Metrics for GTR1 distribution

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze57.0ms (0.8%)

Memory

-23.0MiB live, 92.1MiB allocated

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)

sample1.8s (25.6%)

Memory

-1.5MiB live, 2 050.5MiB allocated

Samples

1.1s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 869.0ms

ival-mult: 307.0ms (35.3% of total)

const: 182.0ms (20.9% of total)

ival-log: 87.0ms (10% of total)

ival-<=: 83.0ms (9.6% of total)

ival-div: 64.0ms (7.4% of total)

ival-sub: 39.0ms (4.5% of total)

ival-add: 37.0ms (4.3% of total)

ival-pi: 32.0ms (3.7% of total)

ival-and: 24.0ms (2.8% of total)

exact: 11.0ms (1.3% of total)

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

Bogosity

explain1.1s (15.9%)

Memory

-5.2MiB live, 274.9MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

359.0ms

512×

valid

Compiler

Compiled 301 to 56 computations (81.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 344.0ms

ival-mult: 328.0ms (95.4% of total)

ival-log: 5.0ms (1.5% of total)

ival-div: 4.0ms (1.2% of total)

ival-pi: 2.0ms (0.6% of total)

ival-add: 2.0ms (0.6% of total)

ival-sub: 2.0ms (0.6% of total)

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

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

exact: 0.0ms (0% of total)

preprocess212.0ms (3%)

Memory

6.8MiB live, 157.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	130
1	148	122
2	625	120
3	3614	120
4	7843	120
0	13	24
0	23	24
1	51	24
2	159	24
3	643	24
4	2738	24
5	4459	24
6	7758	24
0	8602	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
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

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

Status

Accuracy

Program

▶

98.7%

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

Compiler

Compiled 24 to 13 computations (45.8% saved)

simplify181.0ms (2.6%)

Memory

23.6MiB live, 184.3MiB allocated

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	64	(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
cost-diff	64	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	91
0	23	91
1	51	91
2	159	91
3	643	91
4	2738	91
5	4459	91
6	7758	91
0	8602	81

Stop Event

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

Calls

Call 1

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

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

localize34.0ms (0.5%)

Memory

-17.1MiB live, 58.6MiB allocated

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	0.171875	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
accuracy	0.30697250976844204	(/.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	0.37109375	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Samples

25.0ms

256×

valid

Compiler

Compiled 184 to 28 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 8.0ms (46.4% of total)

ival-log: 3.0ms (17.4% of total)

ival-div: 2.0ms (11.6% of total)

ival-sub: 2.0ms (11.6% of total)

ival-pi: 1.0ms (5.8% of total)

ival-add: 1.0ms (5.8% of total)

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

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

exact: 0.0ms (0% of total)

series57.0ms (0.8%)

Memory

-12.5MiB live, 108.5MiB allocated

Counts

7 → 43

Calls

Call 1

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

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

Calls

6 calls:

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

simplify150.0ms (2.1%)

Memory

38.9MiB live, 214.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	197	1444
1	582	1399
2	2271	1346
0	8793	1288

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

rewrite208.0ms (2.9%)

Memory

-23.5MiB live, 314.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	65
0	23	65
1	98	65
2	768	63
0	8525	55

Stop Event

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

Counts

7 → 609

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 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) alpha)) (-.f32 alpha #s(literal 1 binary32)))
(*.f32 (neg.f32 (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) (-.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 (/.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) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 (.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(*.f32 (+.f32 (neg.f32 alpha) #s(literal -1 binary32)) (-.f32 #s(literal 1 binary32) alpha))
(*.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #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 #s(literal 1 binary32) (neg.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))))
(*.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha))
(*.f32 (+.f32 #s(literal 1 binary32) alpha) (neg.f32 (-.f32 #s(literal 1 binary32) alpha)))
(*.f32 (+.f32 #s(literal 1 binary32) alpha) (-.f32 alpha #s(literal 1 binary32)))
(*.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 #s(literal -1 binary32) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)))
(.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha))))
(*.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #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)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))) (.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))) (+.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 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)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) #s(literal 3 binary32))) (fma.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (*.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))))))
(/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (*.f32 (neg.f32 alpha) alpha))))
(/.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 (neg.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)))) (fma.f32 alpha alpha (+.f32 #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 8 binary32)) #s(literal 1 binary32)) #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 (-.f32 (pow.f32 alpha #s(literal 12 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (+.f32 (pow.f32 alpha #s(literal 8 binary32)) #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 12 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 18 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (+.f32 (pow.f32 alpha #s(literal 12 binary32)) #s(literal 1 binary32)) (pow.f32 alpha #s(literal 6 binary32))) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(/.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)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))) (fma.f32 alpha alpha (+.f32 #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 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(/.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)))
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(/.f32 (neg.f32 (*.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) cosTheta)) (neg.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 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)))) (neg.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 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) (fma.f32 alpha alpha (+.f32 #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))) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))
(/.f32 cosTheta (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (*.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))) (*.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (*.f32 cosTheta (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))) (*.f32 cosTheta (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)))))
(fma.f32 (.f32 cosTheta #s(literal 1 binary32)) (.f32 alpha alpha) (.f32 (.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (.f32 cosTheta #s(literal 1 binary32)) (.f32 alpha alpha) (*.f32 cosTheta #s(literal -1 binary32)))
(fma.f32 (.f32 cosTheta alpha) alpha (.f32 (*.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (.f32 cosTheta alpha) alpha (.f32 cosTheta #s(literal -1 binary32)))
(fma.f32 (fma.f32 alpha cosTheta cosTheta) alpha (*.f32 (fma.f32 alpha cosTheta cosTheta) #s(literal -1 binary32)))
(fma.f32 (.f32 (.f32 alpha alpha) cosTheta) #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) #s(literal 1 binary32)))
(fma.f32 (.f32 cosTheta (.f32 alpha alpha)) #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (.f32 cosTheta (.f32 alpha alpha)) #s(literal 1 binary32) (*.f32 cosTheta #s(literal -1 binary32)))
(fma.f32 #s(literal -1 binary32) cosTheta (.f32 (.f32 alpha alpha) cosTheta))
(fma.f32 cosTheta #s(literal -1 binary32) (.f32 cosTheta (.f32 alpha alpha)))
(fma.f32 cosTheta (.f32 alpha alpha) (.f32 (*.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 cosTheta (.f32 alpha alpha) (.f32 cosTheta #s(literal -1 binary32)))
(fma.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) cosTheta) (*.f32 #s(literal 1 binary32) (neg.f32 cosTheta)))
(fma.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 alpha alpha)) (.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -1 binary32))))
(fma.f32 (*.f32 alpha alpha) cosTheta (neg.f32 cosTheta))
(fma.f32 alpha (fma.f32 alpha cosTheta cosTheta) (*.f32 #s(literal -1 binary32) (fma.f32 alpha cosTheta cosTheta)))
(+.f32 (.f32 (.f32 (.f32 alpha alpha) cosTheta) #s(literal 1 binary32)) (.f32 (neg.f32 cosTheta) #s(literal 1 binary32)))
(+.f32 (.f32 alpha (fma.f32 alpha cosTheta cosTheta)) (.f32 #s(literal -1 binary32) (fma.f32 alpha cosTheta cosTheta)))
(+.f32 (.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) cosTheta)) (.f32 #s(literal 1 binary32) (neg.f32 cosTheta)))
(+.f32 (.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 alpha alpha))) (.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -1 binary32))))
(+.f32 (.f32 (fma.f32 alpha cosTheta cosTheta) alpha) (.f32 (fma.f32 alpha cosTheta cosTheta) #s(literal -1 binary32)))
(+.f32 (neg.f32 cosTheta) (.f32 (.f32 alpha alpha) cosTheta))
(+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta))
(+.f32 (.f32 cosTheta #s(literal -1 binary32)) (.f32 cosTheta (*.f32 alpha alpha)))
(+.f32 (.f32 cosTheta (.f32 alpha alpha)) (.f32 (.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(+.f32 (.f32 cosTheta (.f32 alpha alpha)) (*.f32 cosTheta #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 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(.f32 (.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)))
(.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 (.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal 1 binary32) alpha)) (-.f32 alpha #s(literal 1 binary32)))
(.f32 (.f32 (*.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (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 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(.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 #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)) (neg.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 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) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))
(/.f32 (*.f32 cosTheta cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))) (.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta)))
(fma.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta (*.f32 (neg.f32 cosTheta) cosTheta))
(fma.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta (.f32 (.f32 cosTheta #s(literal -1 binary32)) cosTheta))
(fma.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(fma.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta)))
(fma.f32 cosTheta (.f32 (.f32 alpha alpha) cosTheta) (*.f32 cosTheta (neg.f32 cosTheta)))
(fma.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha)) (.f32 cosTheta (.f32 cosTheta #s(literal -1 binary32))))
(fma.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta) (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))
(+.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 alpha alpha) (*.f32 cosTheta cosTheta)))
(+.f32 (.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta)) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(+.f32 (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta) (.f32 (neg.f32 cosTheta) cosTheta))
(+.f32 (.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta) (.f32 (*.f32 cosTheta #s(literal -1 binary32)) cosTheta))
(+.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha)))
(+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 (*.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(+.f32 (.f32 cosTheta (.f32 (.f32 alpha alpha) cosTheta)) (.f32 cosTheta (neg.f32 cosTheta)))
(+.f32 (.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha))) (.f32 cosTheta (*.f32 cosTheta #s(literal -1 binary32))))

eval77.0ms (1.1%)

Memory: 19.4MiB live, 176.7MiB allocated
Compiler: Compiled 27 523 to 2 882 computations (89.5% saved)

prune33.0ms (0.5%)

Memory

0.1MiB live, 86.2MiB allocated

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	737	20	757
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	737	21	758

Accuracy

99.6%

Counts

758 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	-0.0%	(fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(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)))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
	98.6%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 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))))
	98.6%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 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))))
	98.6%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (.f32 (neg.f32 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))))
	98.5%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha)) (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	85.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))))
	73.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 alpha alpha)) (.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -1 binary32)))) cosTheta))))
	85.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (fma.f32 alpha (+.f32 #s(literal 1 binary32) alpha) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) cosTheta) cosTheta))))
✓	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	96.6%	(/.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)) #s(literal 1 binary32))))
▶	98.7%	(/.f32 (+.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.4%	(/.f32 (+.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) alpha)) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.6%	(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 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))))
	98.4%	(/.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))))
▶	10.4%	#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))))
	64.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))

Compiler

Compiled 1 268 to 759 computations (40.1% saved)

simplify10.0ms (0.1%)

Memory

-23.0MiB live, 15.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f32 #s(literal 1 binary32) alpha)
cost-diff	0	(*.f32 alpha (+.f32 #s(literal 1 binary32) alpha))
cost-diff	0	(/.f32 (+.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) alpha)) (+.f32 (neg.f32 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	64	(+.f32 (*.f32 alpha (+.f32 #s(literal 1 binary32) alpha)) (+.f32 (neg.f32 alpha) #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))) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))))
cost-diff	64	(+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))
cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff	0	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))
cost-diff	0	(/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
cost-diff	0	#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))))
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 alpha #s(literal 1 binary32))
cost-diff	0	(*.f32 (-.f32 alpha #s(literal 1 binary32)) alpha)
cost-diff	0	(/.f32 (+.f32 (.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))))
cost-diff	64	(+.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	471
0	84	467

Stop Event

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

Calls

Call 1

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

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

localize102.0ms (1.4%)

Memory

14.5MiB live, 213.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(neg.f32 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	15.075402229510116	(fma.f32 alpha alpha #s(literal -1 binary32))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	0.0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
accuracy	10.52410620211527	(fma.f32 alpha alpha #s(literal -1 binary32))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	9.318997532243607	(fma.f32 alpha alpha #s(literal -1 binary32))
accuracy	13.075948179514901	(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
accuracy	29.98788023102775	(PI.f32)
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)

Samples

70.0ms

256×

invalid

Compiler

Compiled 958 to 90 computations (90.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-mult: 17.0ms (36% of total)

ival-add: 12.0ms (25.4% of total)

ival-div: 11.0ms (23.3% of total)

ival-log: 3.0ms (6.4% of total)

ival-sub: 2.0ms (4.2% of total)

ival-pi: 1.0ms (2.1% of total)

ival-neg: 1.0ms (2.1% of total)

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

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

exact: 0.0ms (0% of total)

series66.0ms (0.9%)

Memory

-30.2MiB live, 132.1MiB allocated

Counts

25 → 88

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	cosTheta	@	-inf	((+ (* (- alpha 1) alpha) (* (- alpha 1) 1)) (/ (+ (* (- alpha 1) alpha) (* (- alpha 1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (- alpha 1) alpha) (- alpha 1) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* alpha alpha) (+ (* alpha (+ 1 alpha)) (+ (neg alpha) -1)) (/ (+ (* alpha (+ 1 alpha)) (+ (neg alpha) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha (+ 1 alpha)) (+ 1 alpha) (PI) (log (* alpha alpha)) (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (* cosTheta (+ (* alpha alpha) -1)) (neg alpha))
11.0ms	alpha	@	inf	((+ (* (- alpha 1) alpha) (* (- alpha 1) 1)) (/ (+ (* (- alpha 1) alpha) (* (- alpha 1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (- alpha 1) alpha) (- alpha 1) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* alpha alpha) (+ (* alpha (+ 1 alpha)) (+ (neg alpha) -1)) (/ (+ (* alpha (+ 1 alpha)) (+ (neg alpha) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha (+ 1 alpha)) (+ 1 alpha) (PI) (log (* alpha alpha)) (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (* cosTheta (+ (* alpha alpha) -1)) (neg alpha))
10.0ms	alpha	@	0	((+ (* (- alpha 1) alpha) (* (- alpha 1) 1)) (/ (+ (* (- alpha 1) alpha) (* (- alpha 1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (- alpha 1) alpha) (- alpha 1) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* alpha alpha) (+ (* alpha (+ 1 alpha)) (+ (neg alpha) -1)) (/ (+ (* alpha (+ 1 alpha)) (+ (neg alpha) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha (+ 1 alpha)) (+ 1 alpha) (PI) (log (* alpha alpha)) (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (* cosTheta (+ (* alpha alpha) -1)) (neg alpha))
9.0ms	alpha	@	-inf	((+ (* (- alpha 1) alpha) (* (- alpha 1) 1)) (/ (+ (* (- alpha 1) alpha) (* (- alpha 1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (- alpha 1) alpha) (- alpha 1) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* alpha alpha) (+ (* alpha (+ 1 alpha)) (+ (neg alpha) -1)) (/ (+ (* alpha (+ 1 alpha)) (+ (neg alpha) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha (+ 1 alpha)) (+ 1 alpha) (PI) (log (* alpha alpha)) (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (* cosTheta (+ (* alpha alpha) -1)) (neg alpha))
5.0ms	cosTheta	@	inf	((+ (* (- alpha 1) alpha) (* (- alpha 1) 1)) (/ (+ (* (- alpha 1) alpha) (* (- alpha 1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (- alpha 1) alpha) (- alpha 1) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* alpha alpha) (+ (* alpha (+ 1 alpha)) (+ (neg alpha) -1)) (/ (+ (* alpha (+ 1 alpha)) (+ (neg alpha) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha (+ 1 alpha)) (+ 1 alpha) (PI) (log (* alpha alpha)) (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (* cosTheta (+ (* alpha alpha) -1)) (neg alpha))

simplify133.0ms (1.9%)

Memory

-5.9MiB live, 235.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	391	3355
1	1281	3256
2	5236	2952
0	8214	2799

Stop Event

1×	iter limit
1×	node limit

Counts

88 → 87

Calls

Call 1

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

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

rewrite34.0ms (0.5%)

Memory

-14.2MiB live, 24.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	266
0	84	262

Stop Event

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

Counts

25 → 30

Calls

Call 1

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

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

eval13.0ms (0.2%)

Memory: 26.4MiB live, 26.4MiB allocated
Compiler: Compiled 7 123 to 574 computations (91.9% saved)

prune35.0ms (0.5%)

Memory

2.1MiB live, 40.7MiB allocated

Pruning

25 alts after pruning (22 fresh and 3 done)

	Pruned	Kept	Total
New	140	10	150
Fresh	3	12	15
Picked	3	2	5
Done	0	1	1
Total	146	25	171

Accuracy

99.8%

Counts

171 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	-0.0%	(fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(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)))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
	98.6%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 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))))
	98.6%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 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))))
▶	98.6%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (.f32 (neg.f32 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))))
	98.5%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha)) (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	85.8%	(/.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 (fma.f32 alpha (+.f32 #s(literal 1 binary32) alpha) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) cosTheta) cosTheta))))
✓	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	96.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))))
✓	98.7%	(/.f32 (+.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	98.4%	(/.f32 (+.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) alpha)) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.6%	(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 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))))
	98.4%	(/.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))))
	10.6%	#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)) #s(approx (log (* alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))))
▶	96.4%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	64.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))
▶	63.4%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) (log.f32 (*.f32 alpha alpha))))
▶	95.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))))
	63.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (PI.f32)))))
	96.1%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (.f32 (-.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (.f32 alpha alpha)) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32)))) (*.f32 alpha alpha))))
	64.3%	#s(approx (/ (+ (* (- alpha 1) alpha) (* (- alpha 1) 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))))

Compiler

Compiled 1 677 to 983 computations (41.4% saved)

simplify14.0ms (0.2%)

Memory

-27.5MiB live, 12.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (*.f32 alpha alpha))
cost-diff	0	#s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (*.f32 alpha alpha)))
cost-diff	0	(/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha)))
cost-diff	0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))))
cost-diff	0	(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
cost-diff	0	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
cost-diff	0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
cost-diff	64	(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
cost-diff	0	(/.f32 #s(literal -1 binary32) (PI.f32))
cost-diff	0	#s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32)))
cost-diff	0	(/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) (log.f32 (*.f32 alpha alpha)))
cost-diff	0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) (log.f32 (*.f32 alpha alpha))))
cost-diff	0	#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
cost-diff	0	(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.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 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff	0	(pow.f32 alpha #s(literal 6 binary32))
cost-diff	0	(+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))
cost-diff	0	(/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (*.f32 (neg.f32 alpha) alpha))))
cost-diff	0	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (.f32 (neg.f32 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))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	519
0	101	516

Stop Event

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

Calls

Call 1

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

Outputs
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (.f32 (neg.f32 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 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (*.f32 (neg.f32 alpha) alpha))))
(+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))
#s(literal -1 binary32)
(pow.f32 alpha #s(literal 6 binary32))
alpha
#s(literal 6 binary32)
(+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (*.f32 (neg.f32 alpha) alpha)))
#s(literal 1 binary32)
(-.f32 (pow.f32 alpha #s(literal 4 binary32)) (*.f32 (neg.f32 alpha) alpha))
(pow.f32 alpha #s(literal 4 binary32))
#s(literal 4 binary32)
(*.f32 (neg.f32 alpha) alpha)
(neg.f32 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 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 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) (log.f32 (*.f32 alpha alpha)))
#s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32)))
(/.f32 #s(literal -1 binary32) (PI.f32))
#s(literal -1 binary32)
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)
alpha
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (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)
(PI.f32)
(log.f32 (*.f32 alpha alpha))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))))
(/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha)))
#s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (*.f32 alpha alpha)))
(.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (*.f32 alpha alpha))
(-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
#s(literal 1 binary32)
(PI.f32)
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (PI.f32))
(/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(*.f32 alpha alpha)
alpha
(log.f32 (*.f32 alpha alpha))

localize154.0ms (2.2%)

Memory

24.0MiB live, 177.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	0.0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))))
accuracy	0.0	#s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.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) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	0.0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) (log.f32 (*.f32 alpha alpha))))
accuracy	0.0	#s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32)))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
accuracy	0.0	#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
accuracy	6.25171055655178	(fma.f32 alpha alpha #s(literal -1 binary32))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(neg.f32 alpha)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	29.98788023102775	(PI.f32)

Samples

70.0ms

256×

invalid

Compiler

Compiled 963 to 108 computations (88.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-mult: 15.0ms (28.7% of total)

ival-div: 14.0ms (26.8% of total)

ival-pow: 9.0ms (17.2% of total)

ival-add: 5.0ms (9.6% of total)

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

ival-pi: 2.0ms (3.8% of total)

ival-log: 2.0ms (3.8% of total)

exact: 1.0ms (1.9% of total)

ival-neg: 1.0ms (1.9% of total)

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

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

series176.0ms (2.5%)

Memory

-19.2MiB live, 65.4MiB allocated

Counts

24 → 66

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
95.0ms	alpha	@	-inf	((/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (+ -1 (pow alpha 6)) (pow alpha 6) (/ (+ (* 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))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ -1 (PI)) (+ (* alpha alpha) -1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (* (- (/ 1 (PI)) (/ (/ 1 (* alpha alpha)) (PI))) (* alpha alpha)) (PI) (log (* alpha alpha)) (neg alpha) (* alpha alpha))
43.0ms	cosTheta	@	inf	((/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (+ -1 (pow alpha 6)) (pow alpha 6) (/ (+ (* 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))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ -1 (PI)) (+ (* alpha alpha) -1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (* (- (/ 1 (PI)) (/ (/ 1 (* alpha alpha)) (PI))) (* alpha alpha)) (PI) (log (* alpha alpha)) (neg alpha) (* alpha alpha))
12.0ms	alpha	@	0	((/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (+ -1 (pow alpha 6)) (pow alpha 6) (/ (+ (* 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))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ -1 (PI)) (+ (* alpha alpha) -1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (* (- (/ 1 (PI)) (/ (/ 1 (* alpha alpha)) (PI))) (* alpha alpha)) (PI) (log (* alpha alpha)) (neg alpha) (* alpha alpha))
11.0ms	alpha	@	inf	((/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (+ -1 (pow alpha 6)) (pow alpha 6) (/ (+ (* 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))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ -1 (PI)) (+ (* alpha alpha) -1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (* (- (/ 1 (PI)) (/ (/ 1 (* alpha alpha)) (PI))) (* alpha alpha)) (PI) (log (* alpha alpha)) (neg alpha) (* alpha alpha))
9.0ms	cosTheta	@	0	((/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (+ -1 (pow alpha 6)) (pow alpha 6) (/ (+ (* 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))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ -1 (PI)) (+ (* alpha alpha) -1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (* (- (/ 1 (PI)) (/ (/ 1 (* alpha alpha)) (PI))) (* alpha alpha)) (PI) (log (* alpha alpha)) (neg alpha) (* alpha alpha))

simplify161.0ms (2.3%)

Memory

22.6MiB live, 94.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	408	3478
1	1297	3073
2	6120	2897
0	8259	2778

Stop Event

1×	iter limit
1×	node limit

Counts

66 → 66

Calls

Call 1

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

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

rewrite14.0ms (0.2%)

Memory

6.6MiB live, 6.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	369
0	101	366

Stop Event

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

Counts

24 → 26

Calls

Call 1

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

Outputs
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (.f32 (neg.f32 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 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (*.f32 (neg.f32 alpha) alpha))))
(+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))
(pow.f32 alpha #s(literal 6 binary32))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.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 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) (log.f32 (*.f32 alpha alpha)))
#s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32)))
(/.f32 #s(literal -1 binary32) (PI.f32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
#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 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))))
(/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha)))
#s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (*.f32 alpha alpha)))
(.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (*.f32 alpha alpha))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(neg.f32 alpha)
(*.f32 alpha alpha)

eval36.0ms (0.5%)

Memory: -19.5MiB live, 27.5MiB allocated
Compiler: Compiled 6 876 to 526 computations (92.4% saved)

prune54.0ms (0.8%)

Memory

-1.4MiB live, 34.4MiB allocated

Pruning

28 alts after pruning (20 fresh and 8 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	2	15	17
Picked	0	5	5
Done	0	3	3
Total	110	28	138

Accuracy

99.8%

Counts

138 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	-0.0%	(fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #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)))))
▶	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(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)))))
✓	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
	98.6%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 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))))
	98.6%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 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))))
✓	98.6%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (.f32 (neg.f32 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))))
	98.5%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha)) (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	86.1%	(/.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 (fma.f32 alpha (+.f32 #s(literal 1 binary32) alpha) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) cosTheta) cosTheta))))
✓	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	96.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))))
✓	98.7%	(/.f32 (+.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	98.4%	(/.f32 (+.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) alpha)) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.6%	(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 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))))
	98.4%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 #s(approx (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) (.f32 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))))
▶	64.3%	#s(approx (/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (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))))
✓	96.4%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	96.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) #s(approx (log ( alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))))
	64.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))
✓	63.4%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) (log.f32 (*.f32 alpha alpha))))
▶	63.4%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) #s(approx (log (* alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))))
✓	95.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))))
▶	95.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha))))
	63.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (PI.f32)))))
	96.1%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (.f32 (-.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (.f32 alpha alpha)) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32)))) (*.f32 alpha alpha))))

Compiler

Compiled 1 791 to 1 051 computations (41.3% saved)

simplify9.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 alpha alpha))
cost-diff	0	#s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 alpha alpha)))
cost-diff	0	(/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
cost-diff	0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha))))
cost-diff	0	(PI.f32)
cost-diff	0	(/.f32 #s(literal -1/2 binary32) (PI.f32))
cost-diff	0	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))
cost-diff	0	#s(approx (/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (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))))
cost-diff	0	(/.f32 #s(literal -1 binary32) (PI.f32))
cost-diff	0	#s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32)))
cost-diff	0	(/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) #s(approx (log (* alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
cost-diff	0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) #s(approx (log (* alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 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	(/.f32 alpha (.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 (/.f32 alpha (.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(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	(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 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha))))
cost-diff	0	(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 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))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	627
0	128	627

Stop Event

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

Calls

Call 1

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

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

localize235.0ms (3.3%)

Memory

14.1MiB live, 133.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	0.0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha))))
accuracy	0.0	#s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 alpha alpha)))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 cosTheta cosTheta)
accuracy	0.0	(log.f32 alpha)
accuracy	0.0	#s(approx (/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (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))))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) #s(approx (log (* alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))))
accuracy	0.0	#s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32)))
accuracy	0.0	#s(approx (log (* alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
accuracy	29.98788023102775	(PI.f32)
accuracy	5.639123546719196	(fma.f32 alpha (/.f32 alpha (.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(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)))))
accuracy	6.299607789648385	(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
accuracy	11.834573954026752	(fma.f32 alpha alpha #s(literal -1 binary32))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(neg.f32 alpha)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	29.98788023102775	(PI.f32)

Samples

195.0ms

256×

invalid

Compiler

Compiled 1 171 to 145 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 151.0ms

ival-mult: 106.0ms (70% of total)

ival-div: 18.0ms (11.9% of total)

ival-add: 7.0ms (4.6% of total)

ival-sub: 6.0ms (4% of total)

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

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

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

exact: 1.0ms (0.7% of total)

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

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

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

series151.0ms (2.1%)

Memory

0.4MiB live, 109.3MiB allocated

Counts

28 → 88

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
74.0ms	alpha	@	-inf	((/ (* (- (pow alpha 6) 1) (/ 1 (- (+ (pow alpha 4) 1) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (- (pow alpha 6) 1) (/ 1 (- (+ (pow alpha 4) 1) (* (neg alpha) alpha)))) (- (pow alpha 6) 1) (pow alpha 6) (+ (* alpha (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ -1 (PI)) (/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (PI)) (PI) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (* (- (/ 1 (PI)) (/ 1 (* (* alpha alpha) (PI)))) (* alpha alpha)) (log (* alpha alpha)) (neg alpha) (* alpha alpha) (+ (* alpha alpha) -1) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (log (* alpha alpha)) (log alpha) (* cosTheta cosTheta))
42.0ms	alpha	@	inf	((/ (* (- (pow alpha 6) 1) (/ 1 (- (+ (pow alpha 4) 1) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (- (pow alpha 6) 1) (/ 1 (- (+ (pow alpha 4) 1) (* (neg alpha) alpha)))) (- (pow alpha 6) 1) (pow alpha 6) (+ (* alpha (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ -1 (PI)) (/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (PI)) (PI) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (* (- (/ 1 (PI)) (/ 1 (* (* alpha alpha) (PI)))) (* alpha alpha)) (log (* alpha alpha)) (neg alpha) (* alpha alpha) (+ (* alpha alpha) -1) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (log (* alpha alpha)) (log alpha) (* cosTheta cosTheta))
16.0ms	alpha	@	0	((/ (* (- (pow alpha 6) 1) (/ 1 (- (+ (pow alpha 4) 1) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (- (pow alpha 6) 1) (/ 1 (- (+ (pow alpha 4) 1) (* (neg alpha) alpha)))) (- (pow alpha 6) 1) (pow alpha 6) (+ (* alpha (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ -1 (PI)) (/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (PI)) (PI) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (* (- (/ 1 (PI)) (/ 1 (* (* alpha alpha) (PI)))) (* alpha alpha)) (log (* alpha alpha)) (neg alpha) (* alpha alpha) (+ (* alpha alpha) -1) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (log (* alpha alpha)) (log alpha) (* cosTheta cosTheta))
11.0ms	cosTheta	@	0	((/ (* (- (pow alpha 6) 1) (/ 1 (- (+ (pow alpha 4) 1) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (- (pow alpha 6) 1) (/ 1 (- (+ (pow alpha 4) 1) (* (neg alpha) alpha)))) (- (pow alpha 6) 1) (pow alpha 6) (+ (* alpha (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ -1 (PI)) (/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (PI)) (PI) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (* (- (/ 1 (PI)) (/ 1 (* (* alpha alpha) (PI)))) (* alpha alpha)) (log (* alpha alpha)) (neg alpha) (* alpha alpha) (+ (* alpha alpha) -1) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (log (* alpha alpha)) (log alpha) (* cosTheta cosTheta))
2.0ms	cosTheta	@	inf	((/ (* (- (pow alpha 6) 1) (/ 1 (- (+ (pow alpha 4) 1) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (- (pow alpha 6) 1) (/ 1 (- (+ (pow alpha 4) 1) (* (neg alpha) alpha)))) (- (pow alpha 6) 1) (pow alpha 6) (+ (* alpha (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (/ -1 (PI)) (/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (PI)) (PI) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (/ (+ (* alpha alpha) -1) (PI)) (* (- (/ 1 (PI)) (/ 1 (* (* alpha alpha) (PI)))) (* alpha alpha)) (log (* alpha alpha)) (neg alpha) (* alpha alpha) (+ (* alpha alpha) -1) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (log (* alpha alpha)) (log alpha) (* cosTheta cosTheta))

simplify179.0ms (2.5%)

Memory

16.1MiB live, 173.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	463	3749
1	1448	3394
2	6555	3348
0	8272	3219

Stop Event

1×	iter limit
1×	node limit

Counts

88 → 88

Calls

Call 1

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

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

rewrite63.0ms (0.9%)

Memory

-32.1MiB live, 23.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	436
0	128	436

Stop Event

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

Counts

28 → 31

Calls

Call 1

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

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

eval29.0ms (0.4%)

Memory: -10.4MiB live, 26.9MiB allocated
Compiler: Compiled 9 499 to 694 computations (92.7% saved)

prune74.0ms (1%)

Memory

24.9MiB live, 102.6MiB allocated

Pruning

53 alts after pruning (41 fresh and 12 done)

	Pruned	Kept	Total
New	127	27	154
Fresh	1	14	15
Picked	1	4	5
Done	0	8	8
Total	129	53	182

Accuracy

99.9%

Counts

182 → 53

Alt Table

Click to see full alt table

Status	Accuracy	Program
	-0.0%	(fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(literal -1 binary32) (.f32 (.f32 (PI.f32) (+.f32 (.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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(literal -1 binary32) (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(literal -1 binary32) (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(literal -1 binary32) (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) cosTheta) cosTheta)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(literal -1 binary32) (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.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(literal -1 binary32) (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) (+.f32 (.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(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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (.f32 cosTheta cosTheta) alpha) alpha))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) cosTheta) cosTheta)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
✓	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
	98.6%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 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))))
	98.6%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 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))))
✓	98.6%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (.f32 (neg.f32 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))))
	98.5%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha)) (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	85.4%	(/.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 (fma.f32 alpha (+.f32 #s(literal 1 binary32) alpha) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) cosTheta) cosTheta))))
✓	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	96.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))))
✓	98.7%	(/.f32 (+.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	98.4%	(/.f32 (+.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) alpha)) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	98.6%	(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 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))))
	98.4%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 #s(approx (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) (.f32 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))))
	98.0%	(/.f32 #s(approx (* (- (pow alpha 6) 1) (/ 1 (- (+ (pow alpha 4) 1) (* (neg alpha) alpha)))) (.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))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	64.3%	#s(approx (/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (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))))
	63.3%	#s(approx (/ (/ (+ -1 (pow alpha 6)) (+ 1 (- (pow alpha 4) (* (neg alpha) alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (PI.f32)))))
✓	96.4%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	96.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) #s(approx (log ( alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))))
	64.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))
✓	63.4%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) (log.f32 (*.f32 alpha alpha))))
✓	63.4%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (/.f32 #s(literal -1 binary32) (PI.f32))) #s(approx (log (* alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))))
	95.7%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha) (PI.f32))) (.f32 alpha alpha))) #s(approx (log (* alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))))
✓	95.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))))
✓	95.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* alpha alpha) -1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha))))
	96.1%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha))) (.f32 (-.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (.f32 alpha alpha)) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32)))) (*.f32 alpha alpha))))

Compiler

Compiled 4 664 to 1 605 computations (65.6% saved)

regimes111.0ms (1.6%)

Memory

-0.2MiB live, 119.7MiB allocated

Counts

63 → 1

Calls

Call 1

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

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))))

Calls

4 calls:

34.0ms	(/.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))))
29.0ms	(*.f32 alpha alpha)
28.0ms	alpha
17.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.7%	1	`cosTheta`
98.7%	1	`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	`(*.f32 alpha alpha)`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes64.0ms (0.9%)

Memory

-28.8MiB live, 88.3MiB allocated

Counts

46 → 1

Calls

Call 1

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

Calls

4 calls:

18.0ms	(*.f32 alpha alpha)
16.0ms	alpha
13.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
13.0ms	cosTheta

Results

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

Compiler

Compiled 29 to 20 computations (31% saved)

regimes57.0ms (0.8%)

Memory

23.2MiB live, 98.7MiB allocated

Counts

45 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

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))))
14.0ms	cosTheta
13.0ms	alpha
12.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
98.3%	1	`cosTheta`
98.3%	1	`alpha`
98.3%	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))))`
98.3%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes55.0ms (0.8%)

Memory

-9.0MiB live, 106.4MiB allocated

Counts

42 → 1

Calls

Call 1

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

Calls

4 calls:

15.0ms	(*.f32 alpha alpha)
13.0ms	cosTheta
13.0ms	alpha
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))))

Results

Accuracy	Segments	Branch
96.6%	1	`cosTheta`
96.6%	1	`alpha`
96.6%	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))))`
96.6%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes88.0ms (1.2%)

Memory

-8.9MiB live, 77.1MiB allocated

Counts

35 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

33.0ms	(/.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))))
10.0ms	alpha
10.0ms	(*.f32 alpha alpha)
10.0ms	cosTheta

Results

Accuracy	Segments	Branch
63.4%	1	`cosTheta`
63.4%	1	`alpha`
63.4%	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))))`
63.4%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes39.0ms (0.6%)

Memory

39.6MiB live, 76.8MiB allocated

Counts

31 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

11.0ms	(/.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))))
9.0ms	alpha
9.0ms	cosTheta
9.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
63.3%	1	`alpha`
63.3%	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))))`
63.3%	1	`(*.f32 alpha alpha)`
63.3%	1	`cosTheta`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes42.0ms (0.6%)

Memory

-35.1MiB live, 83.1MiB allocated

Counts

29 → 1

Calls

Call 1

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

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

Calls

4 calls:

10.0ms	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))))
8.0ms	(*.f32 alpha alpha)
8.0ms	cosTheta

Results

Accuracy	Segments	Branch
5.4%	1	`cosTheta`
5.4%	1	`alpha`
5.4%	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))))`
5.4%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes9.0ms (0.1%)

Memory

18.0MiB live, 18.0MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
5.0%	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))))`
5.0%	1	`cosTheta`
5.0%	1	`alpha`
5.0%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes7.0ms (0.1%)

Memory

19.4MiB live, 19.4MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
4.8%	1	`alpha`
4.8%	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))))`
4.8%	1	`(*.f32 alpha alpha)`
4.8%	1	`cosTheta`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes7.0ms (0.1%)

Memory

-21.3MiB live, 17.7MiB allocated

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

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

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

Results

Accuracy	Segments	Branch
-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	`(*.f32 alpha alpha)`
-0.0%	1	`cosTheta`

Compiler

Compiled 29 to 20 computations (31% saved)

simplify34.0ms (0.5%)

Memory

-15.0MiB live, 23.7MiB allocated

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

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

soundness818.0ms (11.6%)

Memory

23.6MiB live, 813.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	408	3478
1	1297	3073
2	6120	2897
0	8259	2778
0	13	65
0	23	65
1	98	65
2	768	63
0	8525	55
0	463	3749
1	1448	3394
2	6555	3348
0	8272	3219
0	391	3355
1	1281	3256
2	5236	2952
0	8214	2799
0	197	1444
1	582	1399
2	2271	1346
0	8793	1288

Stop Event

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

Compiler

Compiled 649 to 256 computations (60.6% saved)

preprocess53.0ms (0.7%)

Memory

-4.5MiB live, 110.4MiB allocated

Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 916 to 288 computations (68.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze57.0ms (0.8%)

sample1.8s (25.6%)

explain1.1s (15.9%)

preprocess212.0ms (3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify181.0ms (2.6%)

localize34.0ms (0.5%)

series57.0ms (0.8%)

simplify150.0ms (2.1%)

rewrite208.0ms (2.9%)

eval77.0ms (1.1%)

prune33.0ms (0.5%)

simplify10.0ms (0.1%)

localize102.0ms (1.4%)

series66.0ms (0.9%)

simplify133.0ms (1.9%)

rewrite34.0ms (0.5%)

eval13.0ms (0.2%)

prune35.0ms (0.5%)

simplify14.0ms (0.2%)

localize154.0ms (2.2%)

series176.0ms (2.5%)

simplify161.0ms (2.3%)

rewrite14.0ms (0.2%)

eval36.0ms (0.5%)

prune54.0ms (0.8%)

simplify9.0ms (0.1%)

localize235.0ms (3.3%)

series151.0ms (2.1%)

simplify179.0ms (2.5%)

rewrite63.0ms (0.9%)

eval29.0ms (0.4%)

prune74.0ms (1%)

regimes111.0ms (1.6%)

regimes64.0ms (0.9%)

regimes57.0ms (0.8%)

regimes55.0ms (0.8%)

regimes88.0ms (1.2%)

regimes39.0ms (0.6%)

regimes42.0ms (0.6%)

regimes9.0ms (0.1%)

regimes7.0ms (0.1%)

regimes7.0ms (0.1%)

simplify34.0ms (0.5%)

soundness818.0ms (11.6%)

preprocess53.0ms (0.7%)

end0.0ms (0%)

Profiling