%)

Memory

8.0MiB live, 83.8MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

9 calls:

6.0ms	sinTheta_i
4.0ms	(*.f32 cosTheta_i cosTheta_O)
4.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))
3.0ms	cosTheta_O
3.0ms	sinTheta_O

Results

Accuracy	Segments	Branch
98.7%	1	`cosTheta_i`
98.7%	1	`cosTheta_O`
98.7%	1	`sinTheta_i`
98.7%	1	`sinTheta_O`
98.7%	1	`v`
98.7%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`
98.7%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`
98.7%	1	`(*.f32 cosTheta_i cosTheta_O)`
98.7%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 105 to 78 computations (25.7% saved)

regimes22.0ms (0.2%)

Memory

-29.2MiB live, 59.9MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) #s(literal 1 binary32))
(exp.f32 (/.f32 #s(literal -1 binary32) v))

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

Calls

9 calls:

6.0ms	(*.f32 cosTheta_i cosTheta_O)
3.0ms	cosTheta_O
2.0ms	(+.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))))
2.0ms	sinTheta_i
2.0ms	sinTheta_O

Results

Accuracy	Segments	Branch
98.7%	1	`cosTheta_i`
98.7%	1	`cosTheta_O`
98.7%	1	`sinTheta_i`
98.7%	1	`sinTheta_O`
98.7%	1	`v`
98.7%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`
98.7%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`
98.7%	1	`(*.f32 cosTheta_i cosTheta_O)`
98.7%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 105 to 78 computations (25.7% saved)

regimes15.0ms (0.1%)

Memory

6.4MiB live, 46.0MiB allocated

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) #s(literal 1 binary32))

Outputs
#s(literal 1 binary32)

Calls

9 calls:

2.0ms	sinTheta_i
2.0ms	(+.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))))
2.0ms	v
1.0ms	cosTheta_i
1.0ms	sinTheta_O

Results

Accuracy	Segments	Branch
6.3%	1	`cosTheta_i`
6.3%	1	`cosTheta_O`
6.3%	1	`sinTheta_O`
6.3%	1	`(*.f32 cosTheta_i cosTheta_O)`
6.3%	1	`sinTheta_i`
6.3%	1	`v`
6.3%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`
6.3%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`
6.3%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 105 to 78 computations (25.7% saved)

simplify8.0ms (0.1%)

Memory

-17.4MiB live, 21.9MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary32`
2×	`1-exp_binary64`
2×	`+-commutative_binary32`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	25	40

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness858.0ms (6%)

Memory

34.9MiB live, 903.1MiB allocated

Rules

13 096×	`accelerator-lowering-fma.f32`
13 096×	`accelerator-lowering-fma.f64`
11 284×	`accelerator-lowering-fma.f32`
11 284×	`accelerator-lowering-fma.f64`
8 022×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	278	4128
1	891	3918
2	3129	3629
0	8250	3465
0	310	2678
1	873	2590
2	2642	2358
3	7407	2312
0	8495	2199
0	443	3925
1	1319	3841
2	4394	3697
0	9023	3424
0	744	8384
1	2345	7949
0	8064	7513
0	39	172
1	207	159
2	1632	158
0	8197	148

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

Compiler

Compiled 262 to 204 computations (22.1% saved)

preprocess80.0ms (0.6%)

Memory

-20.0MiB live, 98.3MiB allocated

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 214 to 140 computations (34.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	24	164
1	42	163
2	75	162
3	117	162
4	154	162
5	175	162
6	181	162
7	182	162
0	182	154

Iter	Nodes	Cost
0	24	164
1	42	163
2	75	162
3	117	162
4	154	162
5	175	162
6	181	162
7	182	162
0	182	154

analyze405.0ms (2.8%)

sample6.0s (41.7%)

preprocess320.0ms (2.2%)

explain251.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify269.0ms (1.9%)

localize64.0ms (0.4%)

series81.0ms (0.6%)

rewrite397.0ms (2.8%)

simplify374.0ms (2.6%)

eval79.0ms (0.5%)

prune85.0ms (0.6%)

simplify291.0ms (2%)

localize208.0ms (1.5%)

series58.0ms (0.4%)

rewrite334.0ms (2.3%)

simplify425.0ms (3%)

eval155.0ms (1.1%)

prune151.0ms (1.1%)

simplify10.0ms (0.1%)

localize91.0ms (0.6%)

series74.0ms (0.5%)

rewrite385.0ms (2.7%)

simplify645.0ms (4.5%)

eval162.0ms (1.1%)

prune490.0ms (3.4%)

simplify277.0ms (1.9%)

localize92.0ms (0.6%)

series103.0ms (0.7%)

rewrite303.0ms (2.1%)

simplify358.0ms (2.5%)

eval117.0ms (0.8%)

prune99.0ms (0.7%)

regimes90.0ms (0.6%)

regimes43.0ms (0.3%)

regimes37.0ms (0.3%)

regimes34.0ms (0.2%)

regimes22.0ms (0.2%)

regimes15.0ms (0.1%)

simplify8.0ms (0.1%)

soundness858.0ms (6%)

preprocess80.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	24	164
1	42	163
2	75	162
3	117	162
4	154	162
5	175	162
6	181	162
7	182	162
0	182	154