Metrics for GTR1 distribution

start0.0ms (0%)

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

analyze75.0ms (1.2%)

Memory

-35.3MiB live, 54.3MiB allocated; 24ms 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)

sample1.6s (25.4%)

Memory

65.9MiB live, 1 733.9MiB allocated; 362ms collecting garbage

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.0s

ival-mult: 361.0ms (35.1% of total)

const: 156.0ms (15.2% of total)

ival-<=: 129.0ms (12.5% of total)

ival-log: 122.0ms (11.9% of total)

ival-pi: 71.0ms (6.9% of total)

ival-div: 58.0ms (5.6% of total)

ival-add: 49.0ms (4.8% of total)

ival-sub: 40.0ms (3.9% of total)

ival-and: 25.0ms (2.4% of total)

exact: 11.0ms (1.1% of total)

adjust: 3.0ms (0.3% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain184.0ms (2.9%)

Memory

32.8MiB live, 219.9MiB allocated; 21ms 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	1	255

Precision?

0.0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0.0

Recall?

0/0

Samples

60.0ms

512×

valid

Compiler

Compiled 210 to 43 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 19.0ms (51.8% of total)

ival-log: 5.0ms (13.6% of total)

ival-div: 4.0ms (10.9% of total)

ival-sub: 3.0ms (8.2% of total)

ival-pi: 2.0ms (5.5% of total)

ival-add: 2.0ms (5.5% 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)

preprocess208.0ms (3.3%)

Memory

-49.9MiB live, 129.9MiB allocated; 138ms 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

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.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

▶

98.5%

(/.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)

simplify113.0ms (1.8%)

Memory

20.9MiB live, 162.8MiB allocated; 39ms 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

localize40.0ms (0.6%)

Memory

-20.3MiB live, 68.7MiB allocated; 14ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.1171875	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
accuracy	0.15234375	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
accuracy	0.32259750976844204	(/.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	0.34375	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Samples

28.0ms

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 (49.7% of total)

ival-log: 3.0ms (18.6% of total)

ival-div: 2.0ms (12.4% 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)

series93.0ms (1.5%)

Memory

-8.0MiB live, 88.5MiB allocated; 29ms 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
41.0ms	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))
35.0ms	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))
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))
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))

simplify199.0ms (3.1%)

Memory

26.0MiB live, 217.3MiB allocated; 31ms 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)))

rewrite188.0ms (3%)

Memory

-6.9MiB live, 234.8MiB 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))

eval47.0ms (0.7%)

Memory: 14.1MiB live, 103.5MiB allocated; 6ms collecting garbage
Compiler: Compiled 19 163 to 2 092 computations (89.1% saved)

prune29.0ms (0.5%)

Memory

-24.9MiB live, 74.7MiB allocated; 9ms collecting garbage

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	486	21	507
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	487	21	508

Accuracy

99.9%

Counts

508 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(/.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))))
	98.4%	(/.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))))
▶	82.1%	(/.f32 (/.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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.4%	(/.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))))
	98.3%	(/.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))))
	97.9%	(/.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))))
	97.9%	(/.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 #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))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.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))))
▶	98.5%	(/.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))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (fma.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 (.f32 cosTheta cosTheta) (-.f32 (pow.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 2 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))))
	97.5%	(/.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)))))
	94.8%	(/.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)) #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))))
	98.1%	(/.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))))
▶	98.2%	(/.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))))
	97.6%	#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)))))
	94.6%	#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))))
	67.7%	#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 1 374 to 812 computations (40.9% saved)

simplify8.0ms (0.1%)

Memory

25.7MiB live, 25.7MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(pow.f32 alpha #s(literal 6 binary32))
cost-diff	0	(-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))
cost-diff	0	(/.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))))
cost-diff	0	(/.f32 (/.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 (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 #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))) (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	46	534
0	84	534

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
(/.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 (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 (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 (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 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))
(pow.f32 alpha #s(literal 6 binary32))
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 alpha alpha #s(literal 1 binary32))
(pow.f32 alpha #s(literal 4 binary32))
#s(literal 4 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 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

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
(/.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 (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 (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 (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 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))
(pow.f32 alpha #s(literal 6 binary32))
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 alpha alpha #s(literal 1 binary32))
(pow.f32 alpha #s(literal 4 binary32))
#s(literal 4 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 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

localize157.0ms (2.5%)

Memory

-17.8MiB live, 218.3MiB allocated; 25ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(log.f32 (*.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 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

122.0ms

256×

invalid

Compiler

Compiled 534 to 47 computations (91.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 102.0ms

ival-pi: 29.0ms (28.6% of total)

ival-mult: 25.0ms (24.6% of total)

ival-pow: 16.0ms (15.8% of total)

ival-div: 13.0ms (12.8% of total)

ival-add: 6.0ms (5.9% of total)

ival-sub: 5.0ms (4.9% of total)

ival-log: 5.0ms (4.9% of total)

exact: 1.0ms (1% of total)

adjust: 0.0ms (0% of total)

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

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

series172.0ms (2.7%)

Memory

17.7MiB live, 201.9MiB allocated; 25ms collecting garbage

Counts

24 → 122

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)))
(/.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 (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 (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 (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 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))
(pow.f32 alpha #s(literal 6 binary32))
(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)
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

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

Calls

6 calls:

Time	Variable		Point	Expression
59.0ms	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)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (- (pow alpha 6) 1) (pow alpha 6) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (* (PI) (log (* alpha alpha))))
50.0ms	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)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (- (pow alpha 6) 1) (pow alpha 6) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (* (PI) (log (* alpha alpha))))
22.0ms	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)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (- (pow alpha 6) 1) (pow alpha 6) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (* (PI) (log (* alpha alpha))))
21.0ms	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)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (- (pow alpha 6) 1) (pow alpha 6) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (* (PI) (log (* alpha alpha))))
9.0ms	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)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (- (pow alpha 6) 1) (pow alpha 6) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (* (PI) (log (* alpha alpha))))

simplify200.0ms (3.1%)

Memory

-8.5MiB live, 184.7MiB allocated; 31ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	594	5029
1	1876	4654
0	8627	4508

Stop Event

1×	iter limit
1×	node limit

Counts

122 → 121

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

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

rewrite17.0ms (0.3%)

Memory

26.2MiB live, 26.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	292
0	84	292

Stop Event

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

Counts

24 → 25

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)))
(/.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 (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 (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 (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 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))
(pow.f32 alpha #s(literal 6 binary32))
(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)
(.f32 (PI.f32) (log.f32 (.f32 alpha 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)))
(/.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 (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 (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 (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 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))
(pow.f32 alpha #s(literal 6 binary32))
(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)
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

eval23.0ms (0.4%)

Memory: 2.1MiB live, 45.2MiB allocated; 6ms collecting garbage
Compiler: Compiled 10 124 to 880 computations (91.3% saved)

prune43.0ms (0.7%)

Memory

-29.5MiB live, 71.6MiB allocated; 13ms collecting garbage

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	186	12	198
Fresh	5	11	16
Picked	4	1	5
Done	0	0	0
Total	195	24	219

Accuracy

99.9%

Counts

219 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(/.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)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
	97.4%	(/.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))))
	98.3%	(/.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))))
	97.9%	(/.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))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.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))))
✓	98.5%	(/.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))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (fma.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 (.f32 cosTheta cosTheta) (-.f32 (pow.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 2 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))))
▶	97.5%	(/.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)))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
▶	52.5%	(/.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))))
	94.8%	(/.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))))
	97.5%	(/.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)))))
	94.9%	(/.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)))))
	98.1%	(/.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))))
	81.7%	(/.f32 #s(approx (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (-.f32 (.f32 (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) 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))))
	97.9%	(/.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))))
	97.3%	(/.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))))
▶	98.3%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (.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))))
	97.7%	#s(approx (/ (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (.f32 alpha alpha) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	79.5%	#s(approx (/ (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (PI.f32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (log.f32 (*.f32 alpha alpha))))
	94.6%	#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))))
	67.7%	#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 1 732 to 1 052 computations (39.3% saved)

simplify8.0ms (0.1%)

Memory

17.4MiB live, 17.4MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#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)))
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)) (.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))))
cost-diff	0	#s(approx (* (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) alpha))
cost-diff	0	(.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) alpha)) alpha)
cost-diff	0	#s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) alpha)) alpha))
cost-diff	0	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (.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))))
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	(.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 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 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 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	66	646
0	104	642

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

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

localize149.0ms (2.3%)

Memory

1.3MiB live, 234.5MiB allocated; 23ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
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)) (.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)))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	0.0	#s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) alpha)) alpha))
accuracy	0.0	#s(approx (* (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) 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 alpha)
accuracy	0.0	(cbrt.f32 (PI.f32))
accuracy	29.98788023102775	(PI.f32)

Samples

92.0ms

256×

invalid

Compiler

Compiled 528 to 53 computations (90% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-mult: 37.0ms (51% of total)

ival-div: 11.0ms (15.2% of total)

ival-add: 7.0ms (9.6% of total)

ival-sub: 6.0ms (8.3% of total)

ival-log: 5.0ms (6.9% of total)

ival-cbrt: 2.0ms (2.8% of total)

ival-pow2: 2.0ms (2.8% of total)

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

exact: 1.0ms (1.4% 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)

series88.0ms (1.4%)

Memory

20.9MiB live, 161.3MiB allocated; 19ms collecting garbage

Counts

22 → 100

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	alpha	@	-inf	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)) (* (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) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (PI) (cbrt (PI)) (log alpha) (NAN) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (log (* alpha alpha)))
20.0ms	alpha	@	0	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)) (* (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) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (PI) (cbrt (PI)) (log alpha) (NAN) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (log (* alpha alpha)))
17.0ms	alpha	@	inf	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)) (* (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) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (PI) (cbrt (PI)) (log alpha) (NAN) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (log (* alpha alpha)))
10.0ms	cosTheta	@	inf	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)) (* (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) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (PI) (cbrt (PI)) (log alpha) (NAN) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (log (* alpha alpha)))
8.0ms	cosTheta	@	0	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)) (* (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) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (PI) (cbrt (PI)) (log alpha) (NAN) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (log (* alpha alpha)))

simplify174.0ms (2.7%)

Memory

-24.2MiB live, 213.8MiB allocated; 45ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	459	3706
1	1491	3521
2	7007	3268
0	8164	3205

Stop Event

1×	iter limit
1×	node limit

Counts

100 → 99

Calls

Call 1

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

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

rewrite20.0ms (0.3%)

Memory

-1.3MiB live, 44.8MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	394
0	104	390

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

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

eval20.0ms (0.3%)

Memory: -2.9MiB live, 51.4MiB allocated; 7ms collecting garbage
Compiler: Compiled 9 646 to 766 computations (92.1% saved)

prune42.0ms (0.7%)

Memory

20.0MiB live, 65.9MiB allocated; 3ms collecting garbage

Pruning

27 alts after pruning (24 fresh and 3 done)

	Pruned	Kept	Total
New	172	12	184
Fresh	6	12	18
Picked	3	2	5
Done	0	1	1
Total	181	27	208

Accuracy

100.0%

Counts

208 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(/.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)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
	97.4%	(/.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))))
▶	98.3%	(/.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))))
	97.9%	(/.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 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #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))))
✓	98.5%	(/.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))))
✓	97.5%	(/.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)))))
	98.1%	(/.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)))))
	57.6%	(/.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))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	94.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
▶	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)))))
▶	94.8%	(/.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))))
	94.9%	(/.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)))))
	98.1%	(/.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))))
▶	97.0%	(/.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)))))
▶	52.3%	(/.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 (.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))))
	97.3%	(/.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))))
	97.4%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (.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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	67.7%	(/.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)))))
	97.7%	#s(approx (/ (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (.f32 alpha alpha) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	79.5%	#s(approx (/ (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (PI.f32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (log.f32 (*.f32 alpha alpha))))
	67.7%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
	94.5%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
	94.6%	#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))))

Compiler

Compiled 1 992 to 1 216 computations (39% saved)

simplify120.0ms (1.9%)

Memory

4.1MiB live, 97.0MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)
cost-diff	0	#s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha))
cost-diff	0	(/.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 (.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))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(*.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha)
cost-diff	0	(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)
cost-diff	0	#s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha))
cost-diff	0	(/.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)))))
cost-diff	0	#s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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))))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
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 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
cost-diff	0	(/.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))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	1	(+.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	67	733
0	108	733
1	219	715
2	681	715
3	3818	715
0	8392	674

Stop Event

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

Calls

Call 1

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

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

localize206.0ms (3.2%)

Memory

-22.8MiB live, 166.7MiB allocated; 13ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.27734375	(/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)
accuracy	0.32259750976844204	(/.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 (.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))))
accuracy	0.3359375	(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)
accuracy	14.93699570318965	(.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))
accuracy	0.32259750976844204	(/.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)))))
accuracy	0.3359375	(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)
accuracy	0.34375	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
accuracy	0.34940578094771496	#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
accuracy	0.051081310925979805	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
accuracy	0.32259750976844204	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)))))
accuracy	0.3431051592182509	#s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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))))
accuracy	0.359375	(.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))
accuracy	0.09855007300974952	(log.f32 (*.f32 alpha alpha))
accuracy	0.32259750976844204	(/.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	0.34375	(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
accuracy	1.2626708227829158	#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
accuracy	0.15234375	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
accuracy	0.32259750976844204	(/.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))))
accuracy	0.34375	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
accuracy	0.45703125	(/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))

Samples

114.0ms

256×

valid

Compiler

Compiled 585 to 53 computations (90.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 93.0ms

ival-mult: 55.0ms (58.8% of total)

ival-div: 13.0ms (13.9% of total)

ival-add: 7.0ms (7.5% of total)

ival-sub: 5.0ms (5.3% of total)

ival-log: 5.0ms (5.3% of total)

ival-pow: 3.0ms (3.2% of total)

ival-cbrt: 2.0ms (2.1% of total)

ival-pow2: 2.0ms (2.1% of total)

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

exact: 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)

series130.0ms (2.1%)

Memory

8.0MiB live, 109.6MiB allocated; 5ms collecting garbage

Counts

22 → 109

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
46.0ms	alpha	@	0	((+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (- (* alpha alpha) 1) (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 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) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (log (* alpha alpha)) (PI)) (log (* alpha alpha)) (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (* (* (PI) (+ (* (log (* alpha alpha)) (- (* alpha alpha) 1)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))) (* cosTheta cosTheta)) (/ (/ 1 alpha) alpha))
39.0ms	alpha	@	-inf	((+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (- (* alpha alpha) 1) (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 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) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (log (* alpha alpha)) (PI)) (log (* alpha alpha)) (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (* (* (PI) (+ (* (log (* alpha alpha)) (- (* alpha alpha) 1)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))) (* cosTheta cosTheta)) (/ (/ 1 alpha) alpha))
19.0ms	alpha	@	inf	((+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (- (* alpha alpha) 1) (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 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) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (log (* alpha alpha)) (PI)) (log (* alpha alpha)) (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (* (* (PI) (+ (* (log (* alpha alpha)) (- (* alpha alpha) 1)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))) (* cosTheta cosTheta)) (/ (/ 1 alpha) alpha))
8.0ms	cosTheta	@	inf	((+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (- (* alpha alpha) 1) (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 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) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (log (* alpha alpha)) (PI)) (log (* alpha alpha)) (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (* (* (PI) (+ (* (log (* alpha alpha)) (- (* alpha alpha) 1)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))) (* cosTheta cosTheta)) (/ (/ 1 alpha) alpha))
8.0ms	cosTheta	@	0	((+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (- (* alpha alpha) 1) (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 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) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (log (* alpha alpha)) (PI)) (log (* alpha alpha)) (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (* (* (PI) (+ (* (log (* alpha alpha)) (- (* alpha alpha) 1)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))) (* cosTheta cosTheta)) (/ (/ 1 alpha) alpha))

simplify268.0ms (4.2%)

Memory

-2.8MiB live, 148.5MiB allocated; 52ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	574	4950
1	1934	4535
0	9486	4429

Stop Event

1×	iter limit
1×	node limit

Counts

109 → 108

Calls

Call 1

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

rewrite176.0ms (2.8%)

Memory

16.1MiB live, 152.9MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	421
0	108	399
1	390	333
2	2812	333
0	8926	302

Stop Event

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

Counts

22 → 542

Calls

Call 1

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

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

eval126.0ms (2%)

Memory: 1.9MiB live, 191.6MiB allocated; 11ms collecting garbage
Compiler: Compiled 53 772 to 4 037 computations (92.5% saved)

prune85.0ms (1.3%)

Memory

-30.0MiB live, 114.3MiB allocated; 10ms collecting garbage

Pruning

35 alts after pruning (30 fresh and 5 done)

	Pruned	Kept	Total
New	1 040	22	1 062
Fresh	11	8	19
Picked	3	2	5
Done	0	3	3
Total	1 054	35	1 089

Accuracy

100.0%

Counts

1 089 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(/.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))))
	97.6%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)))))
✓	-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))))
	94.6%	(/.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))))
	97.5%	(/.f32 (/.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 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.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))))
	94.6%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (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))))
	94.5%	(/.f32 (/.f32 (+.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) #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 (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))))
	97.3%	(/.f32 (/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal -2 binary32))) alpha) alpha)) (PI.f32)) (log.f32 (pow.f32 (.f32 alpha alpha) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
✓	98.5%	(/.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))))
✓	97.5%	(/.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)))))
	98.1%	(/.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)))))
	57.6%	(/.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))))
	94.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
	97.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (log.f32 (pow.f32 alpha (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) #s(literal 2 binary32))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))
✓	94.8%	(/.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))))
	97.3%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal 1 binary32))) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)))))
	94.5%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 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))))
	52.2%	(/.f32 #s(approx (- (* alpha alpha) 1) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal -6 binary32))) (.f32 alpha alpha)) (+.f32 (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal -4 binary32))) (pow.f32 alpha #s(literal -2 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))))
	97.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal -2 binary32))) (.f32 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)))))
	96.5%	(/.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 (.f32 (log.f32 (.f32 alpha alpha)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
✓	97.0%	(/.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)))))
	97.3%	(/.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 #s(literal 2 binary32) (log.f32 (pow.f32 alpha (PI.f32)))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	94.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	96.7%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) alpha) (/.f32 #s(literal 1 binary32) 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)))))
	97.4%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ (/ 1 alpha) alpha)) alpha) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) 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)))))
	67.7%	(/.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)))))
	67.7%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)))))
	66.0%	(/.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))))
	98.1%	(.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (/.f32 (-.f32 alpha #s(literal 1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))))
	94.4%	#s(approx (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (PI.f32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha)))))
	67.7%	#s(approx (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
	94.5%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
	94.6%	#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))))

Compiler

Compiled 4 046 to 1 236 computations (69.5% saved)

regimes99.0ms (1.6%)

Memory

6.4MiB live, 103.7MiB allocated; 8ms collecting garbage

Counts

68 → 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 (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))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 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 (/.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)) #s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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 #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)))) (/.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) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 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 (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)) #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)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) #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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal 1 binary32))) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #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)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (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))) (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)) (.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 (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 #s(approx ( (- 1 (/ (/ 1 alpha) alpha)) alpha) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) 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 #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 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (/.f32 (-.f32 alpha #s(literal 1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (.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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.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 #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 (.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 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (.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 (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (-.f32 (.f32 (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) 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 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) alpha) (/.f32 #s(literal 1 binary32) 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 #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)))))
(/.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 (.f32 (log.f32 (.f32 alpha alpha)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) #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))) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (log.f32 (pow.f32 alpha (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) #s(literal 2 binary32))))
#s(approx (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (PI.f32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha)))))
(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (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 #s(approx (- (* alpha alpha) 1) (.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal -2 binary32))) (.f32 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 (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 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 #s(literal 2 binary32) (log.f32 (pow.f32 alpha (PI.f32)))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.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)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (*.f32 cosTheta cosTheta))))
(/.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 (/.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 (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 (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) (.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 (.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 (/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal -2 binary32))) alpha) alpha)) (PI.f32)) (log.f32 (pow.f32 (.f32 alpha alpha) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
#s(approx (/ (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (PI.f32)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32)))) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (/.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 (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 (/ (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (.f32 alpha alpha) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.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)))) (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 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (fma.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 (.f32 cosTheta cosTheta) (-.f32 (pow.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 2 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #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) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.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 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.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) (pow.f32 alpha #s(literal -6 binary32))) (.f32 alpha alpha)) (+.f32 (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal -4 binary32))) (pow.f32 alpha #s(literal -2 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))))

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))))

Calls

4 calls:

34.0ms	(*.f32 alpha alpha)
29.0ms	cosTheta
16.0ms	(/.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))))
16.0ms	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)

regimes72.0ms (1.1%)

Memory

-2.2MiB live, 89.8MiB allocated; 9ms collecting garbage

Counts

48 → 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 (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))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 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 (/.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)) #s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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 #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)))) (/.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) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 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 (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)) #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)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) #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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal 1 binary32))) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #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)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (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))) (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)) (.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 (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 #s(approx ( (- 1 (/ (/ 1 alpha) alpha)) alpha) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) 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 #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 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (/.f32 (-.f32 alpha #s(literal 1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (.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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.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 #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 (.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 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (.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 (/ (- (pow alpha 6) 1) (- (+ (* alpha alpha) 1) (pow alpha 4))) (-.f32 (.f32 (.f32 (fma.f32 #s(literal -2 binary32) (.f32 alpha alpha) #s(literal 1 binary32)) 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 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) alpha) (/.f32 #s(literal 1 binary32) 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 #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)))))
(/.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 (.f32 (log.f32 (.f32 alpha alpha)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) #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))) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (log.f32 (pow.f32 alpha (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) #s(literal 2 binary32))))
#s(approx (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (PI.f32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha)))))
(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (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 #s(approx (- (* alpha alpha) 1) (.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal -2 binary32))) (.f32 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)))))

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:

24.0ms	(*.f32 alpha alpha)
23.0ms	cosTheta
12.0ms	(/.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))))
12.0ms	alpha

Results

Accuracy	Segments	Branch
98.5%	1	`(*.f32 alpha alpha)`
98.5%	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))))`
98.5%	1	`cosTheta`
98.5%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes32.0ms (0.5%)

Memory

9.4MiB live, 56.1MiB allocated; 2ms collecting garbage

Counts

24 → 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 (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))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 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 (/.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)) #s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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 #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)))) (/.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) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 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 (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)) #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)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) #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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal 1 binary32))) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #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)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))

Outputs

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

Calls

4 calls:

11.0ms	(*.f32 alpha alpha)
7.0ms	alpha
7.0ms	(/.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	cosTheta

Results

Accuracy	Segments	Branch
98.4%	1	`cosTheta`
98.4%	1	`(*.f32 alpha alpha)`
98.4%	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))))`
98.4%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes54.0ms (0.9%)

Memory

-12.3MiB live, 43.8MiB allocated; 10ms 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 (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))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 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 (/.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)) #s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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 #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)))) (/.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) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 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 (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)) #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)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) #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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal 1 binary32))) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))

Outputs

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

Calls

4 calls:

6.0ms	(*.f32 alpha alpha)
6.0ms	(/.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	cosTheta

Results

Accuracy	Segments	Branch
97.6%	1	`(*.f32 alpha alpha)`
97.6%	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))))`
97.6%	1	`cosTheta`
97.6%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes47.0ms (0.7%)

Memory

-7.0MiB live, 39.8MiB allocated; 2ms 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 (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))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 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 (/.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)) #s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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 #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)))) (/.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) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 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 (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))

Outputs

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

Calls

4 calls:

25.0ms	cosTheta
9.0ms	(*.f32 alpha alpha)
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))))
5.0ms	alpha

Results

Accuracy	Segments	Branch
97.5%	1	`cosTheta`
97.5%	1	`(*.f32 alpha alpha)`
97.5%	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))))`
97.5%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes27.0ms (0.4%)

Memory

40.4MiB live, 40.4MiB allocated; 0ms collecting garbage

Counts

15 → 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 (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))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 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 (/.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)) #s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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 #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)))) (/.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) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 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 (/ (/ (- (pow alpha 4) 1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (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)) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))

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))))
8.0ms	alpha
5.0ms	(*.f32 alpha alpha)
4.0ms	cosTheta

Results

Accuracy	Segments	Branch
94.8%	1	`cosTheta`
94.8%	1	`(*.f32 alpha alpha)`
94.8%	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))))`
94.8%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes10.0ms (0.2%)

Memory

-31.1MiB live, 15.2MiB allocated; 3ms collecting garbage

Counts

4 → 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 (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 (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))))

Calls

4 calls:

4.0ms	alpha
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	cosTheta
2.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
94.6%	1	`(*.f32 alpha alpha)`
94.6%	1	`cosTheta`
94.6%	1	`alpha`
94.6%	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))))`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes7.0ms (0.1%)

Memory

20.0MiB live, 20.0MiB allocated; 0ms 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:

2.0ms	cosTheta
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	(*.f32 alpha alpha)
1.0ms	alpha

Results

Accuracy	Segments	Branch
66.0%	1	`cosTheta`
66.0%	1	`(*.f32 alpha alpha)`
66.0%	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))))`
66.0%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes5.0ms (0.1%)

Memory

14.4MiB live, 14.4MiB 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	`(*.f32 alpha alpha)`
-0.0%	1	`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	`cosTheta`

Compiler

Compiled 29 to 20 computations (31% saved)

simplify21.0ms (0.3%)

Memory

-15.1MiB live, 22.2MiB allocated; 3ms 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)) (.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)) (.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) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (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 (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #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 (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 #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)) (.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)) (.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) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (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 (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log 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)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #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 (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 #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))))

derivations903.0ms (14.2%)

Memory

35.3MiB live, 533.0MiB allocated; 112ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	459	3706
1	1491	3521
2	7007	3268
0	8164	3205
0	594	5029
1	1876	4654
0	8627	4508
0	574	4950
1	1934	4535
0	9486	4429
0	13	65
0	23	65
1	101	65
2	818	63
0	8860	55
0	67	421
0	108	399
1	390	333
2	2812	333
0	8926	302

Stop Event

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

Compiler

Compiled 296 to 86 computations (70.9% saved)

preprocess41.0ms (0.7%)

Memory

5.9MiB live, 51.3MiB allocated; 3ms collecting garbage

Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 736 to 250 computations (66% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze75.0ms (1.2%)

sample1.6s (25.4%)

explain184.0ms (2.9%)

preprocess208.0ms (3.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify113.0ms (1.8%)

localize40.0ms (0.6%)

series93.0ms (1.5%)

simplify199.0ms (3.1%)

rewrite188.0ms (3%)

eval47.0ms (0.7%)

prune29.0ms (0.5%)

simplify8.0ms (0.1%)

localize157.0ms (2.5%)

series172.0ms (2.7%)

simplify200.0ms (3.1%)

rewrite17.0ms (0.3%)

eval23.0ms (0.4%)

prune43.0ms (0.7%)

simplify8.0ms (0.1%)

localize149.0ms (2.3%)

series88.0ms (1.4%)

simplify174.0ms (2.7%)

rewrite20.0ms (0.3%)

eval20.0ms (0.3%)

prune42.0ms (0.7%)

simplify120.0ms (1.9%)

localize206.0ms (3.2%)

series130.0ms (2.1%)

simplify268.0ms (4.2%)

rewrite176.0ms (2.8%)

eval126.0ms (2%)

prune85.0ms (1.3%)

regimes99.0ms (1.6%)

regimes72.0ms (1.1%)

regimes32.0ms (0.5%)

regimes54.0ms (0.9%)

regimes47.0ms (0.7%)

regimes27.0ms (0.4%)

regimes10.0ms (0.2%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

simplify21.0ms (0.3%)

derivations903.0ms (14.2%)

preprocess41.0ms (0.7%)

end0.0ms (0%)

Profiling