Metrics for GTR1 distribution

analyze57.0ms (0.7%)

Memory

9.9MiB live, 132.8MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 40 to 23 computations (42.5% saved)

sample1.4s (17.9%)

Memory

26.4MiB live, 3 069.2MiB allocated

Samples

1.1s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 880.0ms

ival-mult: 287.0ms (32.6% of total)

const: 156.0ms (17.7% of total)

ival-add: 95.0ms (10.8% of total)

ival-log: 89.0ms (10.1% of total)

ival-<=: 89.0ms (10.1% of total)

ival-div: 57.0ms (6.5% of total)

ival-sub: 39.0ms (4.4% of total)

ival-pi: 32.0ms (3.6% of total)

ival-and: 23.0ms (2.6% of total)

exact: 10.0ms (1.1% of total)

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

Bogosity

preprocess416.0ms (5.3%)

Memory

-27.9MiB live, 603.5MiB allocated

Algorithm

2×	egg-herbie

Rules

12 798×	`accelerator-lowering-fma.f32`
12 798×	`accelerator-lowering-fma.f64`
4 578×	`-lowering-.f32`
4 578×	`-lowering-.f64`
2 370×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	150
1	166	146
2	648	144
3	3587	144
4	7869	144
0	13	24
1	41	24
2	149	24
3	628	24
4	2696	24
5	4449	24
6	7748	24
0	8594	21

Stop Event

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

Calls

Call 1

Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

Outputs

(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) 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)))))

Call 2

Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta)))))
(/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta))))
(neg (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta))))))
(neg (/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta)))))
(/ (- (* cosTheta cosTheta) 1) (* (* (PI) (log (* cosTheta cosTheta))) (+ 1 (* (* (- (* cosTheta cosTheta) 1) alpha) alpha))))

Outputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- 1 (* alpha alpha)) (* (* (PI) (log (* alpha alpha))) (+ -1 (* cosTheta (- cosTheta (* alpha (* alpha cosTheta)))))))
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta)))))
(/ (- 1 (* alpha alpha)) (* (* (PI) (log (* alpha alpha))) (+ -1 (* cosTheta (- cosTheta (* alpha (* alpha cosTheta)))))))
(/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta))))
(/ (- 1 (* alpha alpha)) (* (* (PI) (log (* alpha alpha))) (+ -1 (* cosTheta (- cosTheta (* alpha (* alpha cosTheta)))))))
(neg (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta))))))
(/ (+ (* alpha alpha) -1) (* (* (PI) (log (* alpha alpha))) (+ -1 (* cosTheta (- cosTheta (* alpha (* alpha cosTheta)))))))
(neg (/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta)))))
(/ (+ (* alpha alpha) -1) (* (* (PI) (log (* alpha alpha))) (+ -1 (* cosTheta (- cosTheta (* alpha (* alpha cosTheta)))))))
(/ (- (* cosTheta cosTheta) 1) (* (* (PI) (log (* cosTheta cosTheta))) (+ 1 (* (* (- (* cosTheta cosTheta) 1) alpha) alpha))))
(/ (+ (* cosTheta cosTheta) -1) (* (log (* cosTheta cosTheta)) (+ (PI) (* (+ (* cosTheta cosTheta) -1) (* (* alpha alpha) (PI))))))

Symmetry

(abs cosTheta)

(abs alpha)

explain169.0ms (2.1%)

Memory

21.6MiB live, 302.6MiB allocated

FPErrors

Click to see full error table

Overpredictions	Example	Example	Subexpression
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)))`
1	(1.81667029509891e-12 0.9962978363037109)	-	`(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))`
0	-	-	`(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)`
1	(1.81667029509891e-12 0.9962978363037109)	-	`(log.f32 (*.f32 alpha alpha))`
0	-	-	`(*.f32 alpha alpha)`
0	-	-	`(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)`
0	-	-	`(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))`

Explanations

Click to see full explanations table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	1	255

Precision

0.0

Recall

0/0

Confusion?

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

Precision?

0.0

Recall?

0/0

Freqs

test

number	freq
0	255
2	1

Total Confusion?

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

Precision?

0.0

Recall?

0/0

Samples

53.0ms

512×

valid

Compiler

Compiled 238 to 56 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 14.0ms (40.2% of total)

ival-add: 6.0ms (17.2% of total)

ival-log: 6.0ms (17.2% of total)

ival-div: 4.0ms (11.5% of total)

ival-pi: 2.0ms (5.7% of total)

ival-sub: 2.0ms (5.7% 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: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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)

simplify351.0ms (4.4%)

Memory

6.0MiB live, 482.6MiB 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×	`accelerator-lowering-fma.f32`
12 798×	`accelerator-lowering-fma.f64`
4 578×	`-lowering-.f32`
4 578×	`-lowering-.f64`
2 370×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	91
1	41	91
2	149	91
3	628	91
4	2696	91
5	4449	91
6	7748	91
0	8594	81

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(- (* alpha alpha) 1)
(* alpha alpha)
alpha
1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
cosTheta

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

localize44.0ms (0.6%)

Memory

-22.2MiB live, 96.7MiB 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	99.3%	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
✓	accuracy	99.2%	(/.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	98.7%	(.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: 9.0ms (47.8% of total)

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

ival-pi: 2.0ms (10.6% of total)

ival-div: 2.0ms (10.6% 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)

series51.0ms (0.6%)

Memory

17.9MiB live, 90.8MiB allocated

Counts

7 → 132

Calls

Call 1

Inputs
#<alt (- (* alpha alpha) 1)>
#<alt (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))>
#<alt (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (* alpha alpha)>
#<alt (* (PI) (log (* alpha alpha)))>
#<alt (* (- (* alpha alpha) 1) cosTheta)>
#<alt (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)>

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

Calls

33 calls:

Time	Variable		Point	Expression
28.0ms	alpha	@	0	(* (PI) (log (* alpha alpha)))
9.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
2.0ms	alpha	@	0	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	inf	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	-inf	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite352.0ms (4.4%)

Memory

13.4MiB live, 689.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 278×	`-lowering-.f32`
6 278×	`-lowering-.f64`
5 746×	`accelerator-lowering-fma.f32`
5 746×	`accelerator-lowering-fma.f64`
3 952×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	65
1	88	65
2	758	63
0	8437	55

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 609

Calls

Call 1

Inputs
(- (* alpha alpha) 1)
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(* alpha alpha)
(* (PI) (log (* alpha alpha)))
(* (- (* alpha alpha) 1) cosTheta)
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)

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

simplify437.0ms (5.5%)

Memory

-8.2MiB live, 515.4MiB allocated

Algorithm

1×	egg-herbie

Rules

8 466×	`accelerator-lowering-fma.f32`
8 466×	`accelerator-lowering-fma.f64`
5 952×	`-lowering-.f32`
5 952×	`-lowering-.f64`
4 632×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

eval135.0ms (1.7%)

Memory: 19.6MiB live, 132.1MiB allocated
Compiler: Compiled 33 380 to 2 792 computations (91.6% saved)

prune178.0ms (2.2%)

Memory

-18.4MiB live, 253.5MiB allocated

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	855	28	883
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	856	28	884

Accuracy

99.7%

Counts

884 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(fma.f32 (.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 #s(literal 1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))))
	98.1%	(/.f32 (fma.f32 (/.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) (neg.f32 alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	-0.0%	(/.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 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
▶	98.5%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.9%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	98.1%	(/.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) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.3%	(/.f32 (/.f32 (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.3%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.8%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 (.f32 alpha (.f32 alpha 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 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 1 binary32))) (.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.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) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (.f32 alpha alpha)))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (neg.f32 (.f32 alpha alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.2%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (-.f32 #s(literal 1 binary32) (neg.f32 (.f32 alpha alpha)))) (fma.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.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))))
	98.5%	(/.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))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32))))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
	95.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(literal 1 binary32)))
	98.2%	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	66.4%	(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))

Compiler

Compiled 2 120 to 976 computations (54% saved)

simplify11.0ms (0.1%)

Memory

18.6MiB live, 18.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

30×	`-lowering-.f32`
30×	`-lowering-.f64`
16×	`/-lowering-/.f32`
16×	`/-lowering-/.f64`
10×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	556

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))
(- (* alpha alpha) 1)
(* alpha alpha)
alpha
1
(* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)
(+ (* alpha alpha) -1)
-1
(* cosTheta cosTheta)
cosTheta
(/ (+ (* alpha alpha) -1) (* (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (* (PI) (/ 0 0))))
(+ (* alpha alpha) -1)
alpha
-1
(* (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (* (PI) (/ 0 0)))
(+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)
(* cosTheta cosTheta)
cosTheta
1
(* (PI) (/ 0 0))
(PI)
(/ 0 0)
0
(/ (+ (* alpha alpha) -1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(+ (* alpha alpha) -1)
alpha
-1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(* alpha alpha)
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
1
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
(/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1))
(+ (* (* alpha alpha) (* alpha alpha)) -1)
(* alpha alpha)
alpha
-1
(+ (* alpha alpha) 1)
1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))
(- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1))
(* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))
(* alpha (* alpha (* alpha alpha)))
alpha
(* alpha (* alpha alpha))
(* alpha alpha)
(+ (* alpha alpha) 1)
1
(* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta

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

localize329.0ms (4.2%)

Memory

-13.6MiB live, 230.9MiB allocated

Localize:

Found 20 expressions of interest:

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

Samples

94.0ms

256×

invalid

Compiler

Compiled 558 to 39 computations (93% saved)

Precisions

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

ival-mult: 51.0ms (69.5% of total)

ival-div: 10.0ms (13.6% of total)

ival-add: 5.0ms (6.8% of total)

ival-log: 3.0ms (4.1% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series63.0ms (0.8%)

Memory

16.9MiB live, 92.8MiB allocated

Counts

23 → 312

Calls

Call 1

Inputs
#<alt (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))>
#<alt (- (* alpha alpha) 1)>
#<alt (* alpha alpha)>
#<alt (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))>
#<alt (/ (+ (* alpha alpha) -1) (* (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (* (PI) (/ 0 0))))>
#<alt (+ (* alpha alpha) -1)>
#<alt (* (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (* (PI) (/ 0 0)))>
#<alt (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)>
#<alt (/ (+ (* alpha alpha) -1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))>
#<alt (* (PI) (log (* alpha alpha)))>
#<alt (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1))>
#<alt (+ (* (* alpha alpha) (* alpha alpha)) -1)>
#<alt (/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))>
#<alt (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1))>
#<alt (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))>
#<alt (PI)>
#<alt (log (* alpha alpha))>
#<alt (* cosTheta cosTheta)>
#<alt (* (PI) (/ 0 0))>
#<alt (* alpha (* alpha alpha))>

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

Calls

90 calls:

Time	Variable		Point	Expression
18.0ms	alpha	@	inf	(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
12.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))
2.0ms	cosTheta	@	inf	(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	0	(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	inf	(/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite41.0ms (0.5%)

Memory

-15.4MiB live, 21.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

30×	`-lowering-.f32`
30×	`-lowering-.f64`
16×	`/-lowering-/.f32`
16×	`/-lowering-/.f64`
10×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	314

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

23 → 26

Calls

Call 1

Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))
(- (* alpha alpha) 1)
(* alpha alpha)
(* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))
(/ (+ (* alpha alpha) -1) (* (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (* (PI) (/ 0 0))))
(+ (* alpha alpha) -1)
(* (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (* (PI) (/ 0 0)))
(+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)
(/ (+ (* alpha alpha) -1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1))
(+ (* (* alpha alpha) (* alpha alpha)) -1)
(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))
(- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1))
(* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))
(PI)
(log (* alpha alpha))
(* cosTheta cosTheta)
(* (PI) (/ 0 0))
(* alpha (* alpha alpha))

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

simplify799.0ms (10.1%)

Memory

-132.2MiB live, 630.6MiB allocated

Algorithm

1×	egg-herbie

Rules

7 056×	`-lowering-.f32`
7 056×	`-lowering-.f64`
6 790×	`accelerator-lowering-fma.f32`
6 790×	`accelerator-lowering-fma.f64`
4 194×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	616	11422
1	2079	10924
0	9236	10356

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 312

Calls

Call 1

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

eval59.0ms (0.7%)

Memory: 12.5MiB live, 126.2MiB allocated
Compiler: Compiled 28 721 to 727 computations (97.5% saved)

prune57.0ms (0.7%)

Memory

-6.5MiB live, 119.0MiB allocated

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	701	19	720
Fresh	10	13	23
Picked	5	0	5
Done	0	0	0
Total	716	32	748

Accuracy

99.9%

Counts

748 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(fma.f32 (.f32 alpha alpha) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
	95.9%	(fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))) (-.f32 (-.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))))
	98.1%	(/.f32 (fma.f32 (/.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	95.3%	(/.f32 (fma.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
	95.5%	(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
	98.1%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) (neg.f32 alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.5%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	97.9%	(/.f32 (fma.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))))
▶	48.2%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))))
	95.9%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	98.1%	(/.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) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.5%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
	95.6%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	98.1%	(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.8%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 (.f32 alpha (.f32 alpha 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 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 1 binary32))) (.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	48.1%	(/.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 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
	87.6%	(/.f32 (/.f32 (-.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (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) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.0%	(/.f32 (/.f32 (.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	81.6%	(/.f32 (/.f32 #s(literal -1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32))))))
	50.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32))))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 alpha alpha) (-.f32 (fma.f32 cosTheta cosTheta (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha))))))
	95.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.2%	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	66.4%	(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
	66.4%	(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))

Compiler

Compiled 2 352 to 1 074 computations (54.3% saved)

simplify10.0ms (0.1%)

Memory

16.8MiB live, 16.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

40×	`-lowering-.f32`
40×	`-lowering-.f64`
16×	`+-lowering-+.f64`
16×	`+-lowering-+.f32`
14×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	448

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

Inputs
(/ (+ (* alpha alpha) -1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))
(+ (* alpha alpha) -1)
alpha
-1
(* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(* alpha alpha)
(+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)
(* cosTheta cosTheta)
cosTheta
1
(/ (+ (* alpha alpha) -1) (* 1 (* (PI) (/ 0 0))))
(+ (* alpha alpha) -1)
alpha
-1
(* 1 (* (PI) (/ 0 0)))
1
(* (PI) (/ 0 0))
(PI)
(/ 0 0)
0
(/ (* (+ alpha 1) (+ alpha -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(* (+ alpha 1) (+ alpha -1))
(+ alpha 1)
alpha
1
(+ alpha -1)
-1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(* alpha alpha)
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
(/ (+ (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (neg (+ (* alpha alpha) 1))) (* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))))
(+ (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (neg (+ (* alpha alpha) 1)))
(* alpha (* alpha (* alpha alpha)))
alpha
(* alpha (* alpha alpha))
(* alpha alpha)
(+ (* alpha alpha) 1)
1
(neg (+ (* alpha alpha) 1))
(* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))))
(PI)
(* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))
(log (* alpha alpha))
(* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))
(/ (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (PI) (+ (* (+ (* alpha alpha) -1) (log (* alpha alpha))) (/ (log (* alpha alpha)) (* cosTheta cosTheta))))))
(+ (* alpha alpha) -1)
alpha
-1
(* (* cosTheta cosTheta) (* (PI) (+ (* (+ (* alpha alpha) -1) (log (* alpha alpha))) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))))
(* cosTheta cosTheta)
cosTheta
(* (PI) (+ (* (+ (* alpha alpha) -1) (log (* alpha alpha))) (/ (log (* alpha alpha)) (* cosTheta cosTheta))))
(PI)
(+ (* (+ (* alpha alpha) -1) (log (* alpha alpha))) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))
(log (* alpha alpha))
(* alpha alpha)
(/ (log (* alpha alpha)) (* cosTheta cosTheta))

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

localize186.0ms (2.4%)

Memory

14.8MiB live, 211.3MiB allocated

Localize:

Found 20 expressions of interest:

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

Samples

111.0ms

256×

invalid

Compiler

Compiled 450 to 46 computations (89.8% saved)

Precisions

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

ival-add: 42.0ms (45.7% of total)

ival-mult: 34.0ms (37% of total)

ival-div: 9.0ms (9.8% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series30.0ms (0.4%)

Memory

-35.5MiB live, 46.6MiB allocated

Counts

23 → 276

Calls

Call 1

Inputs
#<alt (/ (+ (* alpha alpha) -1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))>
#<alt (+ (* alpha alpha) -1)>
#<alt (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))>
#<alt (* (PI) (log (* alpha alpha)))>
#<alt (/ (+ (* alpha alpha) -1) (* 1 (* (PI) (/ 0 0))))>
#<alt (* 1 (* (PI) (/ 0 0)))>
#<alt (* (PI) (/ 0 0))>
#<alt (/ (* (+ alpha 1) (+ alpha -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (* (+ alpha 1) (+ alpha -1))>
#<alt (+ alpha 1)>
#<alt (+ alpha -1)>
#<alt (/ (+ (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (neg (+ (* alpha alpha) 1))) (* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))))>
#<alt (+ (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (neg (+ (* alpha alpha) 1)))>
#<alt (* alpha (* alpha (* alpha alpha)))>
#<alt (* alpha (* alpha alpha))>
#<alt (/ (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (PI) (+ (* (+ (* alpha alpha) -1) (log (* alpha alpha))) (/ (log (* alpha alpha)) (* cosTheta cosTheta))))))>
#<alt (* (* cosTheta cosTheta) (* (PI) (+ (* (+ (* alpha alpha) -1) (log (* alpha alpha))) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))))>
#<alt (* cosTheta cosTheta)>
#<alt (PI)>
#<alt (log (* alpha alpha))>
#<alt (* alpha alpha)>
#<alt (/ 0 0)>
#<alt (neg (+ (* alpha alpha) 1))>

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

Calls

72 calls:

Time	Variable		Point	Expression
5.0ms	alpha	@	-inf	(/ (* (+ alpha 1) (+ alpha -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	inf	(/ (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (PI) (+ (* (+ (* alpha alpha) -1) (log (* alpha alpha))) (/ (log (* alpha alpha)) (* cosTheta cosTheta))))))
2.0ms	alpha	@	0	(/ (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (PI) (+ (* (+ (* alpha alpha) -1) (log (* alpha alpha))) (/ (log (* alpha alpha)) (* cosTheta cosTheta))))))
1.0ms	alpha	@	-inf	(/ (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (PI) (+ (* (+ (* alpha alpha) -1) (log (* alpha alpha))) (/ (log (* alpha alpha)) (* cosTheta cosTheta))))))
1.0ms	alpha	@	0	(/ (+ (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (neg (+ (* alpha alpha) 1))) (* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))))

rewrite15.0ms (0.2%)

Memory

21.9MiB live, 21.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

40×	`-lowering-.f32`
40×	`-lowering-.f64`
16×	`+-lowering-+.f64`
16×	`+-lowering-+.f32`
14×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	243

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

23 → 25

Calls

Call 1

Inputs
(/ (+ (* alpha alpha) -1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))
(+ (* alpha alpha) -1)
(* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))
(* (PI) (log (* alpha alpha)))
(/ (+ (* alpha alpha) -1) (* 1 (* (PI) (/ 0 0))))
(* 1 (* (PI) (/ 0 0)))
(* (PI) (/ 0 0))
(/ (* (+ alpha 1) (+ alpha -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(* (+ alpha 1) (+ alpha -1))
(+ alpha 1)
(+ alpha -1)
(/ (+ (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (neg (+ (* alpha alpha) 1))) (* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))))
(+ (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (neg (+ (* alpha alpha) 1)))
(* alpha (* alpha (* alpha alpha)))
(* alpha (* alpha alpha))
(/ (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (PI) (+ (* (+ (* alpha alpha) -1) (log (* alpha alpha))) (/ (log (* alpha alpha)) (* cosTheta cosTheta))))))
(* (* cosTheta cosTheta) (* (PI) (+ (* (+ (* alpha alpha) -1) (log (* alpha alpha))) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))))
(* cosTheta cosTheta)
(PI)
(log (* alpha alpha))
(* alpha alpha)
(/ 0 0)
(neg (+ (* alpha alpha) 1))

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

simplify383.0ms (4.8%)

Memory

-5.7MiB live, 552.1MiB allocated

Algorithm

1×	egg-herbie

Rules

6 366×	`-lowering-.f32`
6 366×	`-lowering-.f64`
5 348×	`accelerator-lowering-fma.f32`
5 348×	`accelerator-lowering-fma.f64`
2 902×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	431	7105
1	1438	6885
2	5999	6819
0	8399	6530

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

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

eval41.0ms (0.5%)

Memory: -5.9MiB live, 109.0MiB allocated
Compiler: Compiled 17 289 to 464 computations (97.3% saved)

prune46.0ms (0.6%)

Memory

19.8MiB live, 141.8MiB allocated

Pruning

36 alts after pruning (34 fresh and 2 done)

	Pruned	Kept	Total
New	519	11	530
Fresh	4	23	27
Picked	3	2	5
Done	0	0	0
Total	526	36	562

Accuracy

99.9%

Counts

562 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.9%	(fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))) (-.f32 (-.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))))
	95.8%	(fma.f32 #s(literal 1/2 binary32) (.f32 alpha (/.f32 alpha (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
▶	98.1%	(/.f32 (fma.f32 (/.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.3%	(/.f32 (fma.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (PI.f32) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
▶	95.2%	(/.f32 (fma.f32 (.f32 alpha alpha) (fma.f32 alpha (.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal -1 binary32)) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
	95.5%	(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
	98.1%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) (neg.f32 alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	85.2%	(/.f32 (fma.f32 alpha (.f32 alpha (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
▶	79.7%	(/.f32 (fma.f32 alpha (neg.f32 alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
✓	98.5%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	97.9%	(/.f32 (fma.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))))
	95.9%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	97.5%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
	95.6%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	98.1%	(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	87.6%	(/.f32 (/.f32 (-.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (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) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.0%	(/.f32 (/.f32 (.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	81.6%	(/.f32 (/.f32 #s(literal -1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32))))))
	50.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32))))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 alpha alpha) (-.f32 (fma.f32 cosTheta cosTheta (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha))))))
	95.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.2%	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.3%	(/.f32 (.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
✓	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	48.1%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
	66.4%	(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
	66.4%	(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	65.3%	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
	33.2%	(/.f32 #s(literal -1 binary32) (.f32 (fma.f32 (log.f32 alpha) (/.f32 #s(literal 2 binary32) (.f32 cosTheta cosTheta)) (.f32 (log.f32 alpha) #s(literal -2 binary32))) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
▶	-0.0%	(/.f32 #s(literal -1 binary32) (.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	95.3%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 2 283 to 1 122 computations (50.9% saved)

simplify13.0ms (0.2%)

Memory

-10.6MiB live, 28.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

44×	`-lowering-.f32`
44×	`-lowering-.f64`
22×	`/-lowering-/.f32`
22×	`/-lowering-/.f64`
18×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	599

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1)))))
(- (* alpha alpha) 1)
(* alpha alpha)
alpha
1
(* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1))))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1)))
(/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1))
(+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1)
(+ (* alpha alpha) -1)
-1
(* cosTheta cosTheta)
cosTheta
(+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1)
(* (+ (* alpha alpha) -1) cosTheta)
(* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))
(/ -1 (* 1 (* (PI) (/ 0 0))))
-1
(* 1 (* (PI) (/ 0 0)))
1
(* (PI) (/ 0 0))
(PI)
(/ 0 0)
0
(/ (+ (* alpha (neg alpha)) -1) (* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))))
(+ (* alpha (neg alpha)) -1)
alpha
(neg alpha)
-1
(* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))))
(PI)
(* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))
(log (* alpha alpha))
(* alpha alpha)
(* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))
(+ (* alpha alpha) 1)
1
(/ (+ (* (* alpha alpha) (+ (* alpha (* alpha (+ (* alpha alpha) 1))) -1)) -1) (* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))))
(+ (* (* alpha alpha) (+ (* alpha (* alpha (+ (* alpha alpha) 1))) -1)) -1)
(* alpha alpha)
alpha
(+ (* alpha (* alpha (+ (* alpha alpha) 1))) -1)
(* alpha (+ (* alpha alpha) 1))
(+ (* alpha alpha) 1)
1
-1
(* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))))
(PI)
(* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))
(log (* alpha alpha))
(* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))
(/ (+ (* (/ alpha (+ (* alpha alpha) 1)) (/ (* alpha (* alpha alpha)) 1)) (neg (/ 1 (+ (* alpha alpha) 1)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(+ (* (/ alpha (+ (* alpha alpha) 1)) (/ (* alpha (* alpha alpha)) 1)) (neg (/ 1 (+ (* alpha alpha) 1))))
(/ alpha (+ (* alpha alpha) 1))
alpha
(+ (* alpha alpha) 1)
1
(/ (* alpha (* alpha alpha)) 1)
(* alpha (* alpha alpha))
(* alpha alpha)
(neg (/ 1 (+ (* alpha alpha) 1)))
(/ 1 (+ (* alpha alpha) 1))
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta

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

localize230.0ms (2.9%)

Memory

13.9MiB live, 415.9MiB allocated

Localize:

Found 20 expressions of interest:

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

Samples

128.0ms

256×

invalid

Compiler

Compiled 601 to 54 computations (91% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-mult: 31.0ms (45.5% of total)

ival-div: 20.0ms (29.4% of total)

ival-add: 9.0ms (13.2% of total)

ival-log: 3.0ms (4.4% of total)

ival-neg: 2.0ms (2.9% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series34.0ms (0.4%)

Memory

-16.7MiB live, 64.2MiB allocated

Counts

23 → 264

Calls

Call 1

Inputs
#<alt (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1)))))>
#<alt (- (* alpha alpha) 1)>
#<alt (* alpha alpha)>
#<alt (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1))))>
#<alt (/ -1 (* 1 (* (PI) (/ 0 0))))>
#<alt (* 1 (* (PI) (/ 0 0)))>
#<alt (* (PI) (/ 0 0))>
#<alt (PI)>
#<alt (/ (+ (* alpha (neg alpha)) -1) (* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))))>
#<alt (+ (* alpha (neg alpha)) -1)>
#<alt (neg alpha)>
#<alt (* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))))>
#<alt (/ (+ (* (* alpha alpha) (+ (* alpha (* alpha (+ (* alpha alpha) 1))) -1)) -1) (* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))))>
#<alt (+ (* (* alpha alpha) (+ (* alpha (* alpha (+ (* alpha alpha) 1))) -1)) -1)>
#<alt (+ (* alpha (* alpha (+ (* alpha alpha) 1))) -1)>
#<alt (/ (+ (* (/ alpha (+ (* alpha alpha) 1)) (/ (* alpha (* alpha alpha)) 1)) (neg (/ 1 (+ (* alpha alpha) 1)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (+ (* (/ alpha (+ (* alpha alpha) 1)) (/ (* alpha (* alpha alpha)) 1)) (neg (/ 1 (+ (* alpha alpha) 1))))>
#<alt (/ alpha (+ (* alpha alpha) 1))>
#<alt (+ (* alpha alpha) 1)>
#<alt (log (* alpha alpha))>
#<alt (* cosTheta cosTheta)>
#<alt (* alpha (+ (* alpha alpha) 1))>
#<alt (neg (/ 1 (+ (* alpha alpha) 1)))>

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

Calls

66 calls:

Time	Variable		Point	Expression
4.0ms	alpha	@	-inf	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1)))))
4.0ms	cosTheta	@	inf	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1)))))
2.0ms	alpha	@	0	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1)))))
2.0ms	alpha	@	inf	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1)))))
1.0ms	alpha	@	inf	(* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1))))

rewrite16.0ms (0.2%)

Memory

-1.4MiB live, 37.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

44×	`-lowering-.f32`
44×	`-lowering-.f64`
22×	`/-lowering-/.f32`
22×	`/-lowering-/.f64`
18×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	300

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

23 → 28

Calls

Call 1

Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1)))))
(- (* alpha alpha) 1)
(* alpha alpha)
(* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (* (+ (* alpha alpha) -1) cosTheta) (* (* (+ (* alpha alpha) -1) cosTheta) (* cosTheta cosTheta))) -1))))
(/ -1 (* 1 (* (PI) (/ 0 0))))
(* 1 (* (PI) (/ 0 0)))
(* (PI) (/ 0 0))
(PI)
(/ (+ (* alpha (neg alpha)) -1) (* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))))
(+ (* alpha (neg alpha)) -1)
(neg alpha)
(* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))))
(/ (+ (* (* alpha alpha) (+ (* alpha (* alpha (+ (* alpha alpha) 1))) -1)) -1) (* (PI) (* (log (* alpha alpha)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))))
(+ (* (* alpha alpha) (+ (* alpha (* alpha (+ (* alpha alpha) 1))) -1)) -1)
(+ (* alpha (* alpha (+ (* alpha alpha) 1))) -1)
(/ (+ (* (/ alpha (+ (* alpha alpha) 1)) (/ (* alpha (* alpha alpha)) 1)) (neg (/ 1 (+ (* alpha alpha) 1)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(+ (* (/ alpha (+ (* alpha alpha) 1)) (/ (* alpha (* alpha alpha)) 1)) (neg (/ 1 (+ (* alpha alpha) 1))))
(/ alpha (+ (* alpha alpha) 1))
(+ (* alpha alpha) 1)
(log (* alpha alpha))
(* cosTheta cosTheta)
(* alpha (+ (* alpha alpha) 1))
(neg (/ 1 (+ (* alpha alpha) 1)))

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

simplify499.0ms (6.3%)

Memory

16.8MiB live, 774.2MiB allocated

Algorithm

1×	egg-herbie

Rules

7 112×	`accelerator-lowering-fma.f32`
7 112×	`accelerator-lowering-fma.f64`
6 920×	`-lowering-.f32`
6 920×	`-lowering-.f64`
4 078×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	633	7723
1	2107	7538
0	8163	7158

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

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

eval89.0ms (1.1%)

Memory: -3.2MiB live, 111.4MiB allocated
Compiler: Compiled 22 119 to 802 computations (96.4% saved)

prune164.0ms (2.1%)

Memory

25.0MiB live, 141.6MiB allocated

Pruning

38 alts after pruning (33 fresh and 5 done)

	Pruned	Kept	Total
New	540	9	549
Fresh	5	24	29
Picked	2	3	5
Done	0	2	2
Total	547	38	585

Accuracy

100.0%

Counts

585 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.8%	(fma.f32 (.f32 alpha alpha) (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
	97.4%	(/.f32 (fma.f32 (/.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.3%	(/.f32 (fma.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (PI.f32) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
✓	95.2%	(/.f32 (fma.f32 (.f32 alpha alpha) (fma.f32 alpha (.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal -1 binary32)) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
	85.2%	(/.f32 (fma.f32 (.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
	95.5%	(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
	98.1%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) (neg.f32 alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	78.6%	(/.f32 (fma.f32 alpha (neg.f32 alpha) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 #s(literal 4 binary32) (*.f32 alpha alpha) #s(literal 2 binary32))))
✓	79.7%	(/.f32 (fma.f32 alpha (neg.f32 alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
	62.8%	(/.f32 (fma.f32 alpha (neg.f32 alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 #s(literal 2 binary32) (log.f32 alpha))))
✓	98.5%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	98.5%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) (.f32 cosTheta cosTheta)) #s(literal -1 binary32))))))
	97.9%	(/.f32 (fma.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))))
	95.9%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	97.5%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
	95.6%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	87.6%	(/.f32 (/.f32 (-.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (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) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.0%	(/.f32 (/.f32 (.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	81.6%	(/.f32 (/.f32 #s(literal -1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	50.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32))))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 alpha alpha) (-.f32 (fma.f32 cosTheta cosTheta (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha))))))
	95.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	95.2%	(/.f32 (+.f32 (.f32 (.f32 alpha alpha) (fma.f32 alpha (.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal -1 binary32))) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
	98.2%	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.3%	(/.f32 (.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
✓	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	48.1%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
	98.0%	(/.f32 (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	66.4%	(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
	66.4%	(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	65.3%	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
	33.2%	(/.f32 #s(literal -1 binary32) (.f32 (fma.f32 (log.f32 alpha) (/.f32 #s(literal 2 binary32) (.f32 cosTheta cosTheta)) (.f32 (log.f32 alpha) #s(literal -2 binary32))) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
✓	-0.0%	(/.f32 #s(literal -1 binary32) (.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	95.3%	(.f32 (.f32 alpha alpha) (-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 alpha alpha)))) (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 3 180 to 857 computations (73.1% saved)

regimes166.0ms (2.1%)

Memory

-16.7MiB live, 145.5MiB allocated

Counts

68 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

43.0ms	alpha
38.0ms	(/.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))))
27.0ms	cosTheta
18.0ms	(*.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)

regimes26.0ms (0.3%)

Memory

-3.3MiB live, 38.9MiB allocated

Counts

15 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

10.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
5.0ms	(*.f32 alpha alpha)
5.0ms	alpha
5.0ms	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)

regimes33.0ms (0.4%)

Memory

-0.5MiB live, 39.2MiB allocated

Counts

14 → 1

Calls

Call 1

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

Outputs
(/.f32 (fma.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:

18.0ms	(/.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	cosTheta
5.0ms	(*.f32 alpha alpha)
5.0ms	alpha

Results

Accuracy	Segments	Branch
97.9%	1	`alpha`
97.9%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
97.9%	1	`(*.f32 alpha alpha)`
97.9%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes26.0ms (0.3%)

Memory

-1.5MiB live, 37.2MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

4 calls:

14.0ms	(*.f32 alpha alpha)
4.0ms	(/.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	cosTheta
4.0ms	alpha

Results

Accuracy	Segments	Branch
95.9%	1	`alpha`
95.9%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
95.9%	1	`(*.f32 alpha alpha)`
95.9%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes19.0ms (0.2%)

Memory

-10.4MiB live, 28.6MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

10.0ms	cosTheta
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))))
3.0ms	alpha
3.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
95.9%	1	`cosTheta`
95.9%	1	`alpha`
95.9%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
95.9%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes9.0ms (0.1%)

Memory

27.7MiB live, 27.7MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
65.3%	1	`cosTheta`
65.3%	1	`alpha`
65.3%	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))))`
65.3%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes39.0ms (0.5%)

Memory

-22.0MiB live, 18.8MiB 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 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))

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

(/.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 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))

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

Calls

4 calls:

33.0ms	alpha
2.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
2.0ms	(*.f32 alpha alpha)
2.0ms	cosTheta

Results

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

Compiler

Compiled 37 to 20 computations (45.9% saved)

simplify8.0ms (0.1%)

Memory

16.5MiB live, 16.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary32`
4×	`sub-neg_binary32`
2×	`mul-1-neg_binary32`
2×	`neg-sub0_binary32`
2×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	95
1	42	95
2	45	95
3	50	95

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

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

soundness812.0ms (10.3%)

Memory

-5.8MiB live, 991.9MiB allocated

Rules

8 466×	`accelerator-lowering-fma.f32`
8 466×	`accelerator-lowering-fma.f64`
7 056×	`-lowering-.f32`
7 056×	`-lowering-.f64`
6 790×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	616	11422
1	2079	10924
0	9236	10356
0	431	7105
1	1438	6885
2	5999	6819
0	8399	6530
0	197	2350
1	582	2290
2	2231	2197
0	8730	2075
0	13	65
1	88	65
2	758	63
0	8437	55

Stop Event

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

Compiler

Compiled 321 to 176 computations (45.2% saved)

preprocess40.0ms (0.5%)

Memory

16.4MiB live, 133.9MiB allocated

Remove

(abs alpha)

(abs cosTheta)

Compiler

Compiled 630 to 310 computations (50.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze57.0ms (0.7%)

sample1.4s (17.9%)

preprocess416.0ms (5.3%)

explain169.0ms (2.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify351.0ms (4.4%)

localize44.0ms (0.6%)

series51.0ms (0.6%)

rewrite352.0ms (4.4%)

simplify437.0ms (5.5%)

eval135.0ms (1.7%)

prune178.0ms (2.2%)

simplify11.0ms (0.1%)

localize329.0ms (4.2%)

series63.0ms (0.8%)

rewrite41.0ms (0.5%)

simplify799.0ms (10.1%)

eval59.0ms (0.7%)

prune57.0ms (0.7%)

simplify10.0ms (0.1%)

localize186.0ms (2.4%)

series30.0ms (0.4%)

rewrite15.0ms (0.2%)

simplify383.0ms (4.8%)

eval41.0ms (0.5%)

prune46.0ms (0.6%)

simplify13.0ms (0.2%)

localize230.0ms (2.9%)

series34.0ms (0.4%)

rewrite16.0ms (0.2%)

simplify499.0ms (6.3%)

eval89.0ms (1.1%)

prune164.0ms (2.1%)

regimes166.0ms (2.1%)

regimes26.0ms (0.3%)

regimes33.0ms (0.4%)

regimes26.0ms (0.3%)

regimes19.0ms (0.2%)

regimes9.0ms (0.1%)

regimes39.0ms (0.5%)

simplify8.0ms (0.1%)

soundness812.0ms (10.3%)

preprocess40.0ms (0.5%)

end0.0ms (0%)

Profiling