Metrics for GTR1 distribution

analyze59.0ms (0.7%)

Memory

-3.3MiB live, 123.0MiB 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)

sample1.4s (17.5%)

Memory

14.5MiB live, 2 806.4MiB allocated

Samples

1.1s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 860.0ms

ival-mult: 273.0ms (31.7% of total)

const: 168.0ms (19.5% of total)

ival-log: 125.0ms (14.5% of total)

ival-<=: 83.0ms (9.7% of total)

ival-div: 62.0ms (7.2% of total)

ival-sub: 44.0ms (5.1% of total)

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

ival-pi: 29.0ms (3.4% of total)

ival-and: 23.0ms (2.7% of total)

exact: 11.0ms (1.3% of total)

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

Bogosity

preprocess523.0ms (6.4%)

Memory

-8.0MiB live, 696.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12 798×	`lower-fma.f64`
12 798×	`lower-fma.f32`
4 578×	`lower-*.f64`
4 568×	`lower-*.f32`
2 370×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	130
1	148	122
2	629	120
3	3565	120
4	7829	120
0	13	24
0	23	24
1	51	24
2	159	24
3	643	24
4	2693	24
5	4403	24
6	7704	24
0	8552	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 (PI.f32) (*.f32 (log.f32 (*.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))))

Symmetry

(abs alpha)

(abs cosTheta)

explain286.0ms (3.5%)

Memory

-25.0MiB live, 341.6MiB 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

109.0ms

512×

valid

Compiler

Compiled 238 to 56 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-mult: 30.0ms (45.4% of total)

ival-pi: 20.0ms (30.3% of total)

ival-log: 6.0ms (9.1% of total)

ival-div: 4.0ms (6.1% of total)

ival-add: 2.0ms (3% of total)

ival-sub: 2.0ms (3% of total)

ival-true: 1.0ms (1.5% of total)

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Status

Accuracy

Program

▶

98.5%

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

Compiler

Compiled 26 to 13 computations (50% saved)

simplify451.0ms (5.6%)

Memory

33.1MiB live, 421.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	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))

Rules

12 798×	`lower-fma.f64`
12 798×	`lower-fma.f32`
4 578×	`lower-*.f64`
4 568×	`lower-*.f32`
2 370×	`lower-+.f64`

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	2693	91
5	4403	91
6	7704	91
0	8552	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 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(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 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #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 cosTheta cosTheta))
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
cosTheta

localize65.0ms (0.8%)

Memory

-32.6MiB live, 44.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
✓	accuracy	99.4%	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
✓	accuracy	98.9%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	accuracy	98.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Samples

40.0ms

256×

valid

Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-mult: 23.0ms (72.7% of total)

ival-log: 3.0ms (9.5% of total)

ival-div: 2.0ms (6.3% of total)

ival-pi: 1.0ms (3.2% of total)

ival-add: 1.0ms (3.2% of total)

ival-sub: 1.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series62.0ms (0.8%)

Memory

22.1MiB live, 57.9MiB allocated

Counts

7 → 132

Calls

Call 1

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

Outputs
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (+ 1 (* -1 (pow cosTheta 2)))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt 1>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* (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))))))))>
#<alt (- (* (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))))))))>
#<alt (- (* (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))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (/ 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))))))))>
#<alt (- (+ (* -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))))))))>
#<alt (- (+ (/ 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))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<alt (- (/ 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))))))))>
#<alt (- (+ (* -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))))))))>
#<alt (- (+ (/ 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))))))>
#<alt (/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))>
#<alt (- (+ (* -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)))))>
#<alt (- (+ (* (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)))))>
#<alt (- (+ (* (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)))))>
#<alt (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))>
#<alt (/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 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))>
#<alt (/ (- (+ (/ 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))>
#<alt (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))>
#<alt (/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 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))>
#<alt (/ (- (+ (/ 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))>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -1 cosTheta)>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>

Calls

33 calls:

Time	Variable		Point	Expression
42.0ms	alpha	@	0	(* (PI) (log (* alpha alpha)))
7.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
2.0ms	alpha	@	0	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	inf	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	-inf	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite510.0ms (6.3%)

Memory

12.3MiB live, 405.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 278×	`lower-*.f64`
6 268×	`lower-*.f32`
5 746×	`lower-fma.f64`
5 746×	`lower-fma.f32`
3 952×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	65
0	23	65
1	98	65
2	768	63
0	8446	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
(neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(+.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
(+.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
(+.f32 (/.f32 (.f32 (.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(+.f32 (neg.f32 (neg.f32 (*.f32 alpha alpha))) #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 (.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)) #s(literal 1 binary32)) (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))
(+.f32 (*.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (neg.f32 (+.f32 alpha #s(literal 1 binary32))))
(+.f32 (.f32 alpha (+.f32 alpha #s(literal -1 binary32))) (.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal -1 binary32))))
(+.f32 (.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal -1 binary32))) (.f32 alpha (+.f32 alpha #s(literal -1 binary32))))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal -1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32))))
(fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) (*.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal -1 binary32))))
(fma.f32 (*.f32 alpha alpha) #s(literal 1 binary32) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal -1 binary32)) (*.f32 alpha (+.f32 alpha #s(literal -1 binary32))))
(fma.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
(fma.f32 (.f32 (.f32 alpha alpha) (*.f32 alpha alpha)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.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)))
(fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))
(fma.f32 (exp.f32 (log.f32 alpha)) (exp.f32 (log.f32 alpha)) #s(literal -1 binary32))
(fma.f32 (/.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (/.f32 (.f32 alpha alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (/.f32 (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 alpha #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (*.f32 #s(literal 1 binary32) alpha) alpha #s(literal -1 binary32))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(-.f32 #s(literal 0 binary32) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(-.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(-.f32 (/.f32 (.f32 (.f32 alpha alpha) (*.f32 alpha alpha)) (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 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (-.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha alpha)))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (.f32 alpha alpha))) (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32))))
(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (-.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #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 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (neg.f32 (neg.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))))
(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (neg.f32 (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32))) (neg.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32))) (neg.f32 (-.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha alpha)))))
(/.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32))) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha)))
(/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32)))
(/.f32 (-.f32 (.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 1 binary32))) (.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (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)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal 1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha)))
(/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #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)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.f32 alpha #s(literal -1 binary32))))
(/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)))) (neg.f32 (neg.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)))) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)))) (neg.f32 (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (neg.f32 (*.f32 alpha alpha)))))
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(fma.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha)) (.f32 cosTheta (.f32 cosTheta #s(literal -1 binary32))))
(fma.f32 cosTheta (.f32 (.f32 alpha alpha) cosTheta) (*.f32 cosTheta (neg.f32 cosTheta)))
(fma.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(fma.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)))
(fma.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta (.f32 (.f32 cosTheta #s(literal -1 binary32)) cosTheta))
(fma.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta (*.f32 (neg.f32 cosTheta) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))
(/.f32 (*.f32 cosTheta cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (neg.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 #s(literal 1 binary32) (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)))
(.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta))
(.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(.f32 (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) #s(literal 1 binary32))
(.f32 (+.f32 alpha #s(literal 1 binary32)) (.f32 (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta))
(.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (+.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 (.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (+.f32 alpha #s(literal -1 binary32)))
(.f32 (.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(.f32 (.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (+.f32 alpha #s(literal -1 binary32))) (+.f32 alpha #s(literal 1 binary32)))

simplify400.0ms (4.9%)

Memory

5.4MiB live, 604.7MiB allocated

Algorithm

1×	egg-herbie

Rules

8 466×	`lower-fma.f64`
8 466×	`lower-fma.f32`
5 952×	`lower-*.f64`
5 952×	`lower-*.f32`
4 632×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	197	2350
1	582	2290
2	2231	2197
0	8730	2075

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

eval109.0ms (1.3%)

Memory: 18.1MiB live, 246.3MiB allocated
Compiler: Compiled 33 380 to 2 790 computations (91.6% saved)

prune142.0ms (1.7%)

Memory

-20.5MiB live, 313.8MiB allocated

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	858	25	883
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	859	25	884

Accuracy

99.7%

Counts

884 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(fma.f32 (.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 #s(literal 1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))))
▶	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.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))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
	98.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.8%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	98.2%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (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 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (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 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (neg.f32 (.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))))
▶	97.6%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.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))))
	97.9%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (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))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
▶	7.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))))
	94.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(literal 1 binary32)))
	98.2%	(/.f32 (+.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (neg.f32 (+.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))))
	98.4%	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.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))))
	69.8%	(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
	69.9%	(/.f32 #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 1 694 to 818 computations (51.7% saved)

simplify13.0ms (0.2%)

Memory

-18.8MiB live, 19.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

40×	`lower-*.f64`
32×	`lift-*.f32`
18×	`lower-+.f64`
14×	`lift-/.f32`
14×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	512
0	81	512

Stop Event

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

Calls

Call 1

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

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

localize193.0ms (2.4%)

Memory

20.1MiB live, 329.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
✓	accuracy	100.0%	(.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))
✓	accuracy	100.0%	(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)

Samples

84.0ms

256×

invalid

Compiler

Compiled 546 to 47 computations (91.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-mult: 31.0ms (49.9% of total)

ival-add: 12.0ms (19.3% of total)

ival-div: 9.0ms (14.5% of total)

ival-log: 6.0ms (9.7% of total)

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

ival-pi: 1.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series66.0ms (0.8%)

Memory

-11.5MiB live, 111.7MiB allocated

Counts

24 → 348

Calls

Call 1

Inputs
#<alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))>
#<alt (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))>
#<alt (*.f32 alpha alpha)>
#<alt (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))>
#<alt (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))>
#<alt (fma.f32 alpha alpha #s(literal -1 binary32))>
#<alt (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))>
#<alt (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))>
#<alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))))>
#<alt (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta))))>
#<alt (/.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))))>
#<alt (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (*.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)))>
#<alt (+.f32 alpha #s(literal -1 binary32))>
#<alt (*.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))>
#<alt (/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))>
#<alt (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #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))))>
#<alt (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))>
#<alt (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))>
#<alt (PI.f32)>
#<alt (log.f32 (*.f32 alpha alpha))>
#<alt (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))>
#<alt (.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))>
#<alt (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)>
#<alt (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))>

Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* (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))))))))>
#<alt (- (* (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))))))))>
#<alt (- (* (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))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (/ 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))))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
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#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* -1 cosTheta)>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>

Calls

99 calls:

Time	Variable		Point	Expression
13.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))
10.0ms	cosTheta	@	0	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (* alpha (* alpha (* cosTheta cosTheta)))))
4.0ms	cosTheta	@	inf	(/ (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
3.0ms	cosTheta	@	inf	(/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	0	(/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite17.0ms (0.2%)

Memory

-5.9MiB live, 32.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

40×	`lower-*.f64`
32×	`lift-*.f32`
18×	`lower-+.f64`
14×	`lift-/.f32`
14×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	281
0	81	281

Stop Event

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

Counts

24 → 27

Calls

Call 1

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

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

simplify341.0ms (4.2%)

Memory

35.5MiB live, 627.3MiB allocated

Algorithm

1×	egg-herbie

Rules

5 844×	`lower-*.f64`
5 844×	`lower-*.f32`
5 356×	`lower-fma.f64`
5 356×	`lower-fma.f32`
3 660×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	482	9345
1	1611	8939
2	7294	8930
0	8070	8548

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 344

Calls

Call 1

Inputs
(/ -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))))))))
(/ -1/2 (* (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))))))
(/ -1/2 (* (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) (* (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 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/ 1 (* (pow cosTheta 2) (* (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)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
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(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 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 cosTheta 2) (* (PI) (log (/ -1 alpha)))))
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(/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))
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(/ (+ 1 (pow alpha 3)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))
(/ (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))))) (pow cosTheta 2))
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(/ (+ 1 (pow alpha 3)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))
(/ (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 6))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (* (pow cosTheta 4) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))))) (pow cosTheta 2))
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
-1
(- (pow alpha 2) 1)
(- (* (pow alpha 2) (+ 1 (* -1 alpha))) 1)
(- (* (pow alpha 2) (+ 1 (* alpha (- (pow alpha 2) 1)))) 1)
(pow alpha 5)
(* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (/ 1 (pow alpha 2))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 5)))))
(pow alpha 5)
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) (+ 1 (/ 1 (pow alpha 3))))))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- 1 (/ 1 (pow alpha 2))) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
1
(+ 1 (pow alpha 3))
(+ 1 (pow alpha 3))
(+ 1 (pow alpha 3))
(pow alpha 3)
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(pow alpha 3)
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* -1 (pow cosTheta 2))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (pow cosTheta 2))

Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
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(- (* (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))))))))
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(fma.f32 (.f32 alpha alpha) (fma.f32 (.f32 alpha alpha) (fma.f32 alpha (.f32 alpha (.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 #s(literal -1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.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))))))))
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(.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha))))) (neg.f32 (pow.f32 alpha #s(literal 5 binary32))))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- 1 (/ 1 (pow alpha 2))) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
(neg.f32 (.f32 (pow.f32 alpha #s(literal 5 binary32)) (-.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (*.f32 alpha alpha))))))
1
#s(literal 1 binary32)
(+ 1 (pow alpha 3))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(+ 1 (pow alpha 3))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(+ 1 (pow alpha 3))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ -1 alpha)))
(*.f32 (neg.f32 (log.f32 (neg.f32 alpha))) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (neg.f32 (log.f32 (neg.f32 alpha))) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (neg.f32 (log.f32 (neg.f32 alpha))) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (neg.f32 (log.f32 (neg.f32 alpha))) #s(literal -2 binary32))
(* 2 (* (PI) (log alpha)))
(.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))
(* 2 (* (PI) (log alpha)))
(.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))
(* 2 (* (PI) (log alpha)))
(.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))
(* 2 (* (PI) (log alpha)))
(.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(neg.f32 (.f32 (.f32 (PI.f32) #s(literal -2 binary32)) (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(neg.f32 (.f32 (.f32 (PI.f32) #s(literal -2 binary32)) (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(neg.f32 (.f32 (.f32 (PI.f32) #s(literal -2 binary32)) (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(neg.f32 (.f32 (.f32 (PI.f32) #s(literal -2 binary32)) (log.f32 alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (neg.f32 (log.f32 (neg.f32 alpha))) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (neg.f32 (log.f32 (neg.f32 alpha))) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (neg.f32 (log.f32 (neg.f32 alpha))) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (neg.f32 (log.f32 (neg.f32 alpha))) (.f32 (PI.f32) #s(literal -2 binary32)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 (.f32 alpha alpha) (-.f32 (.f32 cosTheta cosTheta) (/.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 (.f32 alpha alpha) (-.f32 (.f32 cosTheta cosTheta) (/.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 (.f32 alpha alpha) (-.f32 (.f32 cosTheta cosTheta) (/.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha))))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 (.f32 alpha alpha) (-.f32 (.f32 cosTheta cosTheta) (/.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 (.f32 alpha alpha) (-.f32 (.f32 cosTheta cosTheta) (/.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 (.f32 alpha alpha) (-.f32 (.f32 cosTheta cosTheta) (/.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha))))
(* -1 cosTheta)
(neg.f32 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* (pow alpha 2) cosTheta)
(.f32 alpha (.f32 alpha cosTheta))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 alpha (.f32 alpha (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 alpha (.f32 alpha (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 alpha (.f32 alpha (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))))
(* (pow alpha 2) cosTheta)
(.f32 alpha (.f32 alpha cosTheta))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 alpha (.f32 alpha (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 alpha (.f32 alpha (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 alpha (.f32 alpha (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 cosTheta (.f32 alpha (*.f32 alpha cosTheta)))

eval104.0ms (1.3%)

Memory: -18.1MiB live, 136.3MiB allocated
Compiler: Compiled 22 867 to 649 computations (97.2% saved)

prune58.0ms (0.7%)

Memory

16.9MiB live, 172.6MiB allocated

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	651	24	675
Fresh	8	12	20
Picked	5	0	5
Done	0	0	0
Total	664	36	700

Accuracy

99.9%

Counts

700 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.6%	(fma.f32 (.f32 cosTheta cosTheta) (/.f32 (neg.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (+.f32 alpha (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) #s(literal -1 binary32))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (fma.f32 alpha (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
	97.8%	(fma.f32 (.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (+.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))))
	97.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.2%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 alpha (+.f32 #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))))
▶	98.3%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.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))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
	98.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	98.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	7.9%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 alpha alpha) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))))
	94.8%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	86.9%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha) #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.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))))
	98.2%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	79.9%	(/.f32 (/.f32 (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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.6%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))))
▶	96.6%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.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))))
	97.0%	(/.f32 (/.f32 (neg.f32 (.f32 (pow.f32 alpha #s(literal 5 binary32)) (-.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha alpha)))))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.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))))
	97.9%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (neg.f32 (log.f32 alpha)) (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))))
▶	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	50.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
	94.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	94.6%	(/.f32 (+.f32 alpha (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) #s(literal -1 binary32))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	98.4%	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.2%	(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)))))
	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.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))))
	98.0%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	69.8%	(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
	7.9%	(/.f32 #s(literal -1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))
	69.8%	(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	69.9%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))

Compiler

Compiled 2 210 to 1 170 computations (47.1% saved)

simplify11.0ms (0.1%)

Memory

22.5MiB live, 22.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

42×	`lower-*.f64`
34×	`lift-*.f32`
18×	`lift-/.f32`
18×	`lower-+.f64`
18×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	485
0	96	485

Stop Event

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

Calls

Call 1

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

localize198.0ms (2.4%)

Memory

-12.5MiB live, 465.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(*.f32 #s(literal -1 binary32) cosTheta)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(neg.f32 (+.f32 alpha #s(literal 1 binary32)))
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 alpha)
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
✓	accuracy	100.0%	(*.f32 cosTheta (neg.f32 cosTheta))
✓	accuracy	100.0%	(neg.f32 cosTheta)
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)

Samples

113.0ms

256×

invalid

Compiler

Compiled 517 to 55 computations (89.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-mult: 46.0ms (52.3% of total)

ival-div: 12.0ms (13.7% of total)

ival-add: 12.0ms (13.7% of total)

ival-log: 10.0ms (11.4% of total)

ival-sub: 4.0ms (4.6% of total)

ival-neg: 2.0ms (2.3% of total)

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

exact: 1.0ms (1.1% of total)

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

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

series149.0ms (1.8%)

Memory

-1.0MiB live, 195.1MiB allocated

Counts

25 → 324

Calls

Call 1

Inputs
#<alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))>
#<alt (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))>
#<alt (*.f32 alpha alpha)>
#<alt (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))))>
#<alt (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))>
#<alt (fma.f32 alpha alpha #s(literal -1 binary32))>
#<alt (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))>
#<alt (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))>
#<alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))>
#<alt (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32)))>
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#<alt (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))>
#<alt (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))>
#<alt (PI.f32)>
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Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* (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))))))))>
#<alt (- (* (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))))))))>
#<alt (- (* (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))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (/ 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))))))))>
#<alt (- (+ (* -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))))))))>
#<alt (- (+ (/ 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))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<alt (- (/ 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))))))))>
#<alt (- (+ (* -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))))))))>
#<alt (- (+ (/ 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))))))>
#<alt (/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))>
#<alt (- (+ (* -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)))))>
#<alt (- (+ (* (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)))))>
#<alt (- (+ (* (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)))))>
#<alt (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))>
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#<alt (/ (- (+ (/ 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))>
#<alt (/ (- (+ (/ 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))>
#<alt -1>
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#<alt (pow alpha 2)>
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#<alt (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))>
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#<alt (* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
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#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (PI) (log (pow alpha 2)))>
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#<alt (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
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#<alt (pow alpha 2)>
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#<alt (pow alpha 2)>
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#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2))))))) (* 1/2 (/ 1 (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2))))))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2))))))) (* 1/2 (/ 1 (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2))))))))>
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#<alt (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha))))>
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#<alt (+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* 1/2 (/ (* (pow cosTheta 2) (- (pow alpha 2) 1)) (* (PI) (log alpha)))) (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))))))))>
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#<alt (pow alpha 5)>
#<alt (* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 5)))))>
#<alt (pow alpha 5)>
#<alt (* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))>
#<alt (* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) (+ 1 (/ 1 (pow alpha 3))))))>
#<alt (* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- 1 (/ 1 (pow alpha 2))) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))>
#<alt 1>
#<alt (+ 1 (pow alpha 3))>
#<alt (+ 1 (pow alpha 3))>
#<alt (+ 1 (pow alpha 3))>
#<alt (pow alpha 3)>
#<alt (* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))>
#<alt (* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))>
#<alt (* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))>
#<alt (pow alpha 3)>
#<alt (* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))>
#<alt (* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))>
#<alt (* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>

Calls

90 calls:

Time	Variable		Point	Expression
65.0ms	alpha	@	inf	(/ (- (* alpha alpha) 1) (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)))
31.0ms	alpha	@	-inf	(* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2))
8.0ms	cosTheta	@	0	(* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2))
7.0ms	alpha	@	inf	(* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2))
5.0ms	alpha	@	-inf	(/ (- (* alpha alpha) 1) (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)))

rewrite37.0ms (0.5%)

Memory

-8.5MiB live, 31.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

42×	`lower-*.f64`
34×	`lift-*.f32`
18×	`lift-/.f32`
18×	`lower-/.f64`
18×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	257
0	96	257

Stop Event

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

Counts

25 → 28

Calls

Call 1

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

simplify491.0ms (6.1%)

Memory

-3.5MiB live, 936.3MiB allocated

Algorithm

1×	egg-herbie

Rules

9 202×	`lower-fma.f64`
9 202×	`lower-fma.f32`
5 822×	`lower-*.f64`
5 822×	`lower-*.f32`
3 932×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	477	8231
1	1593	7785
2	6576	7578
0	8722	7272

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 322

Calls

Call 1

Inputs
(/ -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))))))))
(/ -1/2 (* (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))))))
(/ -1/2 (* (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) (* (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 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/ 1 (* (pow cosTheta 2) (* (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)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (PI) (log (pow alpha 2)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
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(* -1/2 (/ (pow alpha 2) (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))
(* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))))
(* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))))
(* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))))
(* -1/2 (/ (pow alpha 2) (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))
(* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))))
(* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))))
(* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))))
(/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))
(+ (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))
(+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))
(+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))
(* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))
(/ (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (+ (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (pow cosTheta 2))
(* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))
(/ (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (+ (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (pow cosTheta 2))
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
-1
(- (pow alpha 2) 1)
(- (* (pow alpha 2) (+ 1 (* -1 alpha))) 1)
(- (* (pow alpha 2) (+ 1 (* alpha (- (pow alpha 2) 1)))) 1)
(pow alpha 5)
(* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (/ 1 (pow alpha 2))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 5)))))
(pow alpha 5)
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) (+ 1 (/ 1 (pow alpha 3))))))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- 1 (/ 1 (pow alpha 2))) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
1
(+ 1 (pow alpha 3))
(+ 1 (pow alpha 3))
(+ 1 (pow alpha 3))
(pow alpha 3)
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(pow alpha 3)
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(log alpha)
(log alpha)
(log alpha)
(log alpha)
(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)

Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (.f32 alpha alpha) (fma.f32 (.f32 alpha alpha) (/.f32 (.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 alpha (.f32 alpha (fma.f32 (.f32 alpha alpha) (fma.f32 alpha (.f32 alpha (/.f32 (.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 #s(literal -1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 alpha alpha) (.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(fma.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (PI.f32) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) (log.f32 alpha)))) (.f32 cosTheta (.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))) (-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 alpha alpha) (.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(+.f32 (-.f32 (fma.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (PI.f32) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) (log.f32 alpha)))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)) (pow.f32 alpha #s(literal 6 binary32)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 alpha alpha) (.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))))))) (/.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (PI.f32) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) (log.f32 alpha))))) (.f32 cosTheta (.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 cosTheta cosTheta))))
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(fma.f32 alpha alpha #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (* (pow alpha 2) (+ 1 (* -1 alpha))) 1)
(fma.f32 (*.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha) #s(literal -1 binary32))
(- (* (pow alpha 2) (+ 1 (* alpha (- (pow alpha 2) 1)))) 1)
(fma.f32 alpha (*.f32 alpha (fma.f32 alpha (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1 binary32))) #s(literal -1 binary32))
(pow alpha 5)
(pow.f32 alpha #s(literal 5 binary32))
(* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))
(.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (pow.f32 alpha #s(literal 5 binary32)))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (/ 1 (pow alpha 2))))
(.f32 (pow.f32 alpha #s(literal 5 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha))) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 5)))))
(.f32 (pow.f32 alpha #s(literal 5 binary32)) (+.f32 #s(literal 1 binary32) (+.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 5 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))))
(pow alpha 5)
(pow.f32 alpha #s(literal 5 binary32))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))
(.f32 (pow.f32 alpha #s(literal 5 binary32)) (neg.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)))))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) (+ 1 (/ 1 (pow alpha 3))))))
(.f32 (-.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha)))) (neg.f32 (pow.f32 alpha #s(literal 5 binary32))))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- 1 (/ 1 (pow alpha 2))) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
(.f32 (-.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (.f32 alpha (*.f32 alpha alpha)))) (neg.f32 (pow.f32 alpha #s(literal 5 binary32))))
1
#s(literal 1 binary32)
(+ 1 (pow alpha 3))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(+ 1 (pow alpha 3))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(+ 1 (pow alpha 3))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)

eval45.0ms (0.6%)

Memory: -12.8MiB live, 141.1MiB allocated
Compiler: Compiled 18 445 to 579 computations (96.9% saved)

prune109.0ms (1.3%)

Memory

19.2MiB live, 176.7MiB allocated

Pruning

42 alts after pruning (42 fresh and 0 done)

	Pruned	Kept	Total
New	529	19	548
Fresh	8	23	31
Picked	5	0	5
Done	0	0	0
Total	542	42	584

Accuracy

99.9%

Counts

584 → 42

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.6%	(fma.f32 (.f32 cosTheta cosTheta) (/.f32 (neg.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (+.f32 alpha (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) #s(literal -1 binary32))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (fma.f32 alpha (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (+.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))))
	97.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
▶	98.2%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 alpha (+.f32 #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))))
	94.8%	(/.f32 (fma.f32 (.f32 alpha alpha) #s(literal 1/2 binary32) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha)))
▶	98.3%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.2%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.5%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32))))
	98.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
▶	98.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	7.9%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 alpha alpha) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))))
	94.8%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	69.9%	(/.f32 (fma.f32 alpha #s(literal 1 binary32) (neg.f32 (+.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))))
	86.5%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha) #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.2%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	79.8%	(/.f32 (/.f32 (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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.6%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))))
	96.6%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	96.1%	(/.f32 (/.f32 (.f32 (-.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha alpha)))) (neg.f32 (pow.f32 alpha #s(literal 5 binary32)))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.9%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (neg.f32 (log.f32 alpha)) (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
	50.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
	94.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	94.6%	(/.f32 (+.f32 alpha (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) #s(literal -1 binary32))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	94.4%	(/.f32 (+.f32 alpha (fma.f32 alpha alpha (-.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	94.2%	(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)))))
	94.0%	(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))))
	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.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))))
	98.0%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	96.9%	(/.f32 (.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
	96.9%	(/.f32 (.f32 alpha (.f32 alpha (-.f32 #s(literal 1 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 #s(literal -1 binary32) cosTheta) cosTheta))))
	69.8%	(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
	7.9%	(/.f32 #s(literal -1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))
	69.8%	(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
▶	-0.0%	(/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
	69.8%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32))))
	69.9%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	69.9%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	96.8%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))))
▶	96.5%	(.f32 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 2 314 to 1 306 computations (43.6% saved)

simplify12.0ms (0.1%)

Memory

-5.9MiB live, 32.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

30×	`lower-*.f64`
22×	`lift-*.f32`
18×	`lower-+.f64`
14×	`lift-/.f32`
14×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	436
0	76	436

Stop Event

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

Calls

Call 1

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

localize160.0ms (2%)

Memory

23.8MiB live, 464.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha)))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 (PI.f32) (log.f32 alpha))
✓	accuracy	100.0%	(.f32 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))))
✓	accuracy	100.0%	(log.f32 alpha)
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
✓	accuracy	100.0%	(*.f32 cosTheta (neg.f32 cosTheta))
✓	accuracy	100.0%	(neg.f32 cosTheta)
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)

Samples

86.0ms

256×

invalid

Compiler

Compiled 454 to 45 computations (90.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-mult: 24.0ms (37% of total)

ival-add: 20.0ms (30.8% of total)

ival-div: 10.0ms (15.4% of total)

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

ival-sub: 2.0ms (3.1% of total)

ival-pi: 1.0ms (1.5% of total)

exact: 1.0ms (1.5% of total)

ival-neg: 1.0ms (1.5% of total)

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

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

series25.0ms (0.3%)

Memory

-0.2MiB live, 78.3MiB allocated

Counts

27 → 348

Calls

Call 1

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

Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* (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))))))))>
#<alt (- (* (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))))))))>
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#<alt (/ (- (+ (* -1 (/ (+ (/ (* alpha (- 1 (/ 1 alpha))) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (pow cosTheta 6))) (+ (/ (* alpha (- 1 (/ 1 alpha))) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (+ (/ (* alpha (- 1 (/ 1 alpha))) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (* (pow cosTheta 4) (- (pow alpha 2) 1)))) (+ (/ (* alpha (- 1 (/ 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))>
#<alt (/ (+ (* alpha (- 1 (/ 1 alpha))) (* alpha (- alpha 1))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
#<alt (/ (+ (* -1 (/ (+ (/ (* alpha (- 1 (/ 1 alpha))) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (pow cosTheta 2))) (+ (/ (* alpha (- 1 (/ 1 alpha))) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ (* alpha (- 1 (/ 1 alpha))) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ (* alpha (- 1 (/ 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)))))))) (+ (/ (* alpha (- 1 (/ 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))>
#<alt (/ (- (+ (* -1 (/ (+ (/ (* alpha (- 1 (/ 1 alpha))) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (pow cosTheta 6))) (+ (/ (* alpha (- 1 (/ 1 alpha))) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (+ (/ (* alpha (- 1 (/ 1 alpha))) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (* (pow cosTheta 4) (- (pow alpha 2) 1)))) (+ (/ (* alpha (- 1 (/ 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))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt -1>
#<alt (- alpha 1)>
#<alt (- alpha 1)>
#<alt (- alpha 1)>
#<alt alpha>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt alpha>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt -1>
#<alt (- alpha 1)>
#<alt (- alpha 1)>
#<alt (- alpha 1)>
#<alt alpha>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt alpha>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (* (PI) (log alpha))>
#<alt (* (PI) (log alpha))>
#<alt (* (PI) (log alpha))>
#<alt (* (PI) (log alpha))>
#<alt (* -1 (* (PI) (log (/ 1 alpha))))>
#<alt (* -1 (* (PI) (log (/ 1 alpha))))>
#<alt (* -1 (* (PI) (log (/ 1 alpha))))>
#<alt (* -1 (* (PI) (log (/ 1 alpha))))>
#<alt (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))>

Calls

93 calls:

Time	Variable		Point	Expression
2.0ms	cosTheta	@	inf	(/ (+ (* (+ alpha -1) alpha) (* alpha (+ 1 (/ -1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	cosTheta	@	inf	(/ (+ (* alpha alpha) -1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	-inf	(* 1/2 (* (+ (* cosTheta cosTheta) 1) (/ (+ (* alpha alpha) -1) (* (PI) (log alpha)))))
1.0ms	cosTheta	@	0	(/ (+ (* (+ alpha -1) alpha) (* alpha (+ 1 (/ -1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	0	(* 1/2 (* (+ (* cosTheta cosTheta) 1) (/ (+ (* alpha alpha) -1) (* (PI) (log alpha)))))

rewrite20.0ms (0.2%)

Memory

-29.7MiB live, 50.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

30×	`lower-*.f64`
22×	`lift-*.f32`
18×	`lower-+.f64`
14×	`lift-/.f32`
14×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	242
0	76	242

Stop Event

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

Counts

27 → 32

Calls

Call 1

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

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

simplify450.0ms (5.5%)

Memory

34.2MiB live, 828.9MiB allocated

Algorithm

1×	egg-herbie

Rules

8 460×	`lower-fma.f64`
8 460×	`lower-fma.f32`
5 856×	`lower-*.f64`
5 856×	`lower-*.f32`
4 022×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	445	9285
1	1526	8832
2	6443	8736
0	8488	8371

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 342

Calls

Call 1

Inputs
(/ -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))))))))
(/ -1/2 (* (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))))))
(/ -1/2 (* (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) (* (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 (* (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))
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Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
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eval54.0ms (0.7%)

Memory: -50.7MiB live, 87.1MiB allocated
Compiler: Compiled 18 335 to 539 computations (97.1% saved)

prune74.0ms (0.9%)

Memory

29.8MiB live, 143.8MiB allocated

Pruning

48 alts after pruning (45 fresh and 3 done)

	Pruned	Kept	Total
New	545	15	560
Fresh	7	30	37
Picked	2	3	5
Done	0	0	0
Total	554	48	602

Accuracy

99.9%

Counts

602 → 48

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (+.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))))
	97.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	94.5%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	94.8%	(/.f32 (fma.f32 (.f32 alpha alpha) #s(literal 1/2 binary32) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha)))
	98.3%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) alpha)) (fma.f32 (PI.f32) (log.f32 (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal -1 binary32)))))))
✓	98.3%	(/.f32 (fma.f32 alpha (+.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))))
	94.6%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	97.2%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.3%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (log.f32 alpha))) (/.f32 (PI.f32) (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (*.f32 (neg.f32 (PI.f32)) (log.f32 alpha))))))
	97.5%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32))))
	98.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
✓	98.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	50.7%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))))
	7.9%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 alpha alpha) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))))
	94.8%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	69.9%	(/.f32 (fma.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))))
	69.3%	(/.f32 (fma.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha)))
	86.5%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha) #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.2%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	79.8%	(/.f32 (/.f32 (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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.6%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))))
	96.6%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	96.1%	(/.f32 (/.f32 (.f32 (-.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha alpha)))) (neg.f32 (pow.f32 alpha #s(literal 5 binary32)))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.9%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (neg.f32 (log.f32 alpha)) (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
	94.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	94.6%	(/.f32 (+.f32 alpha (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) #s(literal -1 binary32))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	94.4%	(/.f32 (+.f32 alpha (fma.f32 alpha alpha (-.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	94.2%	(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)))))
	94.0%	(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))))
	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.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))))
	98.0%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	94.5%	(/.f32 (.f32 alpha (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha)) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	96.9%	(/.f32 (.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
	96.9%	(/.f32 (.f32 alpha (.f32 alpha (-.f32 #s(literal 1 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 #s(literal -1 binary32) cosTheta) cosTheta))))
	7.9%	(/.f32 #s(literal -1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))
	69.8%	(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (fma.f32 (.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32))))
	-0.0%	(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
	69.9%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	69.9%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	50.8%	(.f32 (.f32 cosTheta cosTheta) (.f32 #s(literal 1/2 binary32) (+.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
	94.9%	(.f32 #s(literal 1/2 binary32) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 alpha))))
✓	96.5%	(.f32 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))))
	96.1%	(.f32 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 alpha)))))
	69.3%	(.f32 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))
	95.8%	(.f32 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha))))))))

Compiler

Compiled 3 521 to 1 046 computations (70.3% saved)

regimes101.0ms (1.2%)

Memory

6.9MiB live, 120.7MiB allocated

Counts

84 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
(.f32 #s(literal 1/2 binary32) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 alpha))))
(/.f32 (fma.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
(/.f32 (fma.f32 (.f32 alpha alpha) #s(literal 1/2 binary32) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha)))
(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (fma.f32 (.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32))))
(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(.f32 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))
(/.f32 (+.f32 alpha (fma.f32 alpha alpha (-.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
(/.f32 (+.f32 alpha (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) #s(literal -1 binary32))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(literal 1 binary32)))
(/.f32 #s(literal -1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))
(.f32 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (-.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))) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 (.f32 alpha (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha)) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 #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 alpha alpha) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha)))) (.f32 (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))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) 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 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #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 (fma.f32 alpha #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (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 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.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 #s(literal 1 binary32) (neg.f32 (+.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 alpha #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (+.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 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 alpha)))))
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.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 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
(/.f32 (+.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (neg.f32 (+.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 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))))
(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)))))
(/.f32 (.f32 alpha (.f32 alpha (-.f32 #s(literal 1 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 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
(/.f32 (/.f32 (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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (fma.f32 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 (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 alpha alpha) (-.f32 #s(literal 1 binary32) alpha) #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha) #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.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 (fma.f32 alpha (.f32 alpha alpha) #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.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 (fma.f32 alpha (.f32 alpha alpha) #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 (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 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (neg.f32 (.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 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) alpha)) (fma.f32 (PI.f32) (log.f32 (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal -1 binary32)))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))))
(.f32 (.f32 cosTheta cosTheta) (.f32 #s(literal 1/2 binary32) (+.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
(.f32 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha))))))))
(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (log.f32 alpha))) (/.f32 (PI.f32) (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (*.f32 (neg.f32 (PI.f32)) (log.f32 alpha))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (neg.f32 (log.f32 alpha)) (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))))
(/.f32 (/.f32 (.f32 (-.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha alpha)))) (neg.f32 (pow.f32 alpha #s(literal 5 binary32)))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 (/.f32 (neg.f32 (.f32 (pow.f32 alpha #s(literal 5 binary32)) (-.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha alpha)))))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.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))))
(fma.f32 (.f32 cosTheta cosTheta) (/.f32 (neg.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (+.f32 alpha (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) #s(literal -1 binary32))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (fma.f32 alpha (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(fma.f32 (.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 #s(literal 1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))))
(fma.f32 (.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (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 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (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 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

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:

26.0ms	(/.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))))
26.0ms	cosTheta
25.0ms	(*.f32 alpha alpha)
21.0ms	alpha

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 37 to 20 computations (45.9% saved)

regimes45.0ms (0.6%)

Memory

13.6MiB live, 48.4MiB allocated

Counts

36 → 1

Calls

Call 1

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

Calls

4 calls:

15.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
10.0ms	(*.f32 alpha alpha)
10.0ms	alpha
9.0ms	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 37 to 20 computations (45.9% saved)

regimes54.0ms (0.7%)

Memory

-32.0MiB live, 48.2MiB allocated

Counts

32 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

23.0ms	(*.f32 alpha alpha)
9.0ms	(/.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

Results

Accuracy	Segments	Branch
98.4%	1	`cosTheta`
98.4%	1	`alpha`
98.4%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
98.4%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes39.0ms (0.5%)

Memory

6.2MiB live, 42.3MiB allocated

Counts

30 → 1

Calls

Call 1

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

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

Calls

4 calls:

13.0ms	cosTheta
8.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
8.0ms	alpha
8.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
97.5%	1	`cosTheta`
97.5%	1	`alpha`
97.5%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
97.5%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes26.0ms (0.3%)

Memory

28.4MiB live, 28.4MiB allocated

Counts

21 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
97.4%	1	`cosTheta`
97.4%	1	`alpha`
97.4%	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))))`
97.4%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes37.0ms (0.5%)

Memory

-10.4MiB live, 27.1MiB allocated

Counts

20 → 1

Calls

Call 1

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

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

Calls

4 calls:

19.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
6.0ms	(*.f32 alpha alpha)
6.0ms	cosTheta
6.0ms	alpha

Results

Accuracy	Segments	Branch
96.5%	1	`cosTheta`
96.5%	1	`alpha`
96.5%	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))))`
96.5%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes39.0ms (0.5%)

Memory

-12.0MiB live, 31.5MiB allocated

Counts

19 → 1

Calls

Call 1

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

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

Calls

4 calls:

21.0ms	(*.f32 alpha alpha)
6.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
6.0ms	alpha
5.0ms	cosTheta

Results

Accuracy	Segments	Branch
94.9%	1	`alpha`
94.9%	1	`(*.f32 alpha alpha)`
94.9%	1	`cosTheta`
94.9%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes9.0ms (0.1%)

Memory

18.7MiB live, 18.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))

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	alpha
2.0ms	cosTheta

Results

Accuracy	Segments	Branch
-0.0%	1	`cosTheta`
-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)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

simplify11.0ms (0.1%)

Memory

-20.6MiB live, 17.0MiB allocated

Algorithm

1×	egg-herbie

Rules

36×	`*-commutative_binary32`
12×	`+-commutative_binary32`
10×	`sub-neg_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	135
1	68	135
2	77	135
3	86	135
4	88	135

Stop Event

1×

saturated

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

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

soundness1.0s (12.8%)

Memory

-185.1MiB live, 737.8MiB allocated

Rules

9 202×	`lower-fma.f64`
9 202×	`lower-fma.f32`
8 460×	`lower-fma.f64`
8 460×	`lower-fma.f32`
6 278×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	445	9285
1	1526	8832
2	6443	8736
0	8488	8371
0	482	9345
1	1611	8939
2	7294	8930
0	8070	8548
0	13	65
0	23	65
1	98	65
2	768	63
0	8446	55
0	477	8231
1	1593	7785
2	6576	7578
0	8722	7272

Stop Event

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

Compiler

Compiled 653 to 317 computations (51.5% saved)

preprocess66.0ms (0.8%)

Memory

-15.5MiB live, 144.2MiB allocated

Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 950 to 448 computations (52.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze59.0ms (0.7%)

sample1.4s (17.5%)

preprocess523.0ms (6.4%)

explain286.0ms (3.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify451.0ms (5.6%)

localize65.0ms (0.8%)

series62.0ms (0.8%)

rewrite510.0ms (6.3%)

simplify400.0ms (4.9%)

eval109.0ms (1.3%)

prune142.0ms (1.7%)

simplify13.0ms (0.2%)

localize193.0ms (2.4%)

series66.0ms (0.8%)

rewrite17.0ms (0.2%)

simplify341.0ms (4.2%)

eval104.0ms (1.3%)

prune58.0ms (0.7%)

simplify11.0ms (0.1%)

localize198.0ms (2.4%)

series149.0ms (1.8%)

rewrite37.0ms (0.5%)

simplify491.0ms (6.1%)

eval45.0ms (0.6%)

prune109.0ms (1.3%)

simplify12.0ms (0.1%)

localize160.0ms (2%)

series25.0ms (0.3%)

rewrite20.0ms (0.2%)

simplify450.0ms (5.5%)

eval54.0ms (0.7%)

prune74.0ms (0.9%)

regimes101.0ms (1.2%)

regimes45.0ms (0.6%)

regimes54.0ms (0.7%)

regimes39.0ms (0.5%)

regimes26.0ms (0.3%)

regimes37.0ms (0.5%)

regimes39.0ms (0.5%)

regimes9.0ms (0.1%)

simplify11.0ms (0.1%)

soundness1.0s (12.8%)

preprocess66.0ms (0.8%)

end0.0ms (0%)

Profiling