Metrics for GTR1 distribution

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze81.0ms (1.2%)

Memory

-17.3MiB live, 70.0MiB allocated; 34ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0.6%	99.4%	0%	0%	0%	0
0%	0%	0.6%	99.4%	0%	0%	0%	1
0%	0%	0.6%	99.4%	0%	0%	0%	2
0%	0%	0.6%	99.4%	0%	0%	0%	3
0%	0%	0.6%	99.4%	0%	0%	0%	4
50%	0.3%	0.3%	99.4%	0%	0%	0%	5
50%	0.3%	0.3%	99.4%	0%	0%	0%	6
75%	0.5%	0.2%	99.4%	0%	0%	0%	7
75%	0.5%	0.2%	99.4%	0%	0%	0%	8
87.5%	0.6%	0.1%	99.4%	0%	0%	0%	9
87.5%	0.6%	0.1%	99.4%	0%	0%	0%	10
93.7%	0.6%	0%	99.4%	0%	0%	0%	11
93.7%	0.6%	0%	99.4%	0%	0%	0%	12

Compiler

Compiled 40 to 23 computations (42.5% saved)

sample2.1s (29.7%)

Memory

-82.5MiB live, 1 593.7MiB allocated; 1.4s collecting garbage

Samples

1.7s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-mult: 846.0ms (58.3% of total)

ival-<=: 170.0ms (11.7% of total)

const: 118.0ms (8.1% of total)

ival-log: 95.0ms (6.5% of total)

ival-div: 62.0ms (4.3% of total)

ival-sub: 47.0ms (3.2% of total)

ival-add: 40.0ms (2.8% of total)

ival-pi: 30.0ms (2.1% of total)

ival-and: 25.0ms (1.7% of total)

exact: 11.0ms (0.8% of total)

adjust: 3.0ms (0.2% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain192.0ms (2.7%)

Memory

-29.2MiB live, 233.9MiB allocated; 81ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))`
-	-	`(PI.f32)`
-	-	`#s(literal 1 binary32)`
-	-	`cosTheta`
-	-	`alpha`
-	-	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
-	-	`(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))`
-	-	`(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))`
-	-	`(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)`
-	-	`(log.f32 (*.f32 alpha alpha))`
-	-	`(*.f32 alpha alpha)`
-	-	`(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)`
-	-	`(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

85.0ms

512×

valid

Compiler

Compiled 210 to 43 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-add: 29.0ms (45.7% of total)

ival-mult: 20.0ms (31.5% of total)

ival-log: 6.0ms (9.5% of total)

ival-div: 4.0ms (6.3% of total)

ival-sub: 3.0ms (4.7% of total)

ival-pi: 2.0ms (3.2% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

preprocess129.0ms (1.8%)

Memory

-3.9MiB live, 130.1MiB allocated; 35ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	122
1	152	122
2	595	122
3	3333	120
0	13	24
0	23	24
1	55	24
2	221	24
3	1191	24
4	4601	24
0	8344	21

Stop Event

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

Calls

Call 1

Inputs

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Outputs

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))

Symmetry

(abs alpha)

(abs cosTheta)

Compiler

Compiled 24 to 13 computations (45.8% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Status

Accuracy

Program

▶

98.7%

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Compiler

Compiled 24 to 13 computations (45.8% saved)

simplify130.0ms (1.8%)

Memory

7.2MiB live, 105.1MiB allocated; 29ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
cost-diff	1	(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	91
0	23	91
1	55	91
2	221	91
3	1191	91
4	4601	91
0	8344	81

Stop Event

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

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
cosTheta

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(.f32 (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta

localize34.0ms (0.5%)

Memory

-11.0MiB live, 35.9MiB allocated; 1ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.14453125	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
accuracy	0.16796875	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
accuracy	0.3125	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
accuracy	0.38900375976844204	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Samples

24.0ms

256×

valid

Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 8.0ms (49.8% of total)

ival-log: 3.0ms (18.7% of total)

ival-div: 2.0ms (12.5% of total)

ival-pi: 1.0ms (6.2% of total)

ival-add: 1.0ms (6.2% of total)

ival-sub: 1.0ms (6.2% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series56.0ms (0.8%)

Memory

46.7MiB live, 90.0MiB allocated; 7ms collecting garbage

Counts

7 → 43

Calls

Call 1

Inputs
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(*.f32 alpha alpha)
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)

Outputs
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(* cosTheta (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
-1
(- (pow alpha 2) 1)
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(pow alpha 2)
(* 2 (* (PI) (log alpha)))
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(* -1 (pow cosTheta 2))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* -2 (* (PI) (log (/ -1 alpha))))

Calls

6 calls:

Time	Variable		Point	Expression
31.0ms	alpha	@	0	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
9.0ms	alpha	@	inf	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
8.0ms	alpha	@	-inf	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
3.0ms	cosTheta	@	inf	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
3.0ms	cosTheta	@	0	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))

simplify155.0ms (2.2%)

Memory

-25.6MiB live, 161.3MiB allocated; 24ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	197	1450
1	572	1398
2	2417	1236
0	8614	1182

Stop Event

1×	iter limit
1×	node limit

Counts

43 → 43

Calls

Call 1

Inputs
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(* cosTheta (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
-1
(- (pow alpha 2) 1)
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(pow alpha 2)
(* 2 (* (PI) (log alpha)))
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(* -1 (pow cosTheta 2))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* -2 (* (PI) (log (/ -1 alpha))))

Outputs
1
#s(literal 1 binary32)
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(fma.f32 (-.f32 (.f32 (/.f32 (.f32 cosTheta cosTheta) (log.f32 (.f32 alpha alpha))) (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (PI.f32))) (/.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (.f32 cosTheta cosTheta) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(fma.f32 (fma.f32 (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32)) cosTheta) (neg.f32 cosTheta) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))) (.f32 cosTheta cosTheta) (/.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha))) (neg.f32 (PI.f32)))) (.f32 cosTheta cosTheta) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (log.f32 (.f32 alpha alpha)))) (PI.f32)) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (log.f32 (.f32 alpha alpha)))) (PI.f32)) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 6 binary32))) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32))) (*.f32 cosTheta cosTheta))
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(+ 1 (* -1 (pow cosTheta 2)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (fma.f32 (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (PI.f32))) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) #s(literal 1/2 binary32) (/.f32 (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) alpha) (neg.f32 alpha)) (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32)))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (fma.f32 (.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (-.f32 (/.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 cosTheta cosTheta))) (.f32 alpha alpha) (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha)))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(pow alpha 2)
(*.f32 alpha alpha)
(* 2 (* (PI) (log alpha)))
(.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))
(* -1 cosTheta)
(neg.f32 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* -1 (pow cosTheta 2))
(*.f32 (neg.f32 cosTheta) cosTheta)
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (pow cosTheta 2))
(.f32 (.f32 (*.f32 cosTheta cosTheta) alpha) alpha)
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) #s(literal -1 binary32))) alpha) alpha #s(literal 1 binary32))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (neg.f32 (log.f32 alpha)))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (neg.f32 (log.f32 alpha)))) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)))) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(-.f32 (/.f32 (fma.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha))) (/.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha)))) (.f32 cosTheta cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)))) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(fma.f32 (/.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha))) (pow.f32 alpha #s(literal 6 binary32))) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)) (pow.f32 cosTheta #s(literal 4 binary32))) (-.f32 (/.f32 (fma.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha))) (/.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha)))) (.f32 cosTheta cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)))) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha)))))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(* (pow alpha 2) cosTheta)
(.f32 (.f32 alpha alpha) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) #s(literal -1 binary32))) (*.f32 alpha alpha))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (/.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32)))) (.f32 cosTheta cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(fma.f32 (/.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))) (pow.f32 alpha #s(literal 6 binary32))) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)) (pow.f32 cosTheta #s(literal 4 binary32))) (-.f32 (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (/.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32)))) (.f32 cosTheta cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32)))))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))

rewrite187.0ms (2.7%)

Memory

-15.5MiB live, 181.2MiB allocated; 37ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	65
0	23	65
1	101	65
2	818	63
0	8860	55

Stop Event

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

Counts

7 → 372

Calls

Call 1

Inputs
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(*.f32 alpha alpha)
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)

Outputs
(expm1.f32 (*.f32 (log.f32 (neg.f32 alpha)) #s(literal 2 binary32)))
(expm1.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 (neg.f32 alpha) #s(literal 1 binary32))) (-.f32 (neg.f32 alpha) #s(literal 1 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) alpha)) (-.f32 alpha #s(literal 1 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (-.f32 alpha #s(literal 1 binary32))) (+.f32 #s(literal 1 binary32) alpha))
(*.f32 (neg.f32 (+.f32 #s(literal -1 binary32) (neg.f32 alpha))) (-.f32 alpha #s(literal 1 binary32)))
(*.f32 (/.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1 binary32)))
(*.f32 (+.f32 #s(literal -1 binary32) (neg.f32 alpha)) (neg.f32 (-.f32 alpha #s(literal 1 binary32))))
(*.f32 (+.f32 (neg.f32 alpha) #s(literal 1 binary32)) (-.f32 (neg.f32 alpha) #s(literal 1 binary32)))
(*.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha))
(*.f32 (+.f32 #s(literal 1 binary32) alpha) (neg.f32 (neg.f32 (-.f32 alpha #s(literal 1 binary32)))))
(*.f32 (+.f32 #s(literal 1 binary32) alpha) (-.f32 alpha #s(literal 1 binary32)))
(*.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))
(/.f32 (-.f32 (.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))) (+.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (-.f32 (.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))))) (.f32 (/.f32 #s(literal -1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 #s(literal -1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))) (+.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (/.f32 #s(literal -1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
(/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))))
(/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal -1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) #s(literal 3 binary32))) (fma.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (fma.f32 (/.f32 #s(literal -1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 #s(literal -1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (/.f32 #s(literal -1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))))
(/.f32 (+.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal -1 binary32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)))) (neg.f32 (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32))))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)))) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)))) (neg.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)))) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))))
(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (+.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha)))
(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)) (-.f32 alpha #s(literal 1 binary32))))
(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (+.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) alpha) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha)))
(/.f32 (.f32 (+.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.f32 #s(literal 1 binary32) alpha)))
(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha))))
(/.f32 (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))) (pow.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) #s(literal 2 binary32)))
(/.f32 (-.f32 (.f32 (pow.f32 alpha #s(literal 6 binary32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (.f32 (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))) #s(literal 1 binary32))) (*.f32 (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))))
(/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(/.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32))) (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32)))
(/.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (-.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (neg.f32 (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32))))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (neg.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (*.f32 (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha))))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))))
(-.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(-.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (/.f32 #s(literal -1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(fma.f32 (*.f32 #s(literal 1 binary32) (neg.f32 alpha)) (neg.f32 alpha) #s(literal -1 binary32))
(fma.f32 (exp.f32 (log.f32 alpha)) (exp.f32 (log.f32 alpha)) #s(literal -1 binary32))
(fma.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32) (*.f32 (-.f32 alpha #s(literal 1 binary32)) alpha))
(fma.f32 (-.f32 alpha #s(literal 1 binary32)) alpha (*.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32)))
(fma.f32 (neg.f32 alpha) (neg.f32 alpha) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (-.f32 alpha #s(literal 1 binary32)) (*.f32 alpha (-.f32 alpha #s(literal 1 binary32))))
(fma.f32 #s(literal 1 binary32) (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 (*.f32 alpha alpha) #s(literal 1 binary32) #s(literal -1 binary32))
(fma.f32 alpha (-.f32 alpha #s(literal 1 binary32)) (*.f32 #s(literal 1 binary32) (-.f32 alpha #s(literal 1 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(+.f32 (.f32 #s(literal 1 binary32) (-.f32 alpha #s(literal 1 binary32))) (.f32 alpha (-.f32 alpha #s(literal 1 binary32))))
(+.f32 (.f32 alpha (-.f32 alpha #s(literal 1 binary32))) (.f32 #s(literal 1 binary32) (-.f32 alpha #s(literal 1 binary32))))
(+.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) alpha))
(+.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32)))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
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(fma.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 1 binary32) (.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 1 binary32)))
(fma.f32 (.f32 (PI.f32) (log.f32 alpha)) #s(literal 1 binary32) (.f32 (*.f32 (PI.f32) (log.f32 alpha)) #s(literal 1 binary32)))
(fma.f32 (log.f32 (neg.f32 alpha)) (PI.f32) (*.f32 (log.f32 (neg.f32 alpha)) (PI.f32)))
(fma.f32 (cosh.f32 (log.f32 (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (*.f32 (sinh.f32 (log.f32 (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (log.f32 alpha) (PI.f32) (*.f32 (log.f32 alpha) (PI.f32)))
(fma.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (cosh.f32 (log.f32 (PI.f32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (sinh.f32 (log.f32 (PI.f32)))))
(fma.f32 (PI.f32) (log.f32 (neg.f32 alpha)) (*.f32 (PI.f32) (log.f32 (neg.f32 alpha))))
(fma.f32 (PI.f32) (log.f32 alpha) (*.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 #s(literal 1 binary32) (.f32 (log.f32 alpha) (PI.f32)) (.f32 #s(literal 1 binary32) (*.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 alpha)) (.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
(+.f32 (.f32 (cosh.f32 (log.f32 (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (.f32 (sinh.f32 (log.f32 (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(+.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 1 binary32)))
(+.f32 (.f32 (.f32 (PI.f32) (log.f32 alpha)) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) #s(literal 1 binary32)))
(+.f32 (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (cosh.f32 (log.f32 (PI.f32)))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (sinh.f32 (log.f32 (PI.f32)))))
(+.f32 (.f32 (PI.f32) (log.f32 (neg.f32 alpha))) (.f32 (PI.f32) (log.f32 (neg.f32 alpha))))
(+.f32 (.f32 #s(literal 1 binary32) (.f32 (log.f32 alpha) (PI.f32))) (.f32 #s(literal 1 binary32) (.f32 (log.f32 alpha) (PI.f32))))
(+.f32 (.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 alpha))))
(+.f32 (.f32 (log.f32 (neg.f32 alpha)) (PI.f32)) (.f32 (log.f32 (neg.f32 alpha)) (PI.f32)))
(+.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))
(+.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (PI.f32) (log.f32 alpha)))
(.f32 (.f32 cosTheta (+.f32 (neg.f32 alpha) #s(literal 1 binary32))) (-.f32 (neg.f32 alpha) #s(literal 1 binary32)))
(.f32 (.f32 cosTheta (-.f32 alpha #s(literal 1 binary32))) (+.f32 #s(literal 1 binary32) alpha))
(.f32 (.f32 #s(literal 1 binary32) (fma.f32 alpha cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) alpha)) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))
(*.f32 (/.f32 cosTheta (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(*.f32 (neg.f32 (neg.f32 cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (fma.f32 alpha cosTheta cosTheta) (-.f32 alpha #s(literal 1 binary32)))
(*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 alpha) alpha #s(literal 1 binary32)))
(.f32 (+.f32 #s(literal 1 binary32) alpha) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))
(*.f32 (fma.f32 (neg.f32 alpha) alpha #s(literal 1 binary32)) (neg.f32 cosTheta))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 cosTheta #s(literal 1 binary32)))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (neg.f32 (neg.f32 cosTheta)))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(.f32 #s(literal 1 binary32) (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(/.f32 (neg.f32 (*.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) cosTheta)) (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32)))
(/.f32 (neg.f32 (*.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) cosTheta)) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (neg.f32 (*.f32 cosTheta (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)))) (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32)))
(/.f32 (neg.f32 (*.f32 cosTheta (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)))) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (*.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) cosTheta) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (*.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) cosTheta) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))))
(/.f32 (*.f32 cosTheta (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (*.f32 cosTheta (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))))
(fma.f32 cosTheta (.f32 alpha alpha) (.f32 cosTheta #s(literal -1 binary32)))
(fma.f32 (.f32 alpha alpha) cosTheta (.f32 #s(literal -1 binary32) cosTheta))
(+.f32 (.f32 (.f32 alpha alpha) cosTheta) (*.f32 #s(literal -1 binary32) cosTheta))
(+.f32 (.f32 cosTheta (.f32 alpha alpha)) (*.f32 cosTheta #s(literal -1 binary32)))
(neg.f32 (*.f32 (fma.f32 (neg.f32 alpha) alpha #s(literal 1 binary32)) cosTheta))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (+.f32 (neg.f32 alpha) #s(literal 1 binary32))) (-.f32 (neg.f32 alpha) #s(literal 1 binary32)))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (-.f32 alpha #s(literal 1 binary32))) (+.f32 #s(literal 1 binary32) alpha))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal 1 binary32) alpha)) (-.f32 alpha #s(literal 1 binary32)))
(.f32 (.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fabs.f32 cosTheta)) (fabs.f32 cosTheta))
(.f32 (.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (.f32 (fma.f32 (neg.f32 alpha) alpha #s(literal 1 binary32)) cosTheta) (neg.f32 cosTheta))
(.f32 (+.f32 #s(literal 1 binary32) alpha) (.f32 (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta))
(.f32 #s(literal 1 binary32) (.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta))
(/.f32 (neg.f32 (.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta)) (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32)))
(/.f32 (neg.f32 (.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta)) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(fma.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta) (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))
(+.f32 (.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta)) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 (*.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(neg.f32 (.f32 (.f32 (fma.f32 (neg.f32 alpha) alpha #s(literal 1 binary32)) cosTheta) cosTheta))

eval70.0ms (1%)

Memory: 15.2MiB live, 76.4MiB allocated; 5ms collecting garbage
Compiler: Compiled 19 163 to 2 092 computations (89.1% saved)

prune39.0ms (0.6%)

Memory

-2.8MiB live, 43.8MiB allocated; 2ms collecting garbage

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	483	24	507
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	484	24	508

Accuracy

100.0%

Counts

508 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) alpha (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
	98.6%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.6%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))) (pow.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) #s(literal 2 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.6%	(/.f32 (/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (+.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (cbrt.f32 (PI.f32))) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 (PI.f32) #s(literal 2 binary32)) (log.f32 alpha)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (cbrt.f32 (PI.f32)) (log.f32 (pow.f32 (.f32 alpha alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (pow.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 2 binary32)))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta))))))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	96.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
▶	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	68.0%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	97.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
▶	97.6%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
	95.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))

Compiler

Compiled 1 758 to 952 computations (45.8% saved)

simplify9.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))
cost-diff	0	(.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha)))
cost-diff	0	(fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
cost-diff	0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
cost-diff	0	(*.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta)
cost-diff	0	(fma.f32 (*.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
cost-diff	0	(/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
cost-diff	0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
cost-diff	0	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
cost-diff	0	(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
cost-diff	0	(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff	0	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff	0	(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	634
0	111	634

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
(pow.f32 (*.f32 alpha alpha) (PI.f32))
(PI.f32)
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
cosTheta
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(PI.f32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
#s(literal 1 binary32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(*.f32 cosTheta cosTheta)
cosTheta
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
(fma.f32 (*.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta)
(pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
#s(literal 2 binary32)
cosTheta
(neg.f32 cosTheta)
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)
(PI.f32)
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha)))
#s(literal 1/2 binary32)
(/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))
(+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))))
(/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 #s(literal 1 binary32) (PI.f32))
#s(literal 1 binary32)
(PI.f32)
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(*.f32 cosTheta cosTheta)
cosTheta
(/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))
(/.f32 (*.f32 cosTheta cosTheta) (PI.f32))
(pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))
#s(literal 2 binary32)
(log.f32 alpha)
alpha
(*.f32 alpha alpha)
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (PI.f32)))
#s(literal -1/2 binary32)
(*.f32 (log.f32 alpha) (PI.f32))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
(pow.f32 (*.f32 alpha alpha) (PI.f32))
(PI.f32)
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
cosTheta
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(PI.f32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
#s(literal 1 binary32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(*.f32 cosTheta cosTheta)
cosTheta
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
(fma.f32 (*.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta)
(pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
#s(literal 2 binary32)
cosTheta
(neg.f32 cosTheta)
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)
(PI.f32)
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha)))
#s(literal 1/2 binary32)
(/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))
(+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))))
(/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 #s(literal 1 binary32) (PI.f32))
#s(literal 1 binary32)
(PI.f32)
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(*.f32 cosTheta cosTheta)
cosTheta
(/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))
(/.f32 (*.f32 cosTheta cosTheta) (PI.f32))
(pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))
#s(literal 2 binary32)
(log.f32 alpha)
alpha
(*.f32 alpha alpha)
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (PI.f32)))
#s(literal -1/2 binary32)
(*.f32 (log.f32 alpha) (PI.f32))

localize164.0ms (2.3%)

Memory

-17.8MiB live, 258.4MiB allocated; 50ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha)))
accuracy	0.0	(log.f32 alpha)
accuracy	0.0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(neg.f32 cosTheta)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	0.0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 cosTheta cosTheta)
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
accuracy	0.0	(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
accuracy	0.0	(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
accuracy	29.98788023102775	(PI.f32)

Samples

114.0ms

256×

invalid

Compiler

Compiled 596 to 59 computations (90.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 92.0ms

ival-mult: 32.0ms (34.9% of total)

ival-div: 22.0ms (24% of total)

ival-log: 11.0ms (12% of total)

ival-add: 8.0ms (8.7% of total)

ival-pow2: 8.0ms (8.7% of total)

ival-pow: 5.0ms (5.4% of total)

ival-sub: 3.0ms (3.3% of total)

ival-pi: 1.0ms (1.1% of total)

exact: 1.0ms (1.1% of total)

ival-neg: 1.0ms (1.1% of total)

adjust: 0.0ms (0% of total)

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

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

series267.0ms (3.8%)

Memory

-36.4MiB live, 287.8MiB allocated; 129ms collecting garbage

Counts

25 → 155

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
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(/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
(fma.f32 (*.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
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(fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
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(/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))
(PI.f32)
(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
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(neg.f32 cosTheta)
(log.f32 alpha)

Outputs
(/ (- (pow alpha 2) 1) (log (pow (pow alpha 2) (PI))))
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(log (pow (pow alpha 2) (PI)))
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(* (NAN) (PI))
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(- (+ (* -1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2))) (pow alpha 2)) 1)
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(/ 1 (* (PI) (log alpha)))
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(* cosTheta (- (pow alpha 2) 1))
(pow cosTheta 2)
(* -1 cosTheta)
(/ 1 (* (pow cosTheta 2) (log (pow (pow alpha 2) (PI)))))
(/ (- (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (+ (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1)))) (/ 1 (* (pow cosTheta 6) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 2))
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(/ 1 (* (pow cosTheta 2) (* (NAN) (PI))))
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(* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1))))
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(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
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(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
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(* (pow cosTheta 2) (- (+ (* -1 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))))
(* -1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))
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(/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha))))
(/ (+ (* 1/2 (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))) (+ (/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))) (pow cosTheta 2))
(/ (+ (* 1/2 (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))) (+ (/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha)))) (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (+ (* 1/2 (/ 1 (* (pow cosTheta 4) (* (PI) (log alpha))))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log alpha)))))))) (pow cosTheta 2))
(/ (+ (* 1/2 (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))) (+ (* 3/2 (/ (pow alpha 2) (* (pow cosTheta 6) (* (PI) (log alpha))))) (+ (/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha)))) (+ (/ 1/2 (* (pow cosTheta 6) (* (PI) (log alpha)))) (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (+ (* 1/2 (/ 1 (* (pow cosTheta 4) (* (PI) (log alpha))))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log alpha)))))))))) (pow cosTheta 2))
(/ 1/2 (* (pow cosTheta 4) (* (PI) (log alpha))))
(/ (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (/ 1 (* (pow cosTheta 2) (* (PI) (log alpha))))) (pow cosTheta 4))
(/ (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (log alpha)))) (/ 3/2 (* (pow cosTheta 4) (* (PI) (log alpha)))))) (pow cosTheta 4))
(/ (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (log alpha)))) (+ (* 3/2 (/ 1 (* (pow cosTheta 4) (* (PI) (log alpha))))) (* 2 (/ 1 (* (pow cosTheta 6) (* (PI) (log alpha)))))))) (pow cosTheta 4))
(/ 1 (* (pow cosTheta 4) (* (PI) (log alpha))))
(/ (+ (/ 1 (* (PI) (log alpha))) (* 2 (/ 1 (* (pow cosTheta 2) (* (PI) (log alpha)))))) (pow cosTheta 4))
(/ (+ (/ 1 (* (PI) (log alpha))) (+ (/ 2 (* (pow cosTheta 2) (* (PI) (log alpha)))) (/ 3 (* (pow cosTheta 4) (* (PI) (log alpha)))))) (pow cosTheta 4))
(/ (+ (/ 1 (* (PI) (log alpha))) (+ (* 3 (/ 1 (* (pow cosTheta 4) (* (PI) (log alpha))))) (+ (* 4 (/ 1 (* (pow cosTheta 6) (* (PI) (log alpha))))) (/ 2 (* (pow cosTheta 2) (* (PI) (log alpha))))))) (pow cosTheta 4))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
-1
(pow alpha 2)
(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
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(/ -1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))))
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cosTheta
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(* 2 (log alpha))
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(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(- (/ 1 (* (pow cosTheta 2) (* (NAN) (PI)))) (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (NAN) (PI))))))
(- (+ (/ 1 (* (pow alpha 4) (* (pow cosTheta 6) (* (NAN) (PI))))) (/ 1 (* (pow cosTheta 2) (* (NAN) (PI))))) (+ (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (NAN) (PI))))) (/ 1 (* (pow alpha 4) (* (pow cosTheta 4) (* (NAN) (PI)))))))
(- (+ (* -1 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 8) (* (NAN) (PI)))))) (/ 1 (* (pow cosTheta 2) (* (NAN) (PI))))) (+ (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (NAN) (PI)))))) (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (NAN) (PI)))))))
(* (pow alpha 2) (* (pow cosTheta 2) (* (NAN) (PI))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (* (NAN) (PI))) (/ (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2))))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* 1/2 (/ (* (pow alpha 4) (pow cosTheta 2)) (* (PI) (log (/ 1 alpha)))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (pow alpha 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(* -1 (* (pow alpha 4) (pow cosTheta 2)))
(* (pow alpha 4) (+ (* -1 (pow cosTheta 2)) (+ (* 2 (/ (pow cosTheta 2) (pow alpha 2))) (/ 1 (pow alpha 2)))))
(* (pow alpha 4) (- (+ (* -1 (/ (pow cosTheta 2) (pow alpha 4))) (+ (* -1 (pow cosTheta 2)) (+ (* 2 (/ (pow cosTheta 2) (pow alpha 2))) (/ 1 (pow alpha 2))))) (/ 1 (pow alpha 4))))
(* (pow alpha 4) cosTheta)
(* (pow alpha 4) (+ cosTheta (* -2 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 4) (+ cosTheta (+ (* -2 (/ cosTheta (pow alpha 2))) (/ cosTheta (pow alpha 4)))))
(* -1/2 (/ (* (pow alpha 2) (+ (/ 1 (* (PI) (- 1 (pow cosTheta 2)))) (/ (pow cosTheta 2) (* (PI) (pow (- 1 (pow cosTheta 2)) 2))))) (log (/ 1 alpha))))
(* (pow alpha 2) (+ (* -1/2 (/ (+ (/ 1 (* (PI) (- 1 (pow cosTheta 2)))) (/ (pow cosTheta 2) (* (PI) (pow (- 1 (pow cosTheta 2)) 2)))) (log (/ 1 alpha)))) (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))))))))
(* -1/2 (/ (+ (/ 1 (* (PI) (- 1 (pow cosTheta 2)))) (/ (pow cosTheta 2) (* (PI) (pow (- 1 (pow cosTheta 2)) 2)))) (log (/ 1 alpha))))
(* -1 (/ (+ (/ 1 (* (PI) (- 1 (pow cosTheta 2)))) (/ (pow cosTheta 2) (* (PI) (pow (- 1 (pow cosTheta 2)) 2)))) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* -2 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* 1/2 (/ (* (pow alpha 4) (pow cosTheta 2)) (* (PI) (log (/ -1 alpha)))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (pow alpha 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(* 1/2 (/ (* (pow alpha 2) (+ (/ 1 (* (PI) (- 1 (pow cosTheta 2)))) (/ (pow cosTheta 2) (* (PI) (pow (- 1 (pow cosTheta 2)) 2))))) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(* (pow alpha 2) (- (* 1/2 (/ (+ (/ 1 (* (PI) (- 1 (pow cosTheta 2)))) (/ (pow cosTheta 2) (* (PI) (pow (- 1 (pow cosTheta 2)) 2)))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))))))))
(* 1/2 (/ (+ (/ 1 (* (PI) (- 1 (pow cosTheta 2)))) (/ (pow cosTheta 2) (* (PI) (pow (- 1 (pow cosTheta 2)) 2)))) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(/ (+ (/ 1 (* (PI) (- 1 (pow cosTheta 2)))) (/ (pow cosTheta 2) (* (PI) (pow (- 1 (pow cosTheta 2)) 2)))) (+ (log -1) (* -1 (log (/ -1 alpha)))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (log (/ -1 alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))

Calls

6 calls:

Time	Variable		Point	Expression
87.0ms	alpha	@	inf	((/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha)) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (neg cosTheta) (log alpha))
81.0ms	alpha	@	-inf	((/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha)) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (neg cosTheta) (log alpha))
46.0ms	alpha	@	0	((/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha)) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (neg cosTheta) (log alpha))
29.0ms	cosTheta	@	0	((/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha)) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (neg cosTheta) (log alpha))
12.0ms	cosTheta	@	inf	((/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha)) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (neg cosTheta) (log alpha))

simplify166.0ms (2.4%)

Memory

1.6MiB live, 233.1MiB allocated; 39ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	626	4724
1	1989	4430
0	8309	4311

Stop Event

1×	iter limit
1×	node limit

Counts

155 → 154

Calls

Call 1

Inputs
(/ (- (pow alpha 2) 1) (log (pow (pow alpha 2) (PI))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (log (pow (pow alpha 2) (PI))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (log (pow (pow alpha 2) (PI)))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (log (pow (pow alpha 2) (PI))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (log (pow (pow alpha 2) (PI))))))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(log (pow (pow alpha 2) (PI)))
(+ (log (pow (pow alpha 2) (PI))) (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))
(/ (- (pow alpha 2) 1) (* (NAN) (PI)))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (NAN) (PI)))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (NAN) (PI))) (/ (pow (- (pow alpha 2) 1) 2) (* (NAN) (PI))))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (NAN) (PI)))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (NAN) (PI)))))) (/ (pow (- (pow alpha 2) 1) 2) (* (NAN) (PI))))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(* (NAN) (PI))
(+ (* (NAN) (PI)) (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))
(PI)
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(* (PI) (log (pow alpha 2)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(- (pow alpha 2) 1)
(- (+ (* -1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2))) (pow alpha 2)) 1)
(* cosTheta (pow (- (pow alpha 2) 1) 2))
(- (* 1/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))
(- (+ (* 1/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* (pow cosTheta 2) (- (/ (pow alpha 2) (* (PI) (log alpha))) (* 1/2 (/ 1 (* (PI) (log alpha))))))) (* 1/2 (/ 1 (* (PI) (log alpha)))))
(- (+ (* 1/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* (pow cosTheta 2) (- (+ (* (pow cosTheta 2) (- (* 3/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))) (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha))))))) (* 1/2 (/ 1 (* (PI) (log alpha)))))
(- (+ (* 1/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* (pow cosTheta 2) (- (+ (* (pow cosTheta 2) (- (+ (* 3/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* (pow cosTheta 2) (- (* 2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha))))))) (* 1/2 (/ 1 (* (PI) (log alpha)))))) (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha))))))) (* 1/2 (/ 1 (* (PI) (log alpha)))))
(/ 1/2 (* (PI) (log alpha)))
(+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (/ (pow cosTheta 2) (* (PI) (log alpha))))
(+ (* (pow cosTheta 2) (+ (* 3/2 (/ (pow cosTheta 2) (* (PI) (log alpha)))) (/ 1 (* (PI) (log alpha))))) (* 1/2 (/ 1 (* (PI) (log alpha)))))
(+ (* (pow cosTheta 2) (+ (* (pow cosTheta 2) (+ (* 2 (/ (pow cosTheta 2) (* (PI) (log alpha)))) (* 3/2 (/ 1 (* (PI) (log alpha)))))) (/ 1 (* (PI) (log alpha))))) (* 1/2 (/ 1 (* (PI) (log alpha)))))
(/ 1 (* (PI) (log alpha)))
(+ (* 2 (/ (pow cosTheta 2) (* (PI) (log alpha)))) (/ 1 (* (PI) (log alpha))))
(+ (* (pow cosTheta 2) (+ (* 3 (/ (pow cosTheta 2) (* (PI) (log alpha)))) (* 2 (/ 1 (* (PI) (log alpha)))))) (/ 1 (* (PI) (log alpha))))
(+ (* (pow cosTheta 2) (+ (* (pow cosTheta 2) (+ (* 4 (/ (pow cosTheta 2) (* (PI) (log alpha)))) (* 3 (/ 1 (* (PI) (log alpha)))))) (* 2 (/ 1 (* (PI) (log alpha)))))) (/ 1 (* (PI) (log alpha))))
(* cosTheta (- (pow alpha 2) 1))
(pow cosTheta 2)
(* -1 cosTheta)
(/ 1 (* (pow cosTheta 2) (log (pow (pow alpha 2) (PI)))))
(/ (- (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
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(-.f32 (fma.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(-.f32 (fma.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)) (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (pow.f32 alpha #s(literal 6 binary32)) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (/.f32 (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))) (*.f32 alpha alpha))))
(* 1/2 (/ (* (pow alpha 4) (pow cosTheta 2)) (* (PI) (log (/ -1 alpha)))))
(.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (PI.f32))) (/.f32 (*.f32 cosTheta cosTheta) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(.f32 (.f32 #s(literal -1/2 binary32) (-.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (pow.f32 alpha #s(literal 4 binary32)))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (pow alpha 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(.f32 (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (pow.f32 alpha #s(literal 4 binary32)) (PI.f32))) (/.f32 (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 #s(literal -1/2 binary32) (-.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))) (pow.f32 alpha #s(literal 4 binary32)))
(* 1/2 (/ (* (pow alpha 2) (+ (/ 1 (* (PI) (- 1 (pow cosTheta 2)))) (/ (pow cosTheta 2) (* (PI) (pow (- 1 (pow cosTheta 2)) 2))))) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (fma.f32 (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* (pow alpha 2) (- (* 1/2 (/ (+ (/ 1 (* (PI) (- 1 (pow cosTheta 2)))) (/ (pow cosTheta 2) (* (PI) (pow (- 1 (pow cosTheta 2)) 2)))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))))))))
(.f32 (fma.f32 (/.f32 (fma.f32 (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) #s(literal 1/2 binary32) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (.f32 alpha alpha) (PI.f32)) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (.f32 alpha alpha))
(* 1/2 (/ (+ (/ 1 (* (PI) (- 1 (pow cosTheta 2)))) (/ (pow cosTheta 2) (* (PI) (pow (- 1 (pow cosTheta 2)) 2)))) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(.f32 (/.f32 (fma.f32 (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) #s(literal 1/2 binary32))
(/ (+ (/ 1 (* (PI) (- 1 (pow cosTheta 2)))) (/ (pow cosTheta 2) (* (PI) (pow (- 1 (pow cosTheta 2)) 2)))) (+ (log -1) (* -1 (log (/ -1 alpha)))))
(/.f32 (fma.f32 (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))

rewrite18.0ms (0.3%)

Memory

39.2MiB live, 39.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	421
0	111	421

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

25 → 28

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
(fma.f32 (*.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta)
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha)))
(/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))
(PI.f32)
(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(log.f32 (*.f32 alpha alpha))
(*.f32 cosTheta cosTheta)
(neg.f32 cosTheta)
(log.f32 alpha)

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
(fma.f32 (*.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
(+.f32 (.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta)
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(+.f32 (.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha)) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha)))
(/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))
(PI.f32)
(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(log.f32 (*.f32 alpha alpha))
(*.f32 cosTheta cosTheta)
(neg.f32 cosTheta)
(log.f32 alpha)

eval53.0ms (0.8%)

Memory: -44.8MiB live, 57.5MiB allocated; 8ms collecting garbage
Compiler: Compiled 13 629 to 1 069 computations (92.2% saved)

prune54.0ms (0.8%)

Memory

1.3MiB live, 48.4MiB allocated; 2ms collecting garbage

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	209	18	227
Fresh	7	12	19
Picked	4	1	5
Done	0	0	0
Total	220	31	251

Accuracy

100.0%

Counts

251 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) alpha (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.6%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
	98.4%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.6%	(/.f32 (/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (+.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (cbrt.f32 (PI.f32)) (log.f32 (pow.f32 (.f32 alpha alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (pow.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 2 binary32)))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta))))))
▶	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
▶	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))))
	56.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (*.f32 cosTheta cosTheta))))
	96.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
▶	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
	96.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
	98.2%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	98.2%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	68.0%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	97.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	95.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	67.2%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
	56.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (.f32 (-.f32 (fma.f32 (/.f32 alpha cosTheta) (/.f32 alpha cosTheta) (neg.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	97.2%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (.f32 (+.f32 (-.f32 (/.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32) #s(literal 1 binary32)) alpha) alpha) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (pow.f32 alpha #s(literal 4 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	97.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (.f32 #s(literal 1/2 binary32) (/.f32 (fma.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32) #s(literal 1 binary32)) alpha) alpha (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (*.f32 (log.f32 alpha) (PI.f32))))))
	95.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (fma.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))))))
	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
	97.7%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (.f32 (fma.f32 (/.f32 (fma.f32 (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)))) (neg.f32 (log.f32 alpha))) #s(literal -1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (PI.f32))) (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (*.f32 alpha alpha))))

Compiler

Compiled 2 888 to 1 604 computations (44.5% saved)

simplify9.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
cost-diff	0	(.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha)
cost-diff	0	(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha)
cost-diff	0	#s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha))
cost-diff	0	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
cost-diff	0	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
cost-diff	0	(*.f32 (NAN.f32) (PI.f32))
cost-diff	0	#s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32)))
cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff	0	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
cost-diff	0	#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	699
0	115	695

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
(.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))
(*.f32 cosTheta cosTheta)
cosTheta
(.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
(log.f32 (*.f32 alpha alpha))
(PI.f32)
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
#s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32)))
(*.f32 (NAN.f32) (PI.f32))
(NAN.f32)
(PI.f32)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(*.f32 cosTheta cosTheta)
cosTheta
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha))
(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha)
(.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha)
(-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(*.f32 alpha alpha)
alpha
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
#s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))
(.f32 (.f32 alpha alpha) #s(literal -2 binary32))
#s(literal -2 binary32)
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha))))
(.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))
(*.f32 cosTheta cosTheta)
cosTheta
(neg.f32 (log.f32 alpha))
(log.f32 alpha)
(PI.f32)
(.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)))
(/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))
(.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
(.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))
(*.f32 cosTheta cosTheta)
cosTheta
(.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
(log.f32 (*.f32 alpha alpha))
(PI.f32)
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
#s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32)))
(*.f32 (NAN.f32) (PI.f32))
(NAN.f32)
(PI.f32)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(*.f32 cosTheta cosTheta)
cosTheta
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha))
(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha)
(.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha)
(-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(*.f32 alpha alpha)
alpha
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
#s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))
(.f32 (.f32 alpha alpha) #s(literal -2 binary32))
#s(literal -2 binary32)
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha))))
(.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))
(*.f32 cosTheta cosTheta)
cosTheta
(neg.f32 (log.f32 alpha))
(log.f32 alpha)
(PI.f32)
(.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)))
(/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))
(.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))

localize141.0ms (2%)

Memory

25.3MiB live, 168.2MiB allocated; 17ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(neg.f32 (log.f32 alpha))
accuracy	0.0	(log.f32 alpha)
accuracy	0.0	#s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	0.0	#s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	0.0	#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 (NAN.f32) (PI.f32))
accuracy	0.0	(NAN.f32)
accuracy	0.0	#s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32)))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	0.0	#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
accuracy	29.98788023102775	(PI.f32)

Samples

103.0ms

256×

invalid

Compiler

Compiled 552 to 57 computations (89.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-mult: 39.0ms (47.2% of total)

ival-div: 18.0ms (21.8% of total)

ival-log: 8.0ms (9.7% of total)

ival-add: 7.0ms (8.5% of total)

ival-pow: 5.0ms (6.1% of total)

ival-sub: 4.0ms (4.8% of total)

ival-pi: 1.0ms (1.2% of total)

exact: 1.0ms (1.2% of total)

ival-neg: 1.0ms (1.2% of total)

adjust: 0.0ms (0% of total)

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

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

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

series152.0ms (2.2%)

Memory

-41.7MiB live, 159.0MiB allocated; 38ms collecting garbage

Counts

22 → 91

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32)))
(*.f32 (NAN.f32) (PI.f32))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha))
(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha)
(.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
#s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(NAN.f32)
#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(log.f32 alpha)
(neg.f32 (log.f32 alpha))

Outputs
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(* (PI) (log (pow alpha 2)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(/ (- (pow alpha 2) 1) (* (NAN) (PI)))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (NAN) (PI)))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (NAN) (PI))) (/ (pow (- (pow alpha 2) 1) 2) (* (NAN) (PI))))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (NAN) (PI)))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (NAN) (PI)))))) (/ (pow (- (pow alpha 2) 1) 2) (* (NAN) (PI))))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(* (NAN) (PI))
(+ (* (NAN) (PI)) (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))
(/ (- (pow alpha 2) 1) (log (pow (pow alpha 2) (PI))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (log (pow (pow alpha 2) (PI))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (log (pow (pow alpha 2) (PI)))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (log (pow (pow alpha 2) (PI))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (log (pow (pow alpha 2) (PI))))))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(log (pow (pow alpha 2) (PI)))
(+ (log (pow (pow alpha 2) (PI))) (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(/ 1 (* (pow cosTheta 2) (* (NAN) (PI))))
(/ (- (/ 1 (* (NAN) (PI))) (/ 1 (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (NAN) (PI))) (/ 1 (* (pow cosTheta 4) (* (NAN) (* (PI) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (NAN) (PI))) (/ 1 (* (pow cosTheta 4) (* (NAN) (* (PI) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (NAN) (* (PI) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (NAN) (* (PI) (- (pow alpha 2) 1))) (/ (* (NAN) (PI)) (pow cosTheta 2))))
(/ 1 (* (pow cosTheta 2) (log (pow (pow alpha 2) (PI)))))
(/ (- (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (+ (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1)))) (/ 1 (* (pow cosTheta 6) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1)) (/ (log (pow (pow alpha 2) (PI))) (pow cosTheta 2))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
-1
(- (pow alpha 2) 1)
(pow alpha 2)
(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(/ -1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (NAN) (* (PI) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (NAN) (* (PI) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1 (/ (pow cosTheta 2) (* (NAN) (* (PI) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))))
(- (* (pow alpha 2) (- (+ (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (NAN) (* (PI) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (NAN) (* (PI) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2)))))) (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1 (/ (pow cosTheta 2) (* (NAN) (* (PI) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))))
(* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))
(+ (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))) (* (pow alpha 2) (* (pow cosTheta 2) (* (NAN) (PI)))))
(/ -1 alpha)
(/ (- (pow alpha 2) 1) alpha)
(* 2 (log alpha))
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(log alpha)
(* -1 (log alpha))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(- (/ 1 (* (pow cosTheta 2) (* (NAN) (PI)))) (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (NAN) (PI))))))
(- (+ (/ 1 (* (pow alpha 4) (* (pow cosTheta 6) (* (NAN) (PI))))) (/ 1 (* (pow cosTheta 2) (* (NAN) (PI))))) (+ (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (NAN) (PI))))) (/ 1 (* (pow alpha 4) (* (pow cosTheta 4) (* (NAN) (PI)))))))
(- (+ (* -1 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 8) (* (NAN) (PI)))))) (/ 1 (* (pow cosTheta 2) (* (NAN) (PI))))) (+ (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (NAN) (PI)))))) (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (NAN) (PI)))))))
(* (pow alpha 2) (* (pow cosTheta 2) (* (NAN) (PI))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (* (NAN) (PI))) (/ (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2))))
alpha
(* alpha (- 1 (/ 1 (pow alpha 2))))
(* -2 (log (/ 1 alpha)))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* -1 (log (/ 1 alpha)))
(log (/ 1 alpha))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* -1 (* alpha (- (/ 1 (pow alpha 2)) 1)))
(* -2 (log (/ -1 alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(* -1 (+ (log -1) (* -1 (log (/ -1 alpha)))))

Calls

6 calls:

Time	Variable		Point	Expression
74.0ms	alpha	@	-inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (NAN) (PI)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (PI) (log (* alpha alpha)) (NAN) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (log alpha) (neg (log alpha)))
24.0ms	cosTheta	@	inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (NAN) (PI)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (PI) (log (* alpha alpha)) (NAN) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (log alpha) (neg (log alpha)))
21.0ms	alpha	@	inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (NAN) (PI)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (PI) (log (* alpha alpha)) (NAN) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (log alpha) (neg (log alpha)))
20.0ms	alpha	@	0	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (NAN) (PI)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (PI) (log (* alpha alpha)) (NAN) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (log alpha) (neg (log alpha)))
5.0ms	cosTheta	@	-inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (NAN) (PI)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (PI) (log (* alpha alpha)) (NAN) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (log alpha) (neg (log alpha)))

simplify176.0ms (2.5%)

Memory

18.4MiB live, 206.7MiB allocated; 22ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	379	2884
1	1115	2771
2	4715	2580
0	8277	2467

Stop Event

1×	iter limit
1×	node limit

Counts

91 → 90

Calls

Call 1

Inputs
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(* (PI) (log (pow alpha 2)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(/ (- (pow alpha 2) 1) (* (NAN) (PI)))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (NAN) (PI)))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (NAN) (PI))) (/ (pow (- (pow alpha 2) 1) 2) (* (NAN) (PI))))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (NAN) (PI)))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (NAN) (PI)))))) (/ (pow (- (pow alpha 2) 1) 2) (* (NAN) (PI))))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(* (NAN) (PI))
(+ (* (NAN) (PI)) (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))
(/ (- (pow alpha 2) 1) (log (pow (pow alpha 2) (PI))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (log (pow (pow alpha 2) (PI))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (log (pow (pow alpha 2) (PI)))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (log (pow (pow alpha 2) (PI))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (log (pow (pow alpha 2) (PI))))))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(log (pow (pow alpha 2) (PI)))
(+ (log (pow (pow alpha 2) (PI))) (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(/ 1 (* (pow cosTheta 2) (* (NAN) (PI))))
(/ (- (/ 1 (* (NAN) (PI))) (/ 1 (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (NAN) (PI))) (/ 1 (* (pow cosTheta 4) (* (NAN) (* (PI) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (NAN) (PI))) (/ 1 (* (pow cosTheta 4) (* (NAN) (* (PI) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (NAN) (* (PI) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (NAN) (* (PI) (- (pow alpha 2) 1))) (/ (* (NAN) (PI)) (pow cosTheta 2))))
(/ 1 (* (pow cosTheta 2) (log (pow (pow alpha 2) (PI)))))
(/ (- (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (+ (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1)))) (/ 1 (* (pow cosTheta 6) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1)) (/ (log (pow (pow alpha 2) (PI))) (pow cosTheta 2))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
-1
(- (pow alpha 2) 1)
(pow alpha 2)
(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(/ -1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (NAN) (* (PI) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (NAN) (* (PI) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1 (/ (pow cosTheta 2) (* (NAN) (* (PI) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))))
(- (* (pow alpha 2) (- (+ (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (NAN) (* (PI) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (NAN) (* (PI) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2)))))) (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1 (/ (pow cosTheta 2) (* (NAN) (* (PI) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (/ 1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))))
(* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))
(+ (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))) (* (pow alpha 2) (* (pow cosTheta 2) (* (NAN) (PI)))))
(/ -1 alpha)
(/ (- (pow alpha 2) 1) alpha)
(* 2 (log alpha))
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(log alpha)
(* -1 (log alpha))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(- (/ 1 (* (pow cosTheta 2) (* (NAN) (PI)))) (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (NAN) (PI))))))
(- (+ (/ 1 (* (pow alpha 4) (* (pow cosTheta 6) (* (NAN) (PI))))) (/ 1 (* (pow cosTheta 2) (* (NAN) (PI))))) (+ (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (NAN) (PI))))) (/ 1 (* (pow alpha 4) (* (pow cosTheta 4) (* (NAN) (PI)))))))
(- (+ (* -1 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 8) (* (NAN) (PI)))))) (/ 1 (* (pow cosTheta 2) (* (NAN) (PI))))) (+ (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (NAN) (PI)))))) (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (NAN) (PI)))))))
(* (pow alpha 2) (* (pow cosTheta 2) (* (NAN) (PI))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (* (NAN) (PI))) (/ (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2))))
alpha
(* alpha (- 1 (/ 1 (pow alpha 2))))
(* -2 (log (/ 1 alpha)))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* -1 (log (/ 1 alpha)))
(log (/ 1 alpha))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* -1 (* alpha (- (/ 1 (pow alpha 2)) 1)))
(* -2 (log (/ -1 alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(* -1 (+ (log -1) (* -1 (log (/ -1 alpha)))))

Outputs
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(fma.f32 (-.f32 (.f32 (/.f32 (.f32 cosTheta cosTheta) (log.f32 (.f32 alpha alpha))) (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (PI.f32))) (/.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (.f32 cosTheta cosTheta) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(fma.f32 (-.f32 (.f32 (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32)) cosTheta) (neg.f32 cosTheta) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (.f32 cosTheta cosTheta) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(* (PI) (log (pow alpha 2)))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
(/ (- (pow alpha 2) 1) (* (NAN) (PI)))
(/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (NAN.f32)) (PI.f32))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (NAN) (PI)))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (NAN.f32) (PI.f32)))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (NAN) (PI))) (/ (pow (- (pow alpha 2) 1) 2) (* (NAN) (PI))))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(fma.f32 (-.f32 (.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (NAN.f32)) (/.f32 (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (NAN.f32)) (PI.f32))) (*.f32 cosTheta cosTheta) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (NAN.f32)) (PI.f32)))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (NAN) (PI)))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (NAN) (PI)))))) (/ (pow (- (pow alpha 2) 1) 2) (* (NAN) (PI))))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(fma.f32 (-.f32 (.f32 (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32)) cosTheta) (neg.f32 cosTheta) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32))) (.f32 (NAN.f32) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (NAN.f32)) (PI.f32))) (*.f32 cosTheta cosTheta) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (NAN.f32)) (PI.f32)))
(* (NAN) (PI))
(*.f32 (NAN.f32) (PI.f32))
(+ (* (NAN) (PI)) (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))
(fma.f32 (.f32 (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (NAN.f32)) cosTheta) cosTheta (.f32 (NAN.f32) (PI.f32)))
(/ (- (pow alpha 2) 1) (log (pow (pow alpha 2) (PI))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (log (pow (pow alpha 2) (PI))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (log (pow (pow alpha 2) (PI)))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(fma.f32 (-.f32 (.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 cosTheta cosTheta)) (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))) (.f32 cosTheta cosTheta) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (log (pow (pow alpha 2) (PI))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (log (pow (pow alpha 2) (PI))))))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(fma.f32 (fma.f32 (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32)) cosTheta) (neg.f32 cosTheta) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32))) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 cosTheta cosTheta) (neg.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))) (.f32 cosTheta cosTheta) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))
(log (pow (pow alpha 2) (PI)))
(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
(+ (log (pow (pow alpha 2) (PI))) (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))
(fma.f32 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 cosTheta cosTheta) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))
1
#s(literal 1 binary32)
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1 binary32))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (*.f32 alpha alpha)))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (log.f32 (.f32 alpha alpha)))) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (log.f32 (.f32 alpha alpha)))) (PI.f32)) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 6 binary32))) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32))) (*.f32 cosTheta cosTheta))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (.f32 (log.f32 (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))
(/ 1 (* (pow cosTheta 2) (* (NAN) (PI))))
(/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (NAN.f32) (PI.f32))) cosTheta) cosTheta)
(/ (- (/ 1 (* (NAN) (PI))) (/ 1 (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (NAN.f32) (PI.f32))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (NAN.f32))) (.f32 cosTheta cosTheta))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (NAN) (PI))) (/ 1 (* (pow cosTheta 4) (* (NAN) (* (PI) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) (NAN.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (NAN.f32))) (.f32 cosTheta cosTheta))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (NAN) (PI))) (/ 1 (* (pow cosTheta 4) (* (NAN) (* (PI) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (NAN) (* (PI) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) (NAN.f32)) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 6 binary32))) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (PI.f32))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)))) (NAN.f32))) (*.f32 cosTheta cosTheta))
(* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1))))
(.f32 (.f32 (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (NAN.f32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (NAN) (* (PI) (- (pow alpha 2) 1))) (/ (* (NAN) (PI)) (pow cosTheta 2))))
(.f32 (.f32 (NAN.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))
(/ 1 (* (pow cosTheta 2) (log (pow (pow alpha 2) (PI)))))
(/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))
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(.f32 (.f32 (NAN.f32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (*.f32 alpha alpha)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (* (NAN) (PI))) (/ (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2))))
(.f32 (fma.f32 (.f32 (.f32 (NAN.f32) (PI.f32)) cosTheta) cosTheta (.f32 (/.f32 (.f32 (NAN.f32) (PI.f32)) alpha) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha))) (*.f32 alpha alpha))
alpha
(* alpha (- 1 (/ 1 (pow alpha 2))))
(*.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha)
(* -2 (log (/ 1 alpha)))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 (.f32 (*.f32 cosTheta cosTheta) alpha) alpha)
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(.f32 (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha)) (*.f32 alpha alpha))
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(log (/ 1 alpha))
(neg.f32 (log.f32 alpha))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (/.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32)))) (.f32 cosTheta cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(-.f32 (fma.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)) (.f32 (pow.f32 alpha #s(literal 6 binary32)) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (fma.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)))) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32)))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (PI.f32) (*.f32 alpha alpha)))))
(* -1 (* alpha (- (/ 1 (pow alpha 2)) 1)))
(*.f32 (neg.f32 alpha) (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha) #s(literal 1 binary32)))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -1 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(fma.f32 (log.f32 #s(literal -1 binary32)) #s(literal -1 binary32) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))

rewrite17.0ms (0.2%)

Memory

11.0MiB live, 11.0MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	405
0	115	401

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

22 → 23

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32)))
(*.f32 (NAN.f32) (PI.f32))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha))
(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha)
(.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
#s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(NAN.f32)
#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(log.f32 alpha)
(neg.f32 (log.f32 alpha))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
#s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32)))
(*.f32 (NAN.f32) (PI.f32))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha))
(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha)
(.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
#s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(NAN.f32)
#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(log.f32 alpha)
(neg.f32 (log.f32 alpha))

eval18.0ms (0.3%)

Memory: -13.4MiB live, 31.4MiB allocated; 4ms collecting garbage
Compiler: Compiled 8 432 to 698 computations (91.7% saved)

prune31.0ms (0.4%)

Memory

10.7MiB live, 54.8MiB allocated; 7ms collecting garbage

Pruning

34 alts after pruning (32 fresh and 2 done)

	Pruned	Kept	Total
New	152	14	166
Fresh	7	18	25
Picked	4	1	5
Done	0	1	1
Total	163	34	197

Accuracy

100.0%

Counts

197 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) alpha (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.6%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
	98.4%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (cbrt.f32 (PI.f32)) (log.f32 (pow.f32 (.f32 alpha alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (pow.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 2 binary32)))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta))))))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha)) (*.f32 alpha alpha)))))
▶	59.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
	56.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (fma.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) cosTheta) (neg.f32 cosTheta) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha)) (/.f32 (PI.f32) (.f32 alpha alpha)))))))
▶	96.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
	98.2%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
▶	98.3%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
	97.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	98.2%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	98.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) alpha)) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	68.0%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	95.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
▶	97.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	67.2%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
	56.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (.f32 (-.f32 (fma.f32 (/.f32 alpha cosTheta) (/.f32 alpha cosTheta) (neg.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	97.2%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (.f32 (+.f32 (-.f32 (/.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32) #s(literal 1 binary32)) alpha) alpha) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (pow.f32 alpha #s(literal 4 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	97.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (.f32 #s(literal 1/2 binary32) (/.f32 (fma.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32) #s(literal 1 binary32)) alpha) alpha (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (*.f32 (log.f32 alpha) (PI.f32))))))
	95.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (fma.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))))))
	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
	97.7%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (.f32 (fma.f32 (/.f32 (fma.f32 (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)))) (neg.f32 (log.f32 alpha))) #s(literal -1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (PI.f32))) (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (*.f32 alpha alpha))))
	96.1%	#s(approx (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))

Compiler

Compiled 3 188 to 1 779 computations (44.2% saved)

simplify154.0ms (2.2%)

Memory

-1.2MiB live, 183.5MiB allocated; 36ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
cost-diff	0	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
cost-diff	2	(.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
cost-diff	4	(fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha))))
cost-diff	0	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	#s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta))
cost-diff	0	(fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
cost-diff	0	(/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
cost-diff	0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
cost-diff	0	#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	5	(fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	812
0	115	797
1	284	781
2	1114	762
3	6454	762
0	8535	742

Stop Event

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

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (.f32 cosTheta cosTheta) (PI.f32))
(*.f32 cosTheta cosTheta)
cosTheta
(PI.f32)
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(log.f32 (*.f32 alpha alpha))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(log.f32 (*.f32 alpha alpha))
(PI.f32)
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
(fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
#s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta))
(.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(fma.f32 #s(literal -2 binary32) (*.f32 alpha alpha) #s(literal 1 binary32))
#s(literal -2 binary32)
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
cosTheta
(neg.f32 cosTheta)
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(log.f32 (*.f32 alpha alpha))
(PI.f32)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta)
(-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32))
(fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(*.f32 cosTheta cosTheta)
cosTheta
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
#s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))
(.f32 (.f32 alpha alpha) #s(literal -2 binary32))
(*.f32 alpha alpha)
#s(literal -2 binary32)
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha))))
(.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))
(*.f32 cosTheta cosTheta)
cosTheta
(neg.f32 (log.f32 alpha))
(log.f32 alpha)
(PI.f32)
(.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)))
(/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))
(.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
#s(literal 1 binary32)

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
(.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) cosTheta) cosTheta)
(.f32 (.f32 cosTheta cosTheta) (PI.f32))
(.f32 (PI.f32) (.f32 cosTheta cosTheta))
(*.f32 cosTheta cosTheta)
cosTheta
(PI.f32)
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(log.f32 (*.f32 alpha alpha))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(log.f32 (*.f32 alpha alpha))
(PI.f32)
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32))) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
(/.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32))) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 (neg.f32 cosTheta) #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32)))
#s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta))
(.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(fma.f32 #s(literal -2 binary32) (*.f32 alpha alpha) #s(literal 1 binary32))
#s(literal -2 binary32)
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
cosTheta
(neg.f32 cosTheta)
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(log.f32 (*.f32 alpha alpha))
(PI.f32)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))) (log.f32 (.f32 alpha alpha)))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)))
(.f32 #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta)
(-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32))
(fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(*.f32 cosTheta cosTheta)
cosTheta
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (neg.f32 (log.f32 alpha)) (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha))))))
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
#s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
#s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (neg.f32 (log.f32 alpha)) (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha)))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))
(.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (neg.f32 (log.f32 alpha)) (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha))))
(.f32 (.f32 alpha alpha) #s(literal -2 binary32))
(.f32 #s(literal -2 binary32) (.f32 alpha alpha))
(*.f32 alpha alpha)
#s(literal -2 binary32)
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha))))
(.f32 (.f32 (neg.f32 (log.f32 alpha)) (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha))) (PI.f32))
(.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))
(.f32 (.f32 (neg.f32 cosTheta) cosTheta) (log.f32 alpha))
(*.f32 cosTheta cosTheta)
cosTheta
(neg.f32 (log.f32 alpha))
(log.f32 alpha)
(PI.f32)
(.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)))
(.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha)) (/.f32 (PI.f32) (*.f32 alpha alpha)))
(/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))
(*.f32 (/.f32 (log.f32 alpha) alpha) (/.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) alpha))
(.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(*.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
#s(literal 1 binary32)

localize242.0ms (3.4%)

Memory

-3.2MiB live, 284.8MiB allocated; 59ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.30078125	(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))
accuracy	0.3125	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
accuracy	0.3515625	(.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)))
accuracy	0.40234375	(/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))
accuracy	0.16796875	(.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)
accuracy	0.3125	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
accuracy	0.38900375976844204	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
accuracy	11.664291148106754	(.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta)
accuracy	0.31640625	(/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
accuracy	0.35267816871672564	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
accuracy	0.38900375976844204	(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
accuracy	5.607965792376325	#s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta))
accuracy	0.06860250946961356	(log.f32 (*.f32 alpha alpha))
accuracy	0.3125	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
accuracy	0.38900375976844204	(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
accuracy	0.8809764753300806	#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
accuracy	0.21875	(.f32 (.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	0.2623825195368841	(.f32 (.f32 cosTheta cosTheta) (PI.f32))
accuracy	0.3125	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
accuracy	0.38900375976844204	(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))

Samples

171.0ms

256×

valid

Compiler

Compiled 605 to 57 computations (90.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 150.0ms

ival-mult: 56.0ms (37.3% of total)

ival-div: 40.0ms (26.6% of total)

ival-add: 27.0ms (18% of total)

ival-log: 12.0ms (8% of total)

ival-pow: 5.0ms (3.3% of total)

ival-sub: 4.0ms (2.7% of total)

ival-pow2: 3.0ms (2% of total)

ival-neg: 2.0ms (1.3% of total)

ival-pi: 1.0ms (0.7% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series108.0ms (1.5%)

Memory

30.9MiB live, 156.7MiB allocated; 25ms collecting garbage

Counts

26 → 139

Calls

Call 1

Inputs
(fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
(*.f32 alpha alpha)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
(fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
#s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha))))
(.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(.f32 (.f32 cosTheta cosTheta) (PI.f32))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(log.f32 (*.f32 alpha alpha))
(.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta)
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)
(/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))
(.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))

Outputs
(* (PI) (log (pow alpha 2)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (pow alpha 2) 1)
(- (+ (* -1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2))) (pow alpha 2)) 1)
(* cosTheta (pow (- (pow alpha 2) 1) 2))
(* -1 (/ (* (PI) (log alpha)) (pow alpha 2)))
(+ (* -1 (/ (* (PI) (log alpha)) (pow alpha 2))) (* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2)))))
(* -1 (log alpha))
(+ (* -1 (log alpha)) (* (pow cosTheta 2) (log alpha)))
(/ (- (pow alpha 2) 1) (log (pow (pow alpha 2) (PI))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (log (pow (pow alpha 2) (PI))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (log (pow (pow alpha 2) (PI)))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (log (pow (pow alpha 2) (PI))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (log (pow (pow alpha 2) (PI))))))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(* (pow cosTheta 2) (PI))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(/ 1 cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1))) cosTheta)
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(* -1 (/ (log alpha) (pow alpha 2)))
(+ (* -1 (/ (log alpha) (pow alpha 2))) (/ (* (pow cosTheta 2) (log alpha)) (pow alpha 2)))
(+ (* -1 (/ (* (PI) (log alpha)) (pow alpha 2))) (/ (* (pow cosTheta 2) (* (PI) (log alpha))) (pow alpha 2)))
(* 2 (* (PI) (log alpha)))
(+ (* -2 (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2)))))) (* 2 (* (PI) (log alpha))))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2)))))
(* (pow cosTheta 2) (- (+ (* -1 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))))
(* -1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))
(* (pow cosTheta 2) (- (+ (* -1 (pow (- (pow alpha 2) 1) 2)) (/ (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (+ (* -1 (/ (* (PI) (log alpha)) (* (pow alpha 2) (pow cosTheta 2)))) (/ (* (PI) (log alpha)) (pow alpha 2)))))
(* (pow cosTheta 2) (log alpha))
(* (pow cosTheta 2) (+ (log alpha) (* -1 (/ (log alpha) (pow cosTheta 2)))))
(/ 1 (* (pow cosTheta 2) (log (pow (pow alpha 2) (PI)))))
(/ (- (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (+ (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1)))) (/ 1 (* (pow cosTheta 6) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 2))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(/ (* (pow cosTheta 2) (log alpha)) (pow alpha 2))
(* (pow cosTheta 2) (+ (* -1 (/ (log alpha) (* (pow alpha 2) (pow cosTheta 2)))) (/ (log alpha) (pow alpha 2))))
(/ (* (pow cosTheta 2) (* (PI) (log alpha))) (pow alpha 2))
(* (pow cosTheta 2) (+ (* -1 (/ (* (PI) (log alpha)) (* (pow alpha 2) (pow cosTheta 2)))) (/ (* (PI) (log alpha)) (pow alpha 2))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2))))))
(* (pow cosTheta 2) (+ (* -2 (* (pow alpha 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2))))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* -1 (* cosTheta (- (* -1 (- (pow alpha 2) 1)) (/ 1 (pow cosTheta 2)))))
(+ (* -2 (* (pow cosTheta 2) (* (PI) (log alpha)))) (* 2 (* (PI) (log alpha))))
(+ (* -2 (* (pow cosTheta 2) (* (PI) (log alpha)))) (+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha)))))))
-1
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(pow alpha 2)
(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(* 1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (PI) (log alpha))))
(+ (* 1/2 (/ (* (pow alpha 2) (+ 1 (* 2 (pow cosTheta 2)))) (* (PI) (log alpha)))) (* 1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (PI) (log alpha)))))
(+ (* 1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (PI) (log alpha)))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow alpha 2) (pow cosTheta 2)) (* (PI) (log alpha)))) (* 1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (PI) (log alpha)))))))
(- (* -1 (pow cosTheta 2)) 1)
(- (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (+ 1 (* 2 (pow cosTheta 2))))) 1)
(- (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (+ 1 (+ (* -1 (* (pow alpha 2) (pow cosTheta 2))) (* 2 (pow cosTheta 2)))))) 1)
cosTheta
(+ cosTheta (* -2 (* (pow alpha 2) cosTheta)))
(+ cosTheta (* (pow alpha 2) (+ (* -2 cosTheta) (* (pow alpha 2) cosTheta))))
(* -1 (/ (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))) (pow alpha 2)))
(/ (+ (* -1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha)))))) (pow alpha 2))
(* -1 (* (log alpha) (- 1 (pow cosTheta 2))))
(* -1 (* (pow cosTheta 2) (PI)))
(+ (* -1 (* (pow cosTheta 2) (PI))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(* 2 (log alpha))
(* cosTheta (- (/ 1 (pow cosTheta 2)) 1))
(+ (* cosTheta (- (/ 1 (pow cosTheta 2)) 1)) (* (pow alpha 2) cosTheta))
(* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))
(+ (* (pow alpha 2) (pow cosTheta 2)) (* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1)))
(* -1 (/ (* (log alpha) (- 1 (pow cosTheta 2))) (pow alpha 2)))
(* 2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))
(+ (* 2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (+ (* -2 (/ (* (PI) (log (/ 1 alpha))) (pow alpha 2))) (* 2 (/ (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))) (pow alpha 2))))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* 1/2 (/ (* (pow alpha 4) (pow cosTheta 2)) (* (PI) (log (/ 1 alpha)))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (pow alpha 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(* -1 (* (pow alpha 4) (pow cosTheta 2)))
(* (pow alpha 4) (+ (* -1 (pow cosTheta 2)) (+ (* 2 (/ (pow cosTheta 2) (pow alpha 2))) (/ 1 (pow alpha 2)))))
(* (pow alpha 4) (- (+ (* -1 (/ (pow cosTheta 2) (pow alpha 4))) (+ (* -1 (pow cosTheta 2)) (+ (* 2 (/ (pow cosTheta 2) (pow alpha 2))) (/ 1 (pow alpha 2))))) (/ 1 (pow alpha 4))))
(* (pow alpha 4) cosTheta)
(* (pow alpha 4) (+ cosTheta (* -2 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 4) (+ cosTheta (+ (* -2 (/ cosTheta (pow alpha 2))) (/ cosTheta (pow alpha 4)))))
(* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))
(+ (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))) (/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2)))
(* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))
(* -2 (* (PI) (log (/ 1 alpha))))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* -1 (/ (* (pow cosTheta 2) (PI)) (pow alpha 2))) (* (pow cosTheta 2) (PI))))
(* -2 (log (/ 1 alpha)))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (/ (* cosTheta (- (/ 1 (pow cosTheta 2)) 1)) (pow alpha 2))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (/ (* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1)) (pow alpha 2)) (pow cosTheta 2)))
(/ (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2))) (pow alpha 2))
(/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (+ (* -2 (/ (* (PI) (log (/ -1 alpha))) (pow alpha 2))) (* 2 (/ (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))) (pow alpha 2))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* 1/2 (/ (* (pow alpha 4) (pow cosTheta 2)) (* (PI) (log (/ -1 alpha)))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (pow alpha 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(* -1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(+ (* -1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* -1 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2))))
(* -1 (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (log (/ -1 alpha)))
(* -1 (/ (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2))) (pow alpha 2)))
(* -1 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2)))
(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))

Calls

6 calls:

Time	Variable		Point	Expression
27.0ms	alpha	@	0	((+ (* (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha))) (* (log (* alpha alpha)) (PI))) (- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)))) (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (log (* alpha alpha)) (PI)) (* (* cosTheta cosTheta) (PI)) (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) (* (PI) (log (* alpha alpha))) (* (* (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) cosTheta) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))) (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))))
26.0ms	alpha	@	inf	((+ (* (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha))) (* (log (* alpha alpha)) (PI))) (- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)))) (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (log (* alpha alpha)) (PI)) (* (* cosTheta cosTheta) (PI)) (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) (* (PI) (log (* alpha alpha))) (* (* (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) cosTheta) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))) (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))))
22.0ms	alpha	@	-inf	((+ (* (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha))) (* (log (* alpha alpha)) (PI))) (- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)))) (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (log (* alpha alpha)) (PI)) (* (* cosTheta cosTheta) (PI)) (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) (* (PI) (log (* alpha alpha))) (* (* (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) cosTheta) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))) (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))))
12.0ms	cosTheta	@	0	((+ (* (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha))) (* (log (* alpha alpha)) (PI))) (- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)))) (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (log (* alpha alpha)) (PI)) (* (* cosTheta cosTheta) (PI)) (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) (* (PI) (log (* alpha alpha))) (* (* (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) cosTheta) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))) (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))))
10.0ms	cosTheta	@	inf	((+ (* (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha))) (* (log (* alpha alpha)) (PI))) (- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)))) (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (log (* alpha alpha)) (PI)) (* (* cosTheta cosTheta) (PI)) (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) (* (PI) (log (* alpha alpha))) (* (* (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) cosTheta) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))) (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))))

simplify170.0ms (2.4%)

Memory

12.4MiB live, 205.1MiB allocated; 21ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	475	3577
1	1565	3394
2	7082	3211
0	8213	3114

Stop Event

1×	iter limit
1×	node limit

Counts

139 → 138

Calls

Call 1

Inputs
(* (PI) (log (pow alpha 2)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (pow alpha 2) 1)
(- (+ (* -1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2))) (pow alpha 2)) 1)
(* cosTheta (pow (- (pow alpha 2) 1) 2))
(* -1 (/ (* (PI) (log alpha)) (pow alpha 2)))
(+ (* -1 (/ (* (PI) (log alpha)) (pow alpha 2))) (* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2)))))
(* -1 (log alpha))
(+ (* -1 (log alpha)) (* (pow cosTheta 2) (log alpha)))
(/ (- (pow alpha 2) 1) (log (pow (pow alpha 2) (PI))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (log (pow (pow alpha 2) (PI))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (log (pow (pow alpha 2) (PI)))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (log (pow (pow alpha 2) (PI))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (log (pow (pow alpha 2) (PI))))))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(* (pow cosTheta 2) (PI))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(/ 1 cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1))) cosTheta)
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(* -1 (/ (log alpha) (pow alpha 2)))
(+ (* -1 (/ (log alpha) (pow alpha 2))) (/ (* (pow cosTheta 2) (log alpha)) (pow alpha 2)))
(+ (* -1 (/ (* (PI) (log alpha)) (pow alpha 2))) (/ (* (pow cosTheta 2) (* (PI) (log alpha))) (pow alpha 2)))
(* 2 (* (PI) (log alpha)))
(+ (* -2 (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2)))))) (* 2 (* (PI) (log alpha))))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2)))))
(* (pow cosTheta 2) (- (+ (* -1 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))))
(* -1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))
(* (pow cosTheta 2) (- (+ (* -1 (pow (- (pow alpha 2) 1) 2)) (/ (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (+ (* -1 (/ (* (PI) (log alpha)) (* (pow alpha 2) (pow cosTheta 2)))) (/ (* (PI) (log alpha)) (pow alpha 2)))))
(* (pow cosTheta 2) (log alpha))
(* (pow cosTheta 2) (+ (log alpha) (* -1 (/ (log alpha) (pow cosTheta 2)))))
(/ 1 (* (pow cosTheta 2) (log (pow (pow alpha 2) (PI)))))
(/ (- (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (+ (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1)))) (/ 1 (* (pow cosTheta 6) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 2))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(/ (* (pow cosTheta 2) (log alpha)) (pow alpha 2))
(* (pow cosTheta 2) (+ (* -1 (/ (log alpha) (* (pow alpha 2) (pow cosTheta 2)))) (/ (log alpha) (pow alpha 2))))
(/ (* (pow cosTheta 2) (* (PI) (log alpha))) (pow alpha 2))
(* (pow cosTheta 2) (+ (* -1 (/ (* (PI) (log alpha)) (* (pow alpha 2) (pow cosTheta 2)))) (/ (* (PI) (log alpha)) (pow alpha 2))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2))))))
(* (pow cosTheta 2) (+ (* -2 (* (pow alpha 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2))))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* -1 (* cosTheta (- (* -1 (- (pow alpha 2) 1)) (/ 1 (pow cosTheta 2)))))
(+ (* -2 (* (pow cosTheta 2) (* (PI) (log alpha)))) (* 2 (* (PI) (log alpha))))
(+ (* -2 (* (pow cosTheta 2) (* (PI) (log alpha)))) (+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha)))))))
-1
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(pow alpha 2)
(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(* 1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (PI) (log alpha))))
(+ (* 1/2 (/ (* (pow alpha 2) (+ 1 (* 2 (pow cosTheta 2)))) (* (PI) (log alpha)))) (* 1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (PI) (log alpha)))))
(+ (* 1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (PI) (log alpha)))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow alpha 2) (pow cosTheta 2)) (* (PI) (log alpha)))) (* 1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (PI) (log alpha)))))))
(- (* -1 (pow cosTheta 2)) 1)
(- (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (+ 1 (* 2 (pow cosTheta 2))))) 1)
(- (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (+ 1 (+ (* -1 (* (pow alpha 2) (pow cosTheta 2))) (* 2 (pow cosTheta 2)))))) 1)
cosTheta
(+ cosTheta (* -2 (* (pow alpha 2) cosTheta)))
(+ cosTheta (* (pow alpha 2) (+ (* -2 cosTheta) (* (pow alpha 2) cosTheta))))
(* -1 (/ (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))) (pow alpha 2)))
(/ (+ (* -1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha)))))) (pow alpha 2))
(* -1 (* (log alpha) (- 1 (pow cosTheta 2))))
(* -1 (* (pow cosTheta 2) (PI)))
(+ (* -1 (* (pow cosTheta 2) (PI))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(* 2 (log alpha))
(* cosTheta (- (/ 1 (pow cosTheta 2)) 1))
(+ (* cosTheta (- (/ 1 (pow cosTheta 2)) 1)) (* (pow alpha 2) cosTheta))
(* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))
(+ (* (pow alpha 2) (pow cosTheta 2)) (* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1)))
(* -1 (/ (* (log alpha) (- 1 (pow cosTheta 2))) (pow alpha 2)))
(* 2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))
(+ (* 2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (+ (* -2 (/ (* (PI) (log (/ 1 alpha))) (pow alpha 2))) (* 2 (/ (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))) (pow alpha 2))))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* 1/2 (/ (* (pow alpha 4) (pow cosTheta 2)) (* (PI) (log (/ 1 alpha)))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (pow alpha 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(* -1 (* (pow alpha 4) (pow cosTheta 2)))
(* (pow alpha 4) (+ (* -1 (pow cosTheta 2)) (+ (* 2 (/ (pow cosTheta 2) (pow alpha 2))) (/ 1 (pow alpha 2)))))
(* (pow alpha 4) (- (+ (* -1 (/ (pow cosTheta 2) (pow alpha 4))) (+ (* -1 (pow cosTheta 2)) (+ (* 2 (/ (pow cosTheta 2) (pow alpha 2))) (/ 1 (pow alpha 2))))) (/ 1 (pow alpha 4))))
(* (pow alpha 4) cosTheta)
(* (pow alpha 4) (+ cosTheta (* -2 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 4) (+ cosTheta (+ (* -2 (/ cosTheta (pow alpha 2))) (/ cosTheta (pow alpha 4)))))
(* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))
(+ (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))) (/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2)))
(* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))
(* -2 (* (PI) (log (/ 1 alpha))))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* -1 (/ (* (pow cosTheta 2) (PI)) (pow alpha 2))) (* (pow cosTheta 2) (PI))))
(* -2 (log (/ 1 alpha)))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (/ (* cosTheta (- (/ 1 (pow cosTheta 2)) 1)) (pow alpha 2))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (/ (* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1)) (pow alpha 2)) (pow cosTheta 2)))
(/ (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2))) (pow alpha 2))
(/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (+ (* -2 (/ (* (PI) (log (/ -1 alpha))) (pow alpha 2))) (* 2 (/ (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))) (pow alpha 2))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* 1/2 (/ (* (pow alpha 4) (pow cosTheta 2)) (* (PI) (log (/ -1 alpha)))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (pow alpha 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(* -1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(+ (* -1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* -1 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2))))
(* -1 (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (log (/ -1 alpha)))
(* -1 (/ (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2))) (pow alpha 2)))
(* -1 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2)))
(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))

Outputs
(* (PI) (log (pow alpha 2)))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
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(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(/.f32 (-.f32 (-.f32 (.f32 alpha alpha) (.f32 (.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) cosTheta) cosTheta)) #s(literal 1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(fma.f32 (-.f32 (.f32 (/.f32 (.f32 cosTheta cosTheta) (log.f32 (.f32 alpha alpha))) (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 3 binary32)) (PI.f32))) (/.f32 (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (.f32 cosTheta cosTheta) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
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(- (pow alpha 2) 1)
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(* cosTheta (pow (- (pow alpha 2) 1) 2))
(.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) cosTheta)
(* -1 (/ (* (PI) (log alpha)) (pow alpha 2)))
(*.f32 (neg.f32 (PI.f32)) (/.f32 (/.f32 (log.f32 alpha) alpha) alpha))
(+ (* -1 (/ (* (PI) (log alpha)) (pow alpha 2))) (* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2)))))
(fma.f32 (.f32 (.f32 (neg.f32 (PI.f32)) (log.f32 alpha)) cosTheta) cosTheta (.f32 (.f32 (/.f32 (log.f32 alpha) alpha) (/.f32 (PI.f32) alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))
(* -1 (log alpha))
(neg.f32 (log.f32 alpha))
(+ (* -1 (log alpha)) (* (pow cosTheta 2) (log alpha)))
(*.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha))
(/ (- (pow alpha 2) 1) (log (pow (pow alpha 2) (PI))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (log (pow (pow alpha 2) (PI))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(/.f32 (-.f32 (-.f32 (.f32 alpha alpha) (.f32 (.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) cosTheta) cosTheta)) #s(literal 1 binary32)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (log (pow (pow alpha 2) (PI)))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(fma.f32 (-.f32 (.f32 (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 3 binary32)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 cosTheta cosTheta)) (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))) (.f32 cosTheta cosTheta) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (log (pow (pow alpha 2) (PI))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (log (pow (pow alpha 2) (PI))))))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(fma.f32 (-.f32 (.f32 (/.f32 (fma.f32 (.f32 (neg.f32 cosTheta) cosTheta) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 4 binary32)) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 3 binary32))) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 cosTheta cosTheta)) (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))) (.f32 cosTheta cosTheta) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
(* (pow cosTheta 2) (PI))
(.f32 (.f32 cosTheta cosTheta) (PI.f32))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) cosTheta) cosTheta)
(/ 1 cosTheta)
(/.f32 #s(literal 1 binary32) cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1))) cosTheta)
(/.f32 (fma.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)
1
#s(literal 1 binary32)
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* -1 (/ (log alpha) (pow alpha 2)))
(/.f32 (/.f32 (neg.f32 (log.f32 alpha)) alpha) alpha)
(+ (* -1 (/ (log alpha) (pow alpha 2))) (/ (* (pow cosTheta 2) (log alpha)) (pow alpha 2)))
(*.f32 (/.f32 (/.f32 (log.f32 alpha) alpha) alpha) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))
(+ (* -1 (/ (* (PI) (log alpha)) (pow alpha 2))) (/ (* (pow cosTheta 2) (* (PI) (log alpha))) (pow alpha 2)))
(.f32 (.f32 (/.f32 (log.f32 alpha) alpha) (/.f32 (PI.f32) alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))
(* 2 (* (PI) (log alpha)))
(.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))
(+ (* -2 (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2)))))) (* 2 (* (PI) (log alpha))))
(.f32 #s(literal -2 binary32) (-.f32 (.f32 (.f32 (fma.f32 (neg.f32 (PI.f32)) (log.f32 alpha) (.f32 (/.f32 (log.f32 alpha) alpha) (/.f32 (PI.f32) alpha))) (.f32 cosTheta cosTheta)) (.f32 alpha alpha)) (*.f32 (log.f32 alpha) (PI.f32))))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(.f32 (.f32 (PI.f32) (fma.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (*.f32 cosTheta cosTheta))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (log.f32 (.f32 alpha alpha)))) (PI.f32)) (/.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))))) (.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (log.f32 (.f32 alpha alpha)))) (PI.f32)) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 6 binary32))) (.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 3 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))))) (PI.f32))) (*.f32 cosTheta cosTheta))
(* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2)))))
(.f32 (neg.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha))))
(* (pow cosTheta 2) (- (+ (* -1 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))))
(.f32 (-.f32 (/.f32 (fma.f32 (/.f32 alpha cosTheta) (/.f32 alpha cosTheta) (neg.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))) (/.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (.f32 cosTheta cosTheta))
(* -1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))
(.f32 (.f32 (neg.f32 cosTheta) cosTheta) (pow.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)))
(* (pow cosTheta 2) (- (+ (* -1 (pow (- (pow alpha 2) 1) 2)) (/ (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2))))
(.f32 (-.f32 (fma.f32 (/.f32 alpha cosTheta) (/.f32 alpha cosTheta) (neg.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta cosTheta))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (/ (* (PI) (log alpha)) (pow alpha 2))))
(.f32 (fma.f32 (neg.f32 (PI.f32)) (log.f32 alpha) (.f32 (/.f32 (log.f32 alpha) alpha) (/.f32 (PI.f32) alpha))) (*.f32 cosTheta cosTheta))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (log alpha))) (+ (* -1 (/ (* (PI) (log alpha)) (* (pow alpha 2) (pow cosTheta 2)))) (/ (* (PI) (log alpha)) (pow alpha 2)))))
(.f32 (fma.f32 (neg.f32 (PI.f32)) (log.f32 alpha) (/.f32 (fma.f32 (log.f32 alpha) (PI.f32) (/.f32 (.f32 (neg.f32 (PI.f32)) (log.f32 alpha)) (.f32 cosTheta cosTheta))) (.f32 alpha alpha))) (*.f32 cosTheta cosTheta))
(* (pow cosTheta 2) (log alpha))
(.f32 (.f32 (log.f32 alpha) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (log alpha) (* -1 (/ (log alpha) (pow cosTheta 2)))))
(.f32 (-.f32 (log.f32 alpha) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta)) (.f32 cosTheta cosTheta))
(/ 1 (* (pow cosTheta 2) (log (pow (pow alpha 2) (PI)))))
(/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))
(/ (- (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) #s(literal 1 binary32)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32))))) (.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (log (pow (pow alpha 2) (PI)))) (/ 1 (* (pow cosTheta 4) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 2))))) (+ (/ 1 (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1)))) (/ 1 (* (pow cosTheta 6) (* (log (pow (pow alpha 2) (PI))) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) #s(literal 1 binary32)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 6 binary32))) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 3 binary32))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))) (.f32 cosTheta cosTheta))
(* cosTheta (- (pow alpha 2) 1))
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(* cosTheta (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(*.f32 (-.f32 (fma.f32 alpha alpha (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta)
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) cosTheta)
(/ (* (pow cosTheta 2) (log alpha)) (pow alpha 2))
(.f32 (/.f32 (.f32 cosTheta cosTheta) alpha) (/.f32 (log.f32 alpha) alpha))
(* (pow cosTheta 2) (+ (* -1 (/ (log alpha) (* (pow alpha 2) (pow cosTheta 2)))) (/ (log alpha) (pow alpha 2))))
(.f32 (/.f32 (-.f32 (log.f32 alpha) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta)) (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))
(/ (* (pow cosTheta 2) (* (PI) (log alpha))) (pow alpha 2))
(.f32 (/.f32 (.f32 (log.f32 alpha) (PI.f32)) alpha) (/.f32 (*.f32 cosTheta cosTheta) alpha))
(* (pow cosTheta 2) (+ (* -1 (/ (* (PI) (log alpha)) (* (pow alpha 2) (pow cosTheta 2)))) (/ (* (PI) (log alpha)) (pow alpha 2))))
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(fma.f32 (neg.f32 (PI.f32)) (.f32 (.f32 (log.f32 alpha) cosTheta) cosTheta) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha)) (/.f32 (PI.f32) (*.f32 alpha alpha))))
(* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))
(*.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)
(* (pow alpha 2) (+ (* -1 (/ (* (pow cosTheta 2) (PI)) (pow alpha 2))) (* (pow cosTheta 2) (PI))))
(.f32 (fma.f32 (.f32 (PI.f32) cosTheta) cosTheta (.f32 (.f32 (neg.f32 cosTheta) cosTheta) (/.f32 (PI.f32) (.f32 alpha alpha)))) (.f32 alpha alpha))
(* -2 (log (/ 1 alpha)))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* (pow alpha 2) cosTheta)
(.f32 (.f32 alpha alpha) cosTheta)
(* (pow alpha 2) (+ cosTheta (/ (* cosTheta (- (/ 1 (pow cosTheta 2)) 1)) (pow alpha 2))))
(.f32 (.f32 (fma.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)) (/.f32 cosTheta (*.f32 alpha alpha)) cosTheta) alpha) alpha)
(* (pow alpha 2) (pow cosTheta 2))
(.f32 (.f32 (*.f32 cosTheta cosTheta) alpha) alpha)
(* (pow alpha 2) (+ (/ (* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1)) (pow alpha 2)) (pow cosTheta 2)))
(.f32 (fma.f32 (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)) alpha) (/.f32 (.f32 cosTheta cosTheta) alpha) (.f32 cosTheta cosTheta)) (.f32 alpha alpha))
(/ (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2))) (pow alpha 2))
(*.f32 (/.f32 (/.f32 (log.f32 alpha) alpha) alpha) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))
(/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2))
(.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha)) (/.f32 (PI.f32) (*.f32 alpha alpha)))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))
(.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (fma.f32 (neg.f32 (PI.f32)) (.f32 (.f32 (log.f32 alpha) cosTheta) cosTheta) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha)) (/.f32 (PI.f32) (.f32 alpha alpha)))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (+ (* -2 (/ (* (PI) (log (/ -1 alpha))) (pow alpha 2))) (* 2 (/ (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))) (pow alpha 2))))))
(.f32 (fma.f32 (.f32 (.f32 (.f32 #s(literal -2 binary32) cosTheta) cosTheta) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (PI.f32) (/.f32 (fma.f32 (.f32 #s(literal 2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (.f32 alpha alpha))) (*.f32 alpha alpha))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32)))) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 (fma.f32 (.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 alpha #s(literal 4 binary32)))) #s(literal -1 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32)))) (.f32 cosTheta cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(-.f32 (fma.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)) (.f32 (pow.f32 alpha #s(literal 6 binary32)) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (fma.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)))) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (fma.f32 (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (PI.f32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(* 1/2 (/ (* (pow alpha 4) (pow cosTheta 2)) (* (PI) (log (/ -1 alpha)))))
(.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (PI.f32))) (/.f32 (*.f32 cosTheta cosTheta) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(.f32 (/.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) cosTheta) cosTheta (/.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32) #s(literal 1 binary32)) #s(literal -1/2 binary32)) (.f32 alpha alpha))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))) (pow.f32 alpha #s(literal 4 binary32)))
(* (pow alpha 4) (+ (* -1/2 (/ (+ 1 (* 2 (pow cosTheta 2))) (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (pow alpha 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(.f32 (fma.f32 #s(literal -1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32) #s(literal 1 binary32)) alpha) alpha) (/.f32 (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (PI.f32))) (/.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (pow.f32 alpha #s(literal 4 binary32)))
(* -1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(.f32 (.f32 (neg.f32 (PI.f32)) (*.f32 cosTheta cosTheta)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(+ (* -1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* -1 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2))))
(neg.f32 (fma.f32 (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (PI.f32) (.f32 alpha alpha)) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (.f32 cosTheta cosTheta) (PI.f32)))))
(* -1 (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2))))
(.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -1 (/ (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2))) (pow alpha 2)))
(/.f32 (.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (*.f32 alpha alpha))
(* -1 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2)))
(.f32 (neg.f32 (PI.f32)) (/.f32 (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)))
(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal 2 binary32)) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal 2 binary32)) (fma.f32 (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (PI.f32) (.f32 alpha alpha)) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))

rewrite228.0ms (3.2%)

Memory

-27.3MiB live, 259.8MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	546
0	114	535
1	465	516
2	3694	516
0	8418	504

Stop Event

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

Counts

26 → 702

Calls

Call 1

Inputs
(fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
(*.f32 alpha alpha)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
(fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
#s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha))))
(.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(.f32 (.f32 cosTheta cosTheta) (PI.f32))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(log.f32 (*.f32 alpha alpha))
(.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta)
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)
(/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))
(.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))

Outputs
(log.f32 (pow.f32 (.f32 alpha alpha) (.f32 (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32))))
(log.f32 (/.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) cosTheta) (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)))) (pow.f32 (pow.f32 alpha (PI.f32)) #s(literal -2 binary32))))
(log.f32 (pow.f32 (pow.f32 alpha (PI.f32)) (.f32 #s(literal 2 binary32) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))))
(.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (log.f32 (*.f32 alpha alpha)))))
(.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (log.f32 (*.f32 alpha alpha)))))
(.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))
(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (.f32 cosTheta cosTheta) (PI.f32)))
(.f32 (log.f32 (.f32 alpha alpha)) (+.f32 (PI.f32) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (*.f32 cosTheta cosTheta))))
(.f32 (PI.f32) (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))))
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(.f32 alpha (.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 (neg.f32 (log.f32 alpha)) cosTheta) cosTheta (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha))))) #s(literal -2 binary32))))
(/.f32 (.f32 (-.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) #s(literal 2 binary32))) (pow.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) #s(literal 2 binary32))) (.f32 #s(literal -2 binary32) (.f32 alpha alpha))) (.f32 (PI.f32) (-.f32 (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta))) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha))))))
(/.f32 (.f32 (fma.f32 (pow.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 6 binary32)) (pow.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) #s(literal 3 binary32))) (.f32 #s(literal -2 binary32) (.f32 alpha alpha))) (fma.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) (-.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) #s(literal 2 binary32)))))
(/.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (-.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) #s(literal 2 binary32))) (pow.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) #s(literal 2 binary32)))) (.f32 (PI.f32) (-.f32 (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta))) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha))))))
(/.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (fma.f32 (pow.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 6 binary32)) (pow.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) #s(literal 3 binary32)))) (fma.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) (-.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) #s(literal 2 binary32)))))
(/.f32 (-.f32 (pow.f32 (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))) #s(literal 2 binary32)) (pow.f32 (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))) #s(literal 2 binary32))) (-.f32 (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha))))))
(/.f32 (fma.f32 (.f32 (pow.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 6 binary32))) (.f32 #s(literal -8 binary32) (pow.f32 alpha #s(literal 6 binary32))) (.f32 (pow.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) #s(literal 3 binary32)) (.f32 #s(literal -8 binary32) (pow.f32 alpha #s(literal 6 binary32))))) (+.f32 (pow.f32 (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))) #s(literal 2 binary32)) (-.f32 (pow.f32 (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))) #s(literal 2 binary32)) (.f32 (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha))))))))
(-.f32 (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))) (.f32 (.f32 (neg.f32 (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))) (.f32 #s(literal -2 binary32) (*.f32 alpha alpha))))
(-.f32 (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))) (.f32 (neg.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha))) (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32)))))
(fma.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) (.f32 #s(literal -2 binary32) alpha)) alpha (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) (.f32 alpha alpha)) #s(literal -2 binary32) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) alpha) (.f32 #s(literal -2 binary32) alpha) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))) (PI.f32) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 #s(literal -2 binary32) alpha)) alpha (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)) #s(literal -2 binary32) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) alpha) (.f32 #s(literal -2 binary32) alpha) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))) (PI.f32) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (.f32 cosTheta cosTheta)) (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) #s(literal -2 binary32)) (.f32 alpha alpha) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) #s(literal -2 binary32)) (.f32 alpha alpha) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 (.f32 #s(literal -2 binary32) alpha) (.f32 alpha (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32)))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 (.f32 #s(literal -2 binary32) alpha) (.f32 alpha (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32))) (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 #s(literal -2 binary32) (.f32 alpha alpha))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta))) (.f32 (PI.f32) (.f32 #s(literal -2 binary32) (.f32 alpha alpha))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 #s(literal -2 binary32) (.f32 (.f32 alpha alpha) (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32)))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 #s(literal -2 binary32) (.f32 (.f32 alpha alpha) (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 alpha alpha) (.f32 #s(literal -2 binary32) (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 alpha alpha) (.f32 #s(literal -2 binary32) (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32)))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 alpha (.f32 (.f32 #s(literal -2 binary32) alpha) (.f32 (neg.f32 (log.f32 alpha)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (PI.f32)))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 alpha (.f32 (.f32 #s(literal -2 binary32) alpha) (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (PI.f32) (.f32 (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha))) (.f32 #s(literal -2 binary32) (.f32 alpha alpha))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))))
(fma.f32 (PI.f32) (.f32 (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta))) (.f32 #s(literal -2 binary32) (.f32 alpha alpha))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) (.f32 #s(literal -2 binary32) (.f32 alpha alpha))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))
(+.f32 (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (*.f32 (neg.f32 cosTheta) cosTheta)))))
(+.f32 (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (pow.f32 alpha (.f32 (neg.f32 cosTheta) cosTheta)))) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))

eval145.0ms (2.1%)

Memory: 34.9MiB live, 311.5MiB allocated; 34ms collecting garbage
Compiler: Compiled 75 074 to 5 183 computations (93.1% saved)

prune70.0ms (1%)

Memory

-9.5MiB live, 181.5MiB allocated; 17ms collecting garbage

Pruning

38 alts after pruning (36 fresh and 2 done)

	Pruned	Kept	Total
New	1 352	24	1 376
Fresh	15	12	27
Picked	4	1	5
Done	1	1	2
Total	1 372	38	1 410

Accuracy

100.0%

Counts

1 410 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
	59.7%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
	98.6%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))))
	96.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	96.1%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
	98.2%	(/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha)) (*.f32 alpha alpha)))))
	95.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 #s(approx ( (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) cosTheta))))
	96.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
	95.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (log.f32 (*.f32 alpha alpha)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
✓	96.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	98.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (.f32 (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32))))))
	98.2%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.6%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	98.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	97.9%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 (.f32 (neg.f32 (log.f32 alpha)) cosTheta) cosTheta (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha))))))))
	98.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (fma.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)) #s(literal -2 binary32) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))))
	97.9%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha))))))
	95.6%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 #s(approx (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (neg.f32 (log.f32 alpha))) (*.f32 alpha alpha)))))))
	97.7%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) #s(approx (+ ( (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)))) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha)) (/.f32 (PI.f32) (*.f32 alpha alpha)))))))
	95.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) #s(approx (+ ( (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)))) (*.f32 (neg.f32 (PI.f32)) (/.f32 (/.f32 (log.f32 alpha) alpha) alpha))))))
	96.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32)))))
	98.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (*.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha))))))
	95.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	97.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	68.0%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	66.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	98.0%	(.f32 (+.f32 #s(literal 1 binary32) alpha) (/.f32 (-.f32 alpha #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))))
	95.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	97.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
	97.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (*.f32 alpha alpha))) (PI.f32)))
	96.5%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (*.f32 alpha alpha))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
	67.2%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
	56.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (.f32 (-.f32 (fma.f32 (/.f32 alpha cosTheta) (/.f32 alpha cosTheta) (neg.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	95.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (fma.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))))))
	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))

Compiler

Compiled 5 540 to 1 553 computations (72% saved)

regimes130.0ms (1.8%)

Memory

8.1MiB live, 145.8MiB allocated; 18ms collecting garbage

Counts

81 → 1

Calls

Call 1

Inputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (*.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 #s(approx ( (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (.f32 #s(literal 1/2 binary32) (/.f32 (fma.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32) #s(literal 1 binary32)) alpha) alpha (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (*.f32 (log.f32 alpha) (PI.f32))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(.f32 (+.f32 #s(literal 1 binary32) alpha) (/.f32 (-.f32 alpha #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (log.f32 (*.f32 alpha alpha)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 (PI.f32) #s(literal 2 binary32)) (log.f32 alpha)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (*.f32 alpha alpha))) (PI.f32)))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) #s(approx (+ ( (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)))) (*.f32 (neg.f32 (PI.f32)) (/.f32 (/.f32 (log.f32 alpha) alpha) alpha))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) #s(approx (+ ( (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)))) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha)) (/.f32 (PI.f32) (*.f32 alpha alpha)))))))
(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) alpha (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) alpha)) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha)) (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (*.f32 alpha alpha))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (.f32 (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32))))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (fma.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))))
(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 #s(approx (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (neg.f32 (log.f32 alpha))) (*.f32 alpha alpha)))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (*.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (fma.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) cosTheta) (neg.f32 cosTheta) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha)) (/.f32 (PI.f32) (.f32 alpha alpha)))))))
(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 (.f32 (neg.f32 (log.f32 alpha)) cosTheta) cosTheta (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha))))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (PI.f32) (/.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha)))))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (.f32 (-.f32 (fma.f32 (/.f32 alpha cosTheta) (/.f32 alpha cosTheta) (neg.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha))) (PI.f32) (.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (fma.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)) #s(literal -2 binary32) (.f32 (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) alpha) alpha) (neg.f32 (log.f32 alpha)))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (pow.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 2 binary32)))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta))))))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (.f32 (+.f32 (-.f32 (/.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32) #s(literal 1 binary32)) alpha) alpha) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (pow.f32 alpha #s(literal 4 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (+.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (.f32 (fma.f32 (/.f32 (fma.f32 (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)))) (neg.f32 (log.f32 alpha))) #s(literal -1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (PI.f32))) (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (*.f32 alpha alpha))))
(/.f32 (/.f32 (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))) (pow.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) #s(literal 2 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (cbrt.f32 (PI.f32)) (log.f32 (pow.f32 (.f32 alpha alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (cbrt.f32 (PI.f32))) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Outputs

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (*.f32 (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32))))))

Calls

4 calls:

63.0ms	(*.f32 alpha alpha)
22.0ms	alpha
21.0ms	cosTheta
19.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Results

Accuracy	Segments	Branch
98.8%	1	`(*.f32 alpha alpha)`
98.8%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
98.8%	1	`cosTheta`
98.8%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes94.0ms (1.3%)

Memory

-22.3MiB live, 75.6MiB allocated; 14ms collecting garbage

Counts

52 → 1

Calls

Call 1

Inputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (*.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 #s(approx ( (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (* (log (* alpha alpha)) (PI))) (.f32 #s(literal 1/2 binary32) (/.f32 (fma.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32) #s(literal 1 binary32)) alpha) alpha (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (*.f32 (log.f32 alpha) (PI.f32))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(.f32 (+.f32 #s(literal 1 binary32) alpha) (/.f32 (-.f32 alpha #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (log.f32 (*.f32 alpha alpha)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 (PI.f32) #s(literal 2 binary32)) (log.f32 alpha)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (*.f32 alpha alpha))) (PI.f32)))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) #s(approx (+ ( (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)))) (*.f32 (neg.f32 (PI.f32)) (/.f32 (/.f32 (log.f32 alpha) alpha) alpha))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) #s(approx (+ ( (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha)))) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha)) (/.f32 (PI.f32) (*.f32 alpha alpha)))))))
(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) alpha (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) alpha)) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha)) (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (*.f32 alpha alpha))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) cosTheta) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))

Outputs

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))

Calls

4 calls:

14.0ms	cosTheta
13.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
13.0ms	alpha
12.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
98.7%	1	`(*.f32 alpha alpha)`
98.7%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
98.7%	1	`cosTheta`
98.7%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes32.0ms (0.5%)

Memory

23.0MiB live, 65.2MiB allocated; 6ms collecting garbage

Counts

26 → 1

Calls

Call 1

Inputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (*.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 #s(approx ( (- (+ (* alpha alpha) (/ 1 (* cosTheta cosTheta))) 1) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))

Outputs

(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (*.f32 (*.f32 (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))))

Calls

4 calls:

10.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
7.0ms	(*.f32 alpha alpha)
7.0ms	alpha
7.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.6%	1	`(*.f32 alpha alpha)`
98.6%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
98.6%	1	`cosTheta`
98.6%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes27.0ms (0.4%)

Memory

19.1MiB live, 64.0MiB allocated; 3ms collecting garbage

Counts

23 → 1

Calls

Call 1

Inputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (*.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)) (neg.f32 cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))

Outputs

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))

Calls

4 calls:

8.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
6.0ms	alpha
6.0ms	(*.f32 alpha alpha)
6.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.1%	1	`(*.f32 alpha alpha)`
98.1%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
98.1%	1	`cosTheta`
98.1%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes26.0ms (0.4%)

Memory

9.7MiB live, 51.8MiB allocated; 6ms collecting garbage

Counts

19 → 1

Calls

Call 1

Inputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (*.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))

Outputs

(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (*.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha))))))

Calls

4 calls:

9.0ms	alpha
5.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
5.0ms	(*.f32 alpha alpha)
5.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.0%	1	`(*.f32 alpha alpha)`
98.0%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
98.0%	1	`cosTheta`
98.0%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes64.0ms (0.9%)

Memory

-38.2MiB live, 28.2MiB allocated; 68ms collecting garbage

Counts

16 → 1

Calls

Call 1

Inputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (* (pow (+ (* alpha alpha) -1) 2) cosTheta) (neg cosTheta)) (+ (* alpha alpha) -1)) (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))

Outputs

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))

Calls

4 calls:

49.0ms	cosTheta
5.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
4.0ms	(*.f32 alpha alpha)
4.0ms	alpha

Results

Accuracy	Segments	Branch
96.1%	1	`(*.f32 alpha alpha)`
96.1%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
96.1%	1	`cosTheta`
96.1%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes10.0ms (0.1%)

Memory

16.8MiB live, 16.8MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

Inputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (*.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))

Outputs

(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32)))))

Calls

4 calls:

2.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
2.0ms	alpha
2.0ms	(*.f32 alpha alpha)
2.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.0%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
96.0%	1	`cosTheta`
96.0%	1	`(*.f32 alpha alpha)`
96.0%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes20.0ms (0.3%)

Memory

-29.7MiB live, 17.6MiB allocated; 2ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs

(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))

(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))

(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))

Outputs

(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))

Calls

4 calls:

15.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
2.0ms	(*.f32 alpha alpha)
1.0ms	alpha
1.0ms	cosTheta

Results

Accuracy	Segments	Branch
66.6%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
66.6%	1	`cosTheta`
66.6%	1	`(*.f32 alpha alpha)`
66.6%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes5.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs

(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))

(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))

Outputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))

Calls

4 calls:

1.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
1.0ms	alpha
1.0ms	(*.f32 alpha alpha)
1.0ms	cosTheta

Results

Accuracy	Segments	Branch
-0.0%	1	`cosTheta`
-0.0%	1	`(*.f32 alpha alpha)`
-0.0%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
-0.0%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

simplify13.0ms (0.2%)

Memory

27.7MiB live, 27.7MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Stop Event

1×	iter limit
1×	unsound

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (.f32 (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (*.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (log.f32 (pow.f32 (.f32 alpha alpha) (.f32 (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (*.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (log.f32 alpha))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* (* alpha alpha) -2) (+ (* (* (* cosTheta cosTheta) (neg (log alpha))) (PI)) (* (PI) (/ (* (neg (log alpha)) (- 1 (* cosTheta cosTheta))) (* alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))

derivations989.0ms (14.1%)

Memory

3.0MiB live, 1 003.3MiB allocated; 95ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	475	3577
1	1565	3394
2	7082	3211
0	8213	3114
0	13	65
0	23	65
1	101	65
2	818	63
0	8860	55
0	69	546
0	114	535
1	465	516
2	3694	516
0	8418	504
0	379	2884
1	1115	2771
2	4715	2580
0	8277	2467
0	626	4724
1	1989	4430
0	8309	4311
0	197	1450
1	572	1398
2	2417	1236
0	8614	1182

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

Compiler

Compiled 364 to 90 computations (75.3% saved)

preprocess56.0ms (0.8%)

Memory

-11.5MiB live, 34.2MiB allocated; 3ms collecting garbage

Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 940 to 310 computations (67% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze81.0ms (1.2%)

sample2.1s (29.7%)

explain192.0ms (2.7%)

preprocess129.0ms (1.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify130.0ms (1.8%)

localize34.0ms (0.5%)

series56.0ms (0.8%)

simplify155.0ms (2.2%)

rewrite187.0ms (2.7%)

eval70.0ms (1%)

prune39.0ms (0.6%)

simplify9.0ms (0.1%)

localize164.0ms (2.3%)

series267.0ms (3.8%)

simplify166.0ms (2.4%)

rewrite18.0ms (0.3%)

eval53.0ms (0.8%)

prune54.0ms (0.8%)

simplify9.0ms (0.1%)

localize141.0ms (2%)

series152.0ms (2.2%)

simplify176.0ms (2.5%)

rewrite17.0ms (0.2%)

eval18.0ms (0.3%)

prune31.0ms (0.4%)

simplify154.0ms (2.2%)

localize242.0ms (3.4%)

series108.0ms (1.5%)

simplify170.0ms (2.4%)

rewrite228.0ms (3.2%)

eval145.0ms (2.1%)

prune70.0ms (1%)

regimes130.0ms (1.8%)

regimes94.0ms (1.3%)

regimes32.0ms (0.5%)

regimes27.0ms (0.4%)

regimes26.0ms (0.4%)

regimes64.0ms (0.9%)

regimes10.0ms (0.1%)

regimes20.0ms (0.3%)

regimes5.0ms (0.1%)

simplify13.0ms (0.2%)

derivations989.0ms (14.1%)

preprocess56.0ms (0.8%)

end0.0ms (0%)

Profiling