Metrics for GTR1 distribution

analyze60.0ms (0.7%)

Memory

10.5MiB live, 127.5MiB 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)

sample1.7s (18.7%)

Memory

14.7MiB live, 2 755.5MiB allocated

Samples

1.3s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-mult: 437.0ms (41.4% of total)

const: 151.0ms (14.3% of total)

ival-log: 97.0ms (9.2% of total)

ival-div: 92.0ms (8.7% of total)

ival-<=: 87.0ms (8.2% of total)

ival-sub: 68.0ms (6.4% of total)

ival-pi: 46.0ms (4.4% of total)

ival-add: 40.0ms (3.8% of total)

ival-and: 23.0ms (2.2% of total)

exact: 11.0ms (1% of total)

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

Bogosity

preprocess430.0ms (4.8%)

Memory

-39.5MiB live, 548.9MiB 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)

explain162.0ms (1.8%)

Memory

17.2MiB live, 328.5MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`+.f32`	`(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))`	cancellation	1	0

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	255

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

48.0ms

512×

valid

Compiler

Compiled 238 to 56 computations (76.5% saved)

Precisions

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

ival-mult: 15.0ms (47% of total)

ival-log: 6.0ms (18.8% of total)

ival-div: 4.0ms (12.5% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB 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)

simplify328.0ms (3.7%)

Memory

20.8MiB live, 571.3MiB 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

localize42.0ms (0.5%)

Memory

-11.5MiB live, 68.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(.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	99.1%	(/.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))))
✓	accuracy	98.8%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Samples

27.0ms

256×

valid

Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 10.0ms (52.9% of total)

ival-div: 3.0ms (15.9% of total)

ival-log: 3.0ms (15.9% of total)

ival-pi: 1.0ms (5.3% of total)

ival-add: 1.0ms (5.3% of total)

ival-sub: 1.0ms (5.3% of total)

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

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

exact: 0.0ms (0% of total)

series45.0ms (0.5%)

Memory

2.4MiB live, 78.1MiB allocated

Counts

4 → 84

Calls

Call 1

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

Outputs
#<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 (/ -1/2 (* (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 (* -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

21 calls:

Time	Variable		Point	Expression
26.0ms	alpha	@	0	(* (PI) (log (* alpha alpha)))
6.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
2.0ms	cosTheta	@	inf	(/ (- (* 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))))
2.0ms	alpha	@	0	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite356.0ms (4%)

Memory

22.1MiB live, 533.4MiB 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	46
0	23	46
1	98	46
2	768	44
0	8448	39

Stop Event

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

Counts

4 → 456

Calls

Call 1

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

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

simplify437.0ms (4.9%)

Memory

19.2MiB live, 330.4MiB allocated

Algorithm

1×	egg-herbie

Rules

8 090×	`lower-fma.f64`
8 090×	`lower-fma.f32`
5 838×	`lower-*.f64`
5 838×	`lower-*.f32`
4 618×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	185	1959
1	552	1906
2	2134	1849
0	8489	1768

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

eval93.0ms (1%)

Memory: -27.1MiB live, 68.3MiB allocated
Compiler: Compiled 20 819 to 1 766 computations (91.5% saved)

prune168.0ms (1.9%)

Memory

1.0MiB live, 122.3MiB allocated

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	527	13	540
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	528	13	541

Accuracy

99.2%

Counts

541 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.6%	(fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (.f32 (/.f32 #s(literal -1 binary32) (log.f32 (.f32 alpha alpha))) (-.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32)))) (PI.f32)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (PI.f32))))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (neg.f32 (PI.f32))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
	98.2%	(fma.f32 (.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (fma.f32 cosTheta (/.f32 cosTheta (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))))) (.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))))))) (/.f32 (.f32 alpha alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
	96.9%	(fma.f32 cosTheta (neg.f32 (/.f32 (.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
▶	97.9%	(fma.f32 alpha (.f32 alpha (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (*.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
	95.3%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.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))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	97.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	65.9%	(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))))

Compiler

Compiled 1 034 to 444 computations (57.1% saved)

simplify14.0ms (0.2%)

Memory

7.3MiB live, 7.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

58×	`lower-*.f64`
46×	`lift-*.f32`
24×	`lift-/.f32`
24×	`lower-/.f64`
20×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	795
0	120	795

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

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

localize307.0ms (3.5%)

Memory

6.2MiB live, 161.3MiB allocated

Localize:

Found 20 expressions of interest:

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

Samples

133.0ms

256×

invalid

Compiler

Compiled 871 to 69 computations (92.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 107.0ms

ival-mult: 40.0ms (37.4% of total)

ival-log: 29.0ms (27.1% of total)

ival-div: 17.0ms (15.9% of total)

ival-add: 11.0ms (10.3% of total)

ival-pow: 5.0ms (4.7% of total)

ival-sub: 2.0ms (1.9% of total)

ival-neg: 2.0ms (1.9% of total)

ival-pi: 1.0ms (0.9% of total)

exact: 1.0ms (0.9% of total)

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

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

series111.0ms (1.2%)

Memory

-20.0MiB live, 91.5MiB allocated

Counts

11 → 96

Calls

Call 1

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

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

Calls

36 calls:

Time	Variable		Point	Expression
38.0ms	alpha	@	0	(log alpha)
19.0ms	alpha	@	-inf	(log alpha)
15.0ms	alpha	@	0	(* alpha (+ (* 1/2 (/ (* cosTheta cosTheta) (* (* (PI) (log alpha)) (* (+ (* cosTheta (neg cosTheta)) 1) (+ (* cosTheta (neg cosTheta)) 1))))) (/ 1/2 (* (log alpha) (* (PI) (+ (* cosTheta (neg cosTheta)) 1))))))
6.0ms	alpha	@	inf	(log alpha)
4.0ms	alpha	@	-inf	(* alpha (+ (* 1/2 (/ (* cosTheta cosTheta) (* (* (PI) (log alpha)) (* (+ (* cosTheta (neg cosTheta)) 1) (+ (* cosTheta (neg cosTheta)) 1))))) (/ 1/2 (* (log alpha) (* (PI) (+ (* cosTheta (neg cosTheta)) 1))))))

rewrite14.0ms (0.2%)

Memory

30.5MiB live, 30.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

28×	`lower-*.f64`
22×	`lift-*.f32`
10×	`lower-+.f64`
8×	`lift-fma.f32`
8×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	87
0	57	87

Stop Event

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

Counts

11 → 11

Calls

Call 1

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

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

simplify443.0ms (5%)

Memory

-52.2MiB live, 372.4MiB allocated

Algorithm

1×	egg-herbie

Rules

8 408×	`lower-fma.f64`
8 408×	`lower-fma.f32`
5 970×	`lower-*.f64`
5 970×	`lower-*.f32`
2 874×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	1108
1	310	1068
2	1161	1016
3	5125	1016
0	8100	982

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

eval50.0ms (0.6%)

Memory: 24.5MiB live, 62.4MiB allocated
Compiler: Compiled 17 117 to 189 computations (98.9% saved)

prune40.0ms (0.4%)

Memory

-2.6MiB live, 36.8MiB allocated

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	360	4	364
Fresh	0	8	8
Picked	2	3	5
Done	0	0	0
Total	362	15	377

Accuracy

99.2%

Counts

377 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.7%	(fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (.f32 (/.f32 #s(literal -1 binary32) (log.f32 (.f32 alpha alpha))) (-.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32)))) (PI.f32)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (PI.f32))))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (neg.f32 (PI.f32))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))))
	98.2%	(fma.f32 (.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (fma.f32 cosTheta (/.f32 cosTheta (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))))) (.f32 (.f32 (.f32 cosTheta cosTheta) (neg.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))))))) (/.f32 (.f32 alpha alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
	96.9%	(fma.f32 cosTheta (neg.f32 (/.f32 (.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
▶	97.6%	(fma.f32 alpha (.f32 (/.f32 alpha (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 cosTheta cosTheta #s(literal 1/2 binary32))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
	97.4%	(fma.f32 alpha (.f32 alpha (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
✓	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
▶	95.3%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
▶	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.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))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	97.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	65.9%	(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))))

Compiler

Compiled 1 005 to 464 computations (53.8% saved)

simplify368.0ms (4.1%)

Memory

18.0MiB live, 816.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	cost-diff	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))
✓	cost-diff	4096	(fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))
✓	cost-diff	0	(*.f32 (log.f32 alpha) (PI.f32))
✓	cost-diff	0	(/.f32 alpha (*.f32 (log.f32 alpha) (PI.f32)))
✓	cost-diff	0	(.f32 (/.f32 alpha (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 cosTheta cosTheta #s(literal 1/2 binary32)))
✓	cost-diff	0	(fma.f32 alpha (.f32 (/.f32 alpha (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 cosTheta cosTheta #s(literal 1/2 binary32))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
✓	cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	cost-diff	64	(+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))
✓	cost-diff	64	(.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓	cost-diff	64	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
✓	cost-diff	0	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
✓	cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	cost-diff	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))
✓	cost-diff	3360	(fma.f32 (.f32 (log.f32 alpha) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))

Rules

13 948×	`lower-fma.f64`
13 936×	`lower-fma.f32`
5 886×	`lower-*.f64`
5 854×	`lower-*.f32`
3 822×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	438
0	89	413
1	194	395
2	605	395
3	2725	395
0	8053	384

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

localize182.0ms (2.1%)

Memory

-27.9MiB live, 371.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.4%	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
✓	accuracy	99.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	accuracy	98.8%	(*.f32 (log.f32 alpha) (PI.f32))
✓	accuracy	98.8%	(*.f32 (log.f32 alpha) (sqrt.f32 (PI.f32)))
✓	accuracy	99.2%	(/.f32 alpha (*.f32 (log.f32 alpha) (PI.f32)))
✓	accuracy	99.1%	(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))))
✓	accuracy	98.8%	(*.f32 (log.f32 alpha) (PI.f32))
✓	accuracy	98.8%	(.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))
✓	accuracy	99.9%	(.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta)))
✓	accuracy	99.9%	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓	accuracy	99.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	accuracy	98.8%	(.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.8%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	99.1%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
✓	accuracy	98.8%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	accuracy	99.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	accuracy	98.8%	(*.f32 (log.f32 alpha) (PI.f32))
✓	accuracy	98.3%	(*.f32 (log.f32 alpha) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
✓	accuracy	96.9%	(pow.f32 (PI.f32) #s(literal 2/3 binary32))

Samples

100.0ms

256×

valid

Compiler

Compiled 457 to 54 computations (88.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-mult: 31.0ms (41.8% of total)

ival-div: 11.0ms (14.8% of total)

ival-add: 9.0ms (12.1% of total)

ival-log: 6.0ms (8.1% of total)

ival-pow: 5.0ms (6.7% of total)

const: 4.0ms (5.4% of total)

ival-cbrt: 2.0ms (2.7% of total)

ival-sqrt: 2.0ms (2.7% of total)

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

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

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

exact: 1.0ms (1.3% of total)

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

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

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

series64.0ms (0.7%)

Memory

27.2MiB live, 101.8MiB allocated

Counts

18 → 276

Calls

Call 1

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

Outputs
#<alt (* (cbrt (pow (PI) 2)) (log alpha))>
#<alt (* (cbrt (pow (PI) 2)) (log alpha))>
#<alt (* (cbrt (pow (PI) 2)) (log alpha))>
#<alt (* (cbrt (pow (PI) 2)) (log alpha))>
#<alt (* -1 (* (cbrt (pow (PI) 2)) (log (/ 1 alpha))))>
#<alt (* -1 (* (cbrt (pow (PI) 2)) (log (/ 1 alpha))))>
#<alt (* -1 (* (cbrt (pow (PI) 2)) (log (/ 1 alpha))))>
#<alt (* -1 (* (cbrt (pow (PI) 2)) (log (/ 1 alpha))))>
#<alt (* (cbrt (pow (PI) 2)) (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (* (cbrt (pow (PI) 2)) (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (* (cbrt (pow (PI) 2)) (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (* (cbrt (pow (PI) 2)) (+ (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)))))>
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* 1/2 (* (pow alpha 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (+ (* -1/2 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (+ (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))>
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#<alt (* (sqrt (PI)) (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* 1/2 (* (pow alpha 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (+ (* -1/2 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (+ (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))>
#<alt (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))>
#<alt (- (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))>
#<alt (- (+ (* -1/2 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 8) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))>
#<alt (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha))))>
#<alt (+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log alpha)))) (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))))>
#<alt (+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log alpha)))))))>
#<alt (+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log alpha)))) (* 1/2 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log alpha)))))))))>
#<alt (/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha))))>
#<alt (/ (- (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1/2 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))) (* 1/2 (/ 1 (* (PI) (log alpha))))) (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (* 1/2 (/ 1 (* (pow cosTheta 6) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))>
#<alt (/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha))))>
#<alt (/ (- (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1/2 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))) (* 1/2 (/ 1 (* (PI) (log alpha))))) (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (* 1/2 (/ 1 (* (pow cosTheta 6) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))>
#<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))>

Calls

69 calls:

Time	Variable		Point	Expression
25.0ms	cosTheta	@	0	(* (* (PI) (* (log alpha) 2)) (+ 1 (* (neg cosTheta) cosTheta)))
5.0ms	alpha	@	-inf	(/ alpha (* (log alpha) (PI)))
4.0ms	cosTheta	@	inf	(* (* (PI) (* (log alpha) 2)) (+ 1 (* (neg cosTheta) cosTheta)))
3.0ms	alpha	@	inf	(/ alpha (* (log alpha) (PI)))
2.0ms	alpha	@	0	(* (log alpha) (pow (PI) 2/3))

rewrite418.0ms (4.7%)

Memory

11.5MiB live, 638.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 122×	`lower-fma.f64`
5 114×	`lower-fma.f32`
4 878×	`lower-/.f64`
4 868×	`lower-/.f32`
3 668×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	179
0	80	163
1	320	136
2	2255	136
0	8544	134

Stop Event

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

Counts

18 → 1 174

Calls

Call 1

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

Outputs
(exp.f32 (*.f32 #s(literal 2/3 binary32) (log.f32 (PI.f32))))
(exp.f32 (.f32 (.f32 (log.f32 (PI.f32)) #s(literal 1/3 binary32)) #s(literal 2 binary32)))
(exp.f32 (.f32 (log.f32 (.f32 (PI.f32) (PI.f32))) #s(literal 1/3 binary32)))
(exp.f32 (.f32 (.f32 #s(literal 2/3 binary32) (log.f32 (PI.f32))) #s(literal 1 binary32)))
(pow.f32 (PI.f32) #s(literal 2/3 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal 1 binary32))
(pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))
(pow.f32 (sqrt.f32 (PI.f32)) #s(literal 4/3 binary32))
(pow.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal 1/3 binary32))
(pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 2/9 binary32))
(pow.f32 (exp.f32 #s(literal 2/3 binary32)) (log.f32 (PI.f32)))
(cbrt.f32 (*.f32 (PI.f32) (PI.f32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal 1 binary32))
(*.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 2/9 binary32)) (pow.f32 (PI.f32) #s(literal 4/9 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 2/9 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32)) #s(literal 1/3 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 2/9 binary32)) (cbrt.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32))))
(*.f32 (pow.f32 (PI.f32) #s(literal 4/9 binary32)) (pow.f32 (PI.f32) #s(literal 2/9 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (pow.f32 (.f32 (PI.f32) (sqrt.f32 (PI.f32))) #s(literal 1/3 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (cbrt.f32 (.f32 (PI.f32) (sqrt.f32 (PI.f32)))))
(.f32 (pow.f32 (.f32 (PI.f32) (sqrt.f32 (PI.f32))) #s(literal 1/3 binary32)) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 2/9 binary32)) #s(literal 2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/9 binary32)) #s(literal 2 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32)) #s(literal 1/3 binary32)) (pow.f32 (PI.f32) #s(literal 2/9 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 5/3 binary32)) #s(literal 1/3 binary32)) (pow.f32 (PI.f32) #s(literal 1/9 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 4/9 binary32)) #s(literal 1 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 2/9 binary32)) #s(literal 1 binary32)))
(.f32 (cbrt.f32 (.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(*.f32 (cbrt.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32))) (pow.f32 (PI.f32) #s(literal 2/9 binary32)))
(*.f32 (cbrt.f32 (pow.f32 (PI.f32) #s(literal 5/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/9 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (log.f32 alpha))
(*.f32 (log.f32 alpha) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (log.f32 alpha)))
(.f32 (.f32 (log.f32 alpha) (cbrt.f32 (PI.f32))) (cbrt.f32 (PI.f32)))
(*.f32 (PI.f32) (log.f32 alpha))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (log.f32 alpha) (cbrt.f32 (PI.f32))))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (cbrt.f32 (PI.f32)) (log.f32 alpha)))
(*.f32 (log.f32 alpha) (PI.f32))
(.f32 (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (log.f32 alpha)) (cbrt.f32 (PI.f32)))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 alpha)))
(.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (log.f32 alpha)))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))))
(.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (.f32 (log.f32 alpha) #s(literal 1 binary32)) (PI.f32))
(.f32 (.f32 (cbrt.f32 (PI.f32)) (log.f32 alpha)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(neg.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (neg.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))))
(neg.f32 (/.f32 (neg.f32 (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32)))) #s(literal -1 binary32)))
(+.f32 (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (neg.f32 (/.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
(pow.f32 (/.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal -1 binary32))
(fma.f32 alpha (/.f32 alpha (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (neg.f32 (/.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
(fma.f32 (.f32 alpha alpha) (/.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (neg.f32 (/.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (neg.f32 (/.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
(fma.f32 (/.f32 alpha (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (neg.f32 (/.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(-.f32 (/.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
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(fma.f32 #s(literal -1 binary32) cosTheta (.f32 (.f32 alpha alpha) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (-.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 cosTheta (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 cosTheta (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (.f32 cosTheta (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (-.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) 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 (.f32 alpha alpha)) (.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (.f32 (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) cosTheta)))
(/.f32 (.f32 cosTheta (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (-.f32 #s(literal 1 binary32) (.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))))
(/.f32 (.f32 cosTheta (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 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 cosTheta (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (.f32 (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) cosTheta) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (-.f32 #s(literal 1 binary32) (.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))))
(/.f32 (.f32 (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) cosTheta) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) cosTheta) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (neg.f32 (.f32 cosTheta (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)))) (neg.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (-.f32 #s(literal 1 binary32) (.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))))
(/.f32 (neg.f32 (.f32 cosTheta (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 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 (.f32 cosTheta (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)))) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) cosTheta)) (neg.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (-.f32 #s(literal 1 binary32) (.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) 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 alpha (.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) cosTheta)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (fma.f32 (neg.f32 cosTheta) (.f32 cosTheta cosTheta) (pow.f32 (.f32 cosTheta (.f32 alpha alpha)) #s(literal 3 binary32))) (fma.f32 cosTheta cosTheta (-.f32 (.f32 (.f32 cosTheta (.f32 alpha alpha)) (.f32 cosTheta (.f32 alpha alpha))) (.f32 (neg.f32 cosTheta) (.f32 cosTheta (*.f32 alpha alpha))))))
(/.f32 (fma.f32 (neg.f32 cosTheta) (.f32 cosTheta cosTheta) (pow.f32 (.f32 (.f32 alpha alpha) cosTheta) #s(literal 3 binary32))) (fma.f32 cosTheta cosTheta (-.f32 (.f32 (.f32 (.f32 alpha alpha) cosTheta) (.f32 (.f32 alpha alpha) cosTheta)) (.f32 (neg.f32 cosTheta) (.f32 (*.f32 alpha alpha) cosTheta)))))
(/.f32 (+.f32 (pow.f32 (.f32 cosTheta (.f32 alpha alpha)) #s(literal 3 binary32)) (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)))) (fma.f32 (.f32 cosTheta (.f32 alpha alpha)) (.f32 cosTheta (.f32 alpha alpha)) (-.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 cosTheta (.f32 alpha alpha)) (neg.f32 cosTheta)))))
(/.f32 (+.f32 (pow.f32 (.f32 (.f32 alpha alpha) cosTheta) #s(literal 3 binary32)) (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)))) (fma.f32 (.f32 (.f32 alpha alpha) cosTheta) (.f32 (.f32 alpha alpha) cosTheta) (-.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)))))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (+.f32 alpha #s(literal 1 binary32)) (.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta))
(.f32 (.f32 cosTheta (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))

simplify405.0ms (4.6%)

Memory

-3.3MiB live, 752.9MiB allocated

Algorithm

1×	egg-herbie

Rules

7 340×	`lower-fma.f64`
7 340×	`lower-fma.f32`
6 668×	`lower-*.f64`
6 668×	`lower-*.f32`
3 498×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	322	5753
1	1035	5473
2	4113	5440
0	8267	5212

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

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

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

eval215.0ms (2.4%)

Memory: 13.3MiB live, 597.8MiB allocated
Compiler: Compiled 73 006 to 5 534 computations (92.4% saved)

prune769.0ms (8.7%)

Memory

-186.5MiB live, 899.7MiB allocated

Pruning

33 alts after pruning (31 fresh and 2 done)

	Pruned	Kept	Total
New	2 140	30	2 170
Fresh	6	1	7
Picked	4	1	5
Done	2	1	3
Total	2 152	33	2 185

Accuracy

99.9%

Counts

2 185 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(fma.f32 (.f32 alpha alpha) (fma.f32 (.f32 (-.f32 (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (log.f32 alpha) (fma.f32 (.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32))) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))) (/.f32 (.f32 cosTheta cosTheta) (neg.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))) (.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (fma.f32 #s(literal 1/2 binary32) (/.f32 (neg.f32 (.f32 cosTheta cosTheta)) (.f32 (.f32 (log.f32 alpha) (fma.f32 (.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32))) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))) (/.f32 #s(literal 1/2 binary32) (.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
▶	98.3%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.5%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
	94.9%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (E.f32))) (log.f32 (*.f32 alpha alpha))))
	95.3%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))))
✓	95.3%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	95.3%	(/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 alpha alpha) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha)))
	97.2%	(/.f32 (/.f32 (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 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) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	98.1%	(/.f32 (/.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.3%	(/.f32 (/.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
▶	95.4%	(/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (PI.f32))
	97.4%	(/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 alpha) (.f32 #s(literal 2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	95.2%	(/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
	97.9%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 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 (fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.1%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 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 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	97.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
▶	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 cosTheta (PI.f32)) (PI.f32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.5%	(/.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))))
	98.2%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	97.3%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	97.4%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (log.f32 alpha) (.f32 #s(literal 2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))))
	95.1%	(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))))
	65.9%	(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))
	65.9%	(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))))
	64.7%	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
▶	-0.0%	(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
	95.1%	(.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (log.f32 alpha) #s(literal 2 binary32))))
	94.9%	(.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32)))
	94.7%	(.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 2 binary32)))
	97.1%	(.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (log.f32 alpha) (.f32 #s(literal 2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))
	94.8%	(.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))))
	96.7%	(.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 1 539 to 931 computations (39.5% saved)

simplify13.0ms (0.1%)

Memory

-32.8MiB live, 11.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

32×	`lower-*.f64`
28×	`lift-*.f32`
14×	`lift-/.f32`
14×	`lower-/.f64`
12×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	329
0	72	329

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

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

localize132.0ms (1.5%)

Memory

18.4MiB live, 252.4MiB allocated

Localize:

Found 19 expressions of interest:

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

Samples

74.0ms

256×

invalid

Compiler

Compiled 344 to 42 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-mult: 27.0ms (49.1% of total)

ival-div: 10.0ms (18.2% of total)

ival-add: 8.0ms (14.5% of total)

ival-log: 3.0ms (5.5% of total)

ival-sqrt: 2.0ms (3.6% of total)

ival-pi: 1.0ms (1.8% of total)

ival-sub: 1.0ms (1.8% of total)

ival-neg: 1.0ms (1.8% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0%)

Memory

7.4MiB live, 7.4MiB allocated

Counts

10 → 72

Calls

Call 1

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

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

21 calls:

Time	Variable		Point	Expression
1.0ms	alpha	@	-inf	(/ (/ (+ (* alpha alpha) -1) (* (log alpha) 2)) (PI))
0.0ms	alpha	@	0	(/ (/ (+ (* alpha alpha) -1) (* (log alpha) 2)) (PI))
0.0ms	alpha	@	inf	(/ (/ (+ (* alpha alpha) -1) (* (log alpha) 2)) (PI))
0.0ms	alpha	@	inf	(* (log alpha) 2)
0.0ms	alpha	@	-inf	(* (log alpha) 2)

rewrite16.0ms (0.2%)

Memory

-21.9MiB live, 15.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6×	`lift-/.f32`
6×	`lower-*.f64`
6×	`lower-/.f64`
6×	`lift-*.f32`
2×	`lower-sqrt.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
0	27	40

Stop Event

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

Counts

10 → 11

Calls

Call 1

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

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

simplify209.0ms (2.3%)

Memory

20.8MiB live, 286.7MiB allocated

Algorithm

1×	egg-herbie

Rules

4 480×	`lower-*.f64`
4 480×	`lower-*.f32`
3 596×	`lower-fma.f64`
3 596×	`lower-fma.f32`
2 300×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	466
1	145	451
2	436	450
3	1439	396
4	6454	396
0	8389	381

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

eval18.0ms (0.2%)

Memory: 0.1MiB live, 36.9MiB allocated
Compiler: Compiled 5 210 to 87 computations (98.3% saved)

prune50.0ms (0.6%)

Memory

11.4MiB live, 72.0MiB allocated

Pruning

36 alts after pruning (30 fresh and 6 done)

	Pruned	Kept	Total
New	243	5	248
Fresh	1	25	26
Picked	1	4	5
Done	0	2	2
Total	245	36	281

Accuracy

99.9%

Counts

281 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(fma.f32 (.f32 alpha alpha) (fma.f32 (.f32 (-.f32 (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (log.f32 alpha) (fma.f32 (.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32))) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))) (/.f32 (.f32 cosTheta cosTheta) (neg.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))) (.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (fma.f32 #s(literal 1/2 binary32) (/.f32 (neg.f32 (.f32 cosTheta cosTheta)) (.f32 (.f32 (log.f32 alpha) (fma.f32 (.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32))) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))) (/.f32 #s(literal 1/2 binary32) (.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
✓	98.3%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.5%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
	94.9%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (E.f32))) (log.f32 (*.f32 alpha alpha))))
	95.3%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))))
✓	95.3%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	95.3%	(/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 alpha alpha) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha)))
	97.2%	(/.f32 (/.f32 (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 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) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	98.1%	(/.f32 (/.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.3%	(/.f32 (/.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
✓	95.4%	(/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (PI.f32))
	97.4%	(/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 alpha) (.f32 #s(literal 2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	95.2%	(/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
	97.9%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 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 (fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.1%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 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 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	95.4%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (PI.f32))
	97.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	64.7%	(/.f32 (/.f32 #s(literal -1 binary32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (PI.f32))
✓	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 cosTheta (PI.f32)) (PI.f32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.5%	(/.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))))
	98.2%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (fma.f32 (.f32 (log.f32 alpha) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	97.3%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	97.4%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (log.f32 alpha) (.f32 #s(literal 2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))))
	95.1%	(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))))
	65.9%	(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))
	65.9%	(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))))
	64.7%	(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (PI.f32)))
	95.1%	(.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (log.f32 alpha) #s(literal 2 binary32))))
	94.9%	(.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32)))
	94.7%	(.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 2 binary32)))
	97.1%	(.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (log.f32 alpha) (.f32 #s(literal 2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))
	94.8%	(.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))))
	95.1%	(.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha #s(literal -1 binary32)))
	96.7%	(.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)))))
	-0.0%	(*.f32 #s(literal -1 binary32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))

Compiler

Compiled 2 196 to 727 computations (66.9% saved)

regimes86.0ms (1%)

Memory

-17.5MiB live, 91.7MiB allocated

Counts

53 → 1

Calls

Call 1

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

29.0ms	cosTheta
21.0ms	(/.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))))
15.0ms	alpha
14.0ms	(*.f32 alpha 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)

regimes59.0ms (0.7%)

Memory

3.0MiB live, 49.3MiB allocated

Counts

29 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

32.0ms	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	(*.f32 alpha 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)

regimes40.0ms (0.4%)

Memory

-7.3MiB live, 68.4MiB allocated

Counts

28 → 1

Calls

Call 1

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

Calls

4 calls:

11.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
10.0ms	cosTheta
8.0ms	(*.f32 alpha alpha)
8.0ms	alpha

Results

Accuracy	Segments	Branch
97.6%	1	`cosTheta`
97.6%	1	`alpha`
97.6%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
97.6%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes31.0ms (0.4%)

Memory

32.8MiB live, 71.0MiB allocated

Counts

23 → 1

Calls

Call 1

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

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

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)

regimes30.0ms (0.3%)

Memory

-22.8MiB live, 61.8MiB allocated

Counts

20 → 1

Calls

Call 1

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

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:

7.0ms	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	(*.f32 alpha alpha)
6.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.7%	1	`cosTheta`
96.7%	1	`alpha`
96.7%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
96.7%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes23.0ms (0.3%)

Memory

-10.8MiB live, 67.6MiB allocated

Counts

15 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	cosTheta
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))))
5.0ms	alpha
5.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
95.4%	1	`cosTheta`
95.4%	1	`alpha`
95.4%	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))))`
95.4%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes22.0ms (0.2%)

Memory

-1.6MiB live, 39.3MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

4 calls:

8.0ms	cosTheta
5.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
4.0ms	(*.f32 alpha alpha)
4.0ms	alpha

Results

Accuracy	Segments	Branch
95.3%	1	`cosTheta`
95.3%	1	`alpha`
95.3%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
95.3%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes10.0ms (0.1%)

Memory

22.4MiB live, 22.4MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

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
64.7%	1	`cosTheta`
64.7%	1	`alpha`
64.7%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
64.7%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes9.0ms (0.1%)

Memory

-21.3MiB live, 17.8MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

4 calls:

3.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
2.0ms	cosTheta
2.0ms	(*.f32 alpha alpha)
2.0ms	alpha

Results

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

Compiler

Compiled 37 to 20 computations (45.9% saved)

simplify9.0ms (0.1%)

Memory

18.7MiB live, 18.7MiB allocated

Algorithm

1×	egg-herbie

Rules

36×	`*-commutative_binary32`
16×	`+-commutative_binary32`
14×	`neg-sub0_binary32`
14×	`sub-neg_binary32`
12×	`neg-mul-1_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	132
1	70	131
2	82	131
3	93	130
4	100	130
5	104	130
6	110	130
7	114	130
8	115	130

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

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

soundness859.0ms (9.7%)

Memory

14.5MiB live, 764.8MiB allocated

Rules

8 408×	`lower-fma.f64`
8 408×	`lower-fma.f32`
8 090×	`lower-fma.f64`
8 090×	`lower-fma.f32`
7 340×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	466
1	145	451
2	436	450
3	1439	396
4	6454	396
0	8389	381
0	42	179
0	80	163
1	320	136
2	2255	136
0	8544	134
0	322	5753
1	1035	5473
2	4113	5440
0	8267	5212
0	13	46
0	23	46
1	98	46
2	768	44
0	8448	39
0	102	1108
1	310	1068
2	1161	1016
3	5125	1016
0	8100	982
0	185	1959
1	552	1906
2	2134	1849
0	8489	1768

Stop Event

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

Compiler

Compiled 365 to 201 computations (44.9% saved)

preprocess87.0ms (1%)

Memory

6.5MiB live, 123.5MiB allocated

Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 940 to 448 computations (52.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze60.0ms (0.7%)

sample1.7s (18.7%)

preprocess430.0ms (4.8%)

explain162.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify328.0ms (3.7%)

localize42.0ms (0.5%)

series45.0ms (0.5%)

rewrite356.0ms (4%)

simplify437.0ms (4.9%)

eval93.0ms (1%)

prune168.0ms (1.9%)

simplify14.0ms (0.2%)

localize307.0ms (3.5%)

series111.0ms (1.2%)

rewrite14.0ms (0.2%)

simplify443.0ms (5%)

eval50.0ms (0.6%)

prune40.0ms (0.4%)

simplify368.0ms (4.1%)

localize182.0ms (2.1%)

series64.0ms (0.7%)

rewrite418.0ms (4.7%)

simplify405.0ms (4.6%)

eval215.0ms (2.4%)

prune769.0ms (8.7%)

simplify13.0ms (0.1%)

localize132.0ms (1.5%)

series4.0ms (0%)

rewrite16.0ms (0.2%)

simplify209.0ms (2.3%)

eval18.0ms (0.2%)

prune50.0ms (0.6%)

regimes86.0ms (1%)

regimes59.0ms (0.7%)

regimes40.0ms (0.4%)

regimes31.0ms (0.4%)

regimes30.0ms (0.3%)

regimes23.0ms (0.3%)

regimes22.0ms (0.2%)

regimes10.0ms (0.1%)

regimes9.0ms (0.1%)

simplify9.0ms (0.1%)

soundness859.0ms (9.7%)

preprocess87.0ms (1%)

end0.0ms (0%)

Profiling