Details

analyze27.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	12.5%	87.5%	0%	0%	0%	0
0%	0%	12.5%	87.5%	0%	0%	0%	1
50%	6.2%	6.2%	87.5%	0%	0%	0%	2
50%	6.2%	6.2%	87.5%	0%	0%	0%	3
75%	9.4%	3.1%	87.5%	0%	0%	0%	4
75%	9.4%	3.1%	87.5%	0%	0%	0%	5
87.5%	10.9%	1.6%	87.5%	0%	0%	0%	6
87.5%	10.9%	1.6%	87.5%	0%	0%	0%	7
93.8%	11.7%	0.8%	87.5%	0%	0%	0%	8
93.8%	11.7%	0.8%	87.5%	0%	0%	0%	9
96.9%	12.1%	0.4%	87.5%	0%	0%	0%	10
96.9%	12.1%	0.4%	87.5%	0%	0%	0%	11
98.4%	12.3%	0.2%	87.5%	0%	0%	0%	12

Compiler

Compiled 42 to 32 computations (23.8% saved)

sample1.4s (1.5%)

Results

1.4s	8256×	body	256	valid
3.0ms	17×	body	256	invalid

Bogosity

preprocess3.0s (3.4%)

Algorithm

2×

egglog

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

(/.f64 1 (+.f64 (+.f64 1 cosTheta) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 c) c)) c)) (exp.f64 (*.f64 (neg.f64 c) c)))))

Outputs
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(pow.f64 (fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1)
(/.f64 1 (+.f64 (+.f64 1 cosTheta) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 c) c)) c)) (exp.f64 (*.f64 (neg.f64 c) c)))))
(pow.f64 (fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (+.f64 c c))) (*.f64 c (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 c 2))) (+.f64 1 cosTheta)) -1)

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify1.4s (1.6%)

Algorithm

1×

egglog

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Outputs

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)

eval2.0ms (0%)

Compiler: Compiled 49 to 37 computations (24.5% saved)

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.2b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)
▶	0.5b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Status

Error

Program

▶

0.5b

(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)

▶

0.5b

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Compiler

Compiled 51 to 41 computations (19.6% saved)

localize83.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 1 cosTheta) cosTheta)
✓	0.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
✓	0.4b	(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta))
✓	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 128 to 69 computations (46.1% saved)

series127.0ms (0.1%)

Counts

4 → 32

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	cosTheta	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
4.0ms	cosTheta	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
3.0ms	c	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
2.0ms	cosTheta	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
2.0ms	cosTheta	@	inf	(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta))

Compiler

Compiled 10990 to 8000 computations (27.2% saved)

rewrite1.6s (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

94×	`egg-rr`
64×	`egg-rr`
34×	`egg-rr`
33×	`egg-rr`

Counts

4 → 225

Calls

Call 1

Inputs
(sqrt.f64 (PI.f64))
(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(-.f64 (-.f64 1 cosTheta) cosTheta)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (cbrt.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (pow.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (PI.f64)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) -1) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64))))) (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (PI.f64))))) (pow.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (PI.f64)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2)) (cbrt.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (neg.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (PI.f64))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (PI.f64) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (PI.f64)) (.f64 2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (PI.f64)) (/.f64 2 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (PI.f64)) 0) (/.f64 1 (pow.f64 (sqrt.f64 (PI.f64)) -1)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 1 0) (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (PI.f64)) (.f64 0 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) 0))))))
((#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) cosTheta) (pow.f64 (sqrt.f64 (PI.f64)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 2)) (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) cosTheta)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (/.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) cosTheta) 2)) (sqrt.f64 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (/.f64 1 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) -1) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (cbrt.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) cosTheta) 2) (pow.f64 (sqrt.f64 (PI.f64)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (/.f64 1 (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2)) cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1)) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2)) cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (.f64 (cbrt.f64 cosTheta) (sqrt.f64 (PI.f64)))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (cbrt.f64 (pow.f64 cosTheta 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (sqrt.f64 (PI.f64))) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 2)) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1)) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -2)) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) cosTheta))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) cosTheta) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (cbrt.f64 cosTheta) (sqrt.f64 (PI.f64)))) (/.f64 1 (cbrt.f64 (pow.f64 cosTheta 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (/.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) (neg.f64 cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) cosTheta) (/.f64 -1 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) cosTheta)) (/.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) cosTheta) 2)) (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (sqrt.f64 (PI.f64))) (/.f64 -1 cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) 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(fma.f64 cosTheta 2 -1)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (pow.f64 cosTheta 2) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 3) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (.f64 (pow.f64 cosTheta 2) (+.f64 (pow.f64 (+.f64 cosTheta -1) 2) (pow.f64 cosTheta 2))))) (neg.f64 (fma.f64 cosTheta 2 -1)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (fma.f64 cosTheta 2 -1) 0) (/.f64 (neg.f64 (pow.f64 (fma.f64 cosTheta 2 -1) 3)) (+.f64 0 (+.f64 (pow.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) 2) (.f64 0 (fma.f64 cosTheta 2 -1))))) (neg.f64 (fma.f64 cosTheta 2 -1)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (-.f64 (pow.f64 (pow.f64 cosTheta 2) 2) (.f64 (pow.f64 (+.f64 cosTheta -1) 2) (neg.f64 (pow.f64 cosTheta 2))))) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 3) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 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if (!=.f64 (neg.f64 (pow.f64 cosTheta 2)) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 3) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (-.f64 (pow.f64 (pow.f64 cosTheta 2) 2) (.f64 (pow.f64 (+.f64 cosTheta -1) 2) (neg.f64 (pow.f64 cosTheta 2)))))) (neg.f64 (fma.f64 cosTheta 2 -1)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (pow.f64 (+.f64 cosTheta -1) 2) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 3) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (.f64 (pow.f64 cosTheta 2) (+.f64 (pow.f64 (+.f64 cosTheta -1) 2) (pow.f64 cosTheta 2))))) (neg.f64 (fma.f64 cosTheta 2 -1)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 0 0) (/.f64 (neg.f64 (pow.f64 (fma.f64 cosTheta 2 -1) 3)) (+.f64 0 (+.f64 (pow.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) 2) (.f64 0 (fma.f64 cosTheta 2 -1))))) (neg.f64 (fma.f64 cosTheta 2 -1)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (pow.f64 (+.f64 cosTheta -1) 2) (pow.f64 cosTheta 2)) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (pow.f64 (pow.f64 cosTheta 2) 2)) (+.f64 (pow.f64 (+.f64 cosTheta -1) 2) (pow.f64 cosTheta 2))) (neg.f64 (fma.f64 cosTheta 2 -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 cosTheta) (neg.f64 cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 cosTheta) (-.f64 (.f64 (+.f64 cosTheta -1) cosTheta) (pow.f64 cosTheta 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 cosTheta) (+.f64 (.f64 (+.f64 cosTheta -1) cosTheta) (neg.f64 (pow.f64 cosTheta 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 cosTheta -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 cosTheta) (-.f64 1 cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 cosTheta) (.f64 (+.f64 cosTheta -1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) (.f64 0 (neg.f64 (fma.f64 cosTheta 2 -1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) (.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (.f64 cosTheta -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (+.f64 cosTheta -1) -1) (neg.f64 cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (.f64 (.f64 cosTheta -2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (neg.f64 (fma.f64 cosTheta 2 -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (+.f64 cosTheta -1) 2) (neg.f64 (pow.f64 cosTheta 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 cosTheta 2)) (pow.f64 (+.f64 cosTheta -1) 2))))))

simplify4.4s (5%)

Algorithm

1×

egglog

Counts

257 → 317

Calls

Call 1

Inputs
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (*.f64 -1/2 (/.f64 (pow.f64 cosTheta 2) (sqrt.f64 (PI.f64)))))) (/.f64 1 (sqrt.f64 (PI.f64))))
(/.f64 1 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1))
(+.f64 (/.f64 1 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1)) (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))
(+.f64 (/.f64 1 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1)) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 c 3) (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)))) (+.f64 (/.f64 1 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1)) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))))
(/.f64 1 c)
(+.f64 (/.f64 1 c) (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 1 c) 2))))
(+.f64 (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)) (+.f64 (/.f64 1 c) (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 1 c) 2)))))
(+.f64 (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)) (+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 1 c) 2))) (.f64 -1 (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 1 c) 4)))))))
(/.f64 1 c)
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (/.f64 1 c))
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (/.f64 1 c)))
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (+.f64 (.f64 -1 (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 4)))) (/.f64 1 c))))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64)))))) (.f64 -1 (.f64 (+.f64 (.f64 1/2 (sqrt.f64 (PI.f64))) (+.f64 (.f64 3/2 (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))) (pow.f64 cosTheta 4))))))
(/.f64 1 (+.f64 c 1))
(/.f64 1 (+.f64 c 1))
1
(+.f64 1 (*.f64 -2 cosTheta))
(+.f64 1 (*.f64 -2 cosTheta))
(+.f64 1 (*.f64 -2 cosTheta))
(*.f64 -2 cosTheta)
(+.f64 1 (*.f64 -2 cosTheta))
(+.f64 1 (*.f64 -2 cosTheta))
(+.f64 1 (*.f64 -2 cosTheta))
(*.f64 -2 cosTheta)
(+.f64 1 (*.f64 -2 cosTheta))
(+.f64 1 (*.f64 -2 cosTheta))
(+.f64 1 (*.f64 -2 cosTheta))
(fabs.f64 (sqrt.f64 (PI.f64)))
(*.f64 (neg.f64 (cbrt.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2))))
(*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (pow.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (PI.f64)))) 2)))
(*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) -1) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) -1))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64))))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64))))))
(*.f64 (neg.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (PI.f64))))) (pow.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (PI.f64)))) 2))
(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2)) (cbrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2)))
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 1 (sqrt.f64 (PI.f64)))
(*.f64 -1 (neg.f64 (sqrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) 1)
(-.f64 0 (neg.f64 (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (PI.f64)) 1)
(/.f64 (neg.f64 (sqrt.f64 (PI.f64))) -1)
(sqrt.f64 (PI.f64))
(sqrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2))
(pow.f64 (PI.f64) 1/2)
(pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) 1/3)
(pow.f64 (sqrt.f64 (PI.f64)) (*.f64 2 1/2))
(pow.f64 (sqrt.f64 (PI.f64)) (/.f64 2 2))
(pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) 1/2)
(pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2)
(pow.f64 (sqrt.f64 (PI.f64)) 1)
(cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) 1))
(neg.f64 (neg.f64 (sqrt.f64 (PI.f64))))
(if (!=.f64 (sqrt.f64 (PI.f64)) 0) (/.f64 1 (pow.f64 (sqrt.f64 (PI.f64)) -1)) (sqrt.f64 (PI.f64)))
(if (!=.f64 1 0) (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(+.f64 (sqrt.f64 (PI.f64)) (*.f64 0 (sqrt.f64 (PI.f64))))
(+.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) 0))
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(+.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) (*.f64 0 (neg.f64 (fma.f64 cosTheta 2 -1))))
(+.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) (*.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) 0))
(+.f64 1 (*.f64 cosTheta -2))
(+.f64 (*.f64 (+.f64 cosTheta -1) -1) (neg.f64 cosTheta))
(+.f64 1 (.f64 (.f64 cosTheta -2) 1))
(+.f64 0 (neg.f64 (fma.f64 cosTheta 2 -1)))
(+.f64 (pow.f64 (+.f64 cosTheta -1) 2) (neg.f64 (pow.f64 cosTheta 2)))
(+.f64 (neg.f64 (pow.f64 cosTheta 2)) (pow.f64 (+.f64 cosTheta -1) 2))

Outputs
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (*.f64 -1/2 (/.f64 (pow.f64 cosTheta 2) (sqrt.f64 (PI.f64)))))) (/.f64 1 (sqrt.f64 (PI.f64))))
(-.f64 (fma.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (/.f64 (.f64 -1/2 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64))))) (pow.f64 (sqrt.f64 (PI.f64)) -1))
(/.f64 1 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1))
(pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (exp.f64 (pow.f64 cosTheta 2))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1)
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(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
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(if (!=.f64 (-.f64 1 cosTheta) 0) (*.f64 (-.f64 1 cosTheta) (+.f64 1 (/.f64 cosTheta (+.f64 cosTheta -1)))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (-.f64 1 cosTheta) 0) (*.f64 (-.f64 1 cosTheta) (+.f64 (/.f64 cosTheta (-.f64 cosTheta 1)) 1)) (fma.f64 cosTheta -2 1))
(if (!=.f64 (pow.f64 (+.f64 cosTheta -1) 2) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 3) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (-.f64 (pow.f64 (pow.f64 cosTheta 2) 2) (*.f64 (pow.f64 (+.f64 cosTheta -1) 2) (neg.f64 (pow.f64 cosTheta 2)))))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (pow.f64 (-.f64 cosTheta 1) 2) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 1 cosTheta) 3) 2) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (+.f64 (pow.f64 cosTheta 4) (pow.f64 (*.f64 cosTheta (-.f64 cosTheta 1)) 2)) (pow.f64 (pow.f64 (-.f64 cosTheta 1) 2) 2))) (fma.f64 cosTheta -2 1))
(if (!=.f64 (+.f64 0 (fma.f64 cosTheta 2 -1)) 0) (/.f64 (-.f64 0 (pow.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) 2)) (+.f64 0 (fma.f64 cosTheta 2 -1))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (fma.f64 cosTheta 2 -1) 0) (/.f64 (pow.f64 (fma.f64 cosTheta 2 -1) 2) (fma.f64 cosTheta -2 1)) (fma.f64 cosTheta -2 1))
(if (!=.f64 (-.f64 1 (.f64 cosTheta -2)) 0) (/.f64 (-.f64 1 (.f64 (.f64 cosTheta -2) (.f64 cosTheta -2))) (-.f64 1 (*.f64 cosTheta -2))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (-.f64 (.f64 cosTheta 2) -1) 0) (/.f64 (-.f64 (.f64 (pow.f64 cosTheta 2) 4) 1) (-.f64 (*.f64 cosTheta -2) 1)) (fma.f64 cosTheta -2 1))
(if (!=.f64 (-.f64 (neg.f64 cosTheta) (-.f64 1 cosTheta)) 0) (/.f64 (fma.f64 cosTheta 2 -1) (-.f64 (neg.f64 cosTheta) (-.f64 1 cosTheta))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 -1 0) (fma.f64 cosTheta -2 1) (fma.f64 cosTheta -2 1))
(if (!=.f64 (-.f64 (pow.f64 (+.f64 cosTheta -1) 2) (neg.f64 (pow.f64 cosTheta 2))) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (pow.f64 (pow.f64 cosTheta 2) 2)) (-.f64 (pow.f64 (+.f64 cosTheta -1) 2) (neg.f64 (pow.f64 cosTheta 2)))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (+.f64 (pow.f64 (-.f64 cosTheta 1) 2) (pow.f64 cosTheta 2)) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 cosTheta 1) 2) 2) (pow.f64 cosTheta 4)) (+.f64 (pow.f64 (-.f64 cosTheta 1) 2) (pow.f64 cosTheta 2))) (fma.f64 cosTheta -2 1))
(if (!=.f64 (neg.f64 cosTheta) 0) (*.f64 (neg.f64 cosTheta) (+.f64 1 (/.f64 (-.f64 1 cosTheta) (neg.f64 cosTheta)))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (neg.f64 cosTheta) 0) (*.f64 (neg.f64 cosTheta) (+.f64 1 (/.f64 (-.f64 cosTheta 1) cosTheta))) (fma.f64 cosTheta -2 1))
(if (!=.f64 (pow.f64 (+.f64 cosTheta -1) 2) 0) (*.f64 (pow.f64 (+.f64 cosTheta -1) 2) (+.f64 1 (/.f64 (neg.f64 (pow.f64 cosTheta 2)) (pow.f64 (+.f64 cosTheta -1) 2)))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (pow.f64 (-.f64 cosTheta 1) 2) 0) (*.f64 (pow.f64 (-.f64 cosTheta 1) 2) (-.f64 1 (/.f64 (pow.f64 cosTheta 2) (pow.f64 (-.f64 cosTheta 1) 2)))) (fma.f64 cosTheta -2 1))
(if (!=.f64 (pow.f64 cosTheta 2) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 3) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (*.f64 (pow.f64 cosTheta 2) (+.f64 (pow.f64 (+.f64 cosTheta -1) 2) (pow.f64 cosTheta 2))))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (pow.f64 cosTheta 2) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 1 cosTheta) 3) 2) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (+.f64 (pow.f64 cosTheta 4) (pow.f64 (*.f64 cosTheta (-.f64 cosTheta 1)) 2)) (pow.f64 (pow.f64 (-.f64 cosTheta 1) 2) 2))) (fma.f64 cosTheta -2 1))
(if (!=.f64 (fma.f64 cosTheta 2 -1) 0) (/.f64 (neg.f64 (pow.f64 (fma.f64 cosTheta 2 -1) 3)) (+.f64 0 (+.f64 (pow.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) 2) (*.f64 0 (fma.f64 cosTheta 2 -1))))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (fma.f64 cosTheta 2 -1) 0) (/.f64 (pow.f64 (fma.f64 cosTheta 2 -1) 2) (fma.f64 cosTheta -2 1)) (fma.f64 cosTheta -2 1))
(if (!=.f64 (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (-.f64 (pow.f64 (pow.f64 cosTheta 2) 2) (.f64 (pow.f64 (+.f64 cosTheta -1) 2) (neg.f64 (pow.f64 cosTheta 2))))) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 3) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (-.f64 (pow.f64 (pow.f64 cosTheta 2) 2) (.f64 (pow.f64 (+.f64 cosTheta -1) 2) (neg.f64 (pow.f64 cosTheta 2)))))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (+.f64 (+.f64 (pow.f64 cosTheta 4) (pow.f64 (.f64 cosTheta (-.f64 cosTheta 1)) 2)) (pow.f64 (pow.f64 (-.f64 cosTheta 1) 2) 2)) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 1 cosTheta) 3) 2) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (+.f64 (pow.f64 cosTheta 4) (pow.f64 (.f64 cosTheta (-.f64 cosTheta 1)) 2)) (pow.f64 (pow.f64 (-.f64 cosTheta 1) 2) 2))) (fma.f64 cosTheta -2 1))
(if (!=.f64 (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (.f64 (pow.f64 cosTheta 2) (+.f64 (pow.f64 (+.f64 cosTheta -1) 2) (pow.f64 cosTheta 2)))) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 3) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (.f64 (pow.f64 cosTheta 2) (+.f64 (pow.f64 (+.f64 cosTheta -1) 2) (pow.f64 cosTheta 2))))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (+.f64 (+.f64 (pow.f64 cosTheta 4) (pow.f64 (.f64 cosTheta (-.f64 cosTheta 1)) 2)) (pow.f64 (pow.f64 (-.f64 cosTheta 1) 2) 2)) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 1 cosTheta) 3) 2) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (+.f64 (pow.f64 cosTheta 4) (pow.f64 (.f64 cosTheta (-.f64 cosTheta 1)) 2)) (pow.f64 (pow.f64 (-.f64 cosTheta 1) 2) 2))) (fma.f64 cosTheta -2 1))
(if (!=.f64 (+.f64 0 (+.f64 (pow.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) 2) (.f64 0 (fma.f64 cosTheta 2 -1)))) 0) (/.f64 (neg.f64 (pow.f64 (fma.f64 cosTheta 2 -1) 3)) (+.f64 0 (+.f64 (pow.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) 2) (.f64 0 (fma.f64 cosTheta 2 -1))))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (pow.f64 (fma.f64 cosTheta 2 -1) 2) 0) (/.f64 (pow.f64 (fma.f64 cosTheta 2 -1) 2) (fma.f64 cosTheta -2 1)) (fma.f64 cosTheta -2 1))
(if (!=.f64 (neg.f64 (pow.f64 cosTheta 2)) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 3) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (-.f64 (pow.f64 (pow.f64 cosTheta 2) 2) (*.f64 (pow.f64 (+.f64 cosTheta -1) 2) (neg.f64 (pow.f64 cosTheta 2)))))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (neg.f64 (pow.f64 cosTheta 2)) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 1 cosTheta) 3) 2) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (+.f64 (pow.f64 cosTheta 4) (pow.f64 (*.f64 cosTheta (-.f64 cosTheta 1)) 2)) (pow.f64 (pow.f64 (-.f64 cosTheta 1) 2) 2))) (fma.f64 cosTheta -2 1))
(if (!=.f64 (pow.f64 (+.f64 cosTheta -1) 2) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 3) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (*.f64 (pow.f64 cosTheta 2) (+.f64 (pow.f64 (+.f64 cosTheta -1) 2) (pow.f64 cosTheta 2))))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (pow.f64 (-.f64 cosTheta 1) 2) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 1 cosTheta) 3) 2) (pow.f64 (pow.f64 cosTheta 3) 2)) (+.f64 (+.f64 (pow.f64 cosTheta 4) (pow.f64 (*.f64 cosTheta (-.f64 cosTheta 1)) 2)) (pow.f64 (pow.f64 (-.f64 cosTheta 1) 2) 2))) (fma.f64 cosTheta -2 1))
(if (!=.f64 0 0) (/.f64 (neg.f64 (pow.f64 (fma.f64 cosTheta 2 -1) 3)) (+.f64 0 (+.f64 (pow.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) 2) (*.f64 0 (fma.f64 cosTheta 2 -1))))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 0 0) (/.f64 (pow.f64 (fma.f64 cosTheta 2 -1) 2) (fma.f64 cosTheta -2 1)) (fma.f64 cosTheta -2 1))
(if (!=.f64 (+.f64 (pow.f64 (+.f64 cosTheta -1) 2) (pow.f64 cosTheta 2)) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 cosTheta -1) 2) 2) (pow.f64 (pow.f64 cosTheta 2) 2)) (+.f64 (pow.f64 (+.f64 cosTheta -1) 2) (pow.f64 cosTheta 2))) (neg.f64 (fma.f64 cosTheta 2 -1)))
(if (!=.f64 (+.f64 (pow.f64 (-.f64 cosTheta 1) 2) (pow.f64 cosTheta 2)) 0) (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 cosTheta 1) 2) 2) (pow.f64 cosTheta 4)) (+.f64 (pow.f64 (-.f64 cosTheta 1) 2) (pow.f64 cosTheta 2))) (fma.f64 cosTheta -2 1))
(+.f64 (-.f64 1 cosTheta) (neg.f64 cosTheta))
(fma.f64 cosTheta -2 1)
(+.f64 (-.f64 1 cosTheta) (-.f64 (*.f64 (+.f64 cosTheta -1) cosTheta) (pow.f64 cosTheta 2)))
(fma.f64 cosTheta -2 1)
(+.f64 (-.f64 1 cosTheta) (+.f64 (*.f64 (+.f64 cosTheta -1) cosTheta) (neg.f64 (pow.f64 cosTheta 2))))
(fma.f64 cosTheta -2 1)
(+.f64 (*.f64 cosTheta -2) 1)
(fma.f64 cosTheta -2 1)
(+.f64 (neg.f64 cosTheta) (-.f64 1 cosTheta))
(fma.f64 cosTheta -2 1)
(+.f64 (neg.f64 cosTheta) (*.f64 (+.f64 cosTheta -1) -1))
(fma.f64 cosTheta -2 1)
(+.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) (*.f64 0 (neg.f64 (fma.f64 cosTheta 2 -1))))
(fma.f64 cosTheta -2 1)
(+.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) (*.f64 (neg.f64 (fma.f64 cosTheta 2 -1)) 0))
(fma.f64 cosTheta -2 1)
(+.f64 1 (*.f64 cosTheta -2))
(fma.f64 cosTheta -2 1)
(+.f64 (*.f64 (+.f64 cosTheta -1) -1) (neg.f64 cosTheta))
(fma.f64 cosTheta -2 1)
(+.f64 1 (.f64 (.f64 cosTheta -2) 1))
(fma.f64 cosTheta -2 1)
(+.f64 0 (neg.f64 (fma.f64 cosTheta 2 -1)))
(fma.f64 cosTheta -2 1)
(+.f64 (pow.f64 (+.f64 cosTheta -1) 2) (neg.f64 (pow.f64 cosTheta 2)))
(fma.f64 cosTheta -2 1)
(+.f64 (neg.f64 (pow.f64 cosTheta 2)) (pow.f64 (+.f64 cosTheta -1) 2))
(fma.f64 cosTheta -2 1)

localize86.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
✓	0.2b	(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)
✓	0.3b	(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 97 to 65 computations (33% saved)

series84.0ms (0.1%)

Counts

3 → 20

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	cosTheta	@	inf	(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)
2.0ms	cosTheta	@	-inf	(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)
2.0ms	c	@	-inf	(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)
1.0ms	c	@	0	(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)
1.0ms	cosTheta	@	inf	(*.f64 (sqrt.f64 (PI.f64)) cosTheta)

Compiler

Compiled 10220 to 7285 computations (28.7% saved)

rewrite1.5s (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

84×	`egg-rr`
33×	`egg-rr`
26×	`egg-rr`

Counts

3 → 143

Calls

Call 1

Inputs

(*.f64 (sqrt.f64 (PI.f64)) cosTheta)

(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)

(/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2/3) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 cosTheta) (.f64 (cbrt.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 cosTheta (cbrt.f64 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)) (neg.f64 (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64)))) (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 cosTheta (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (PI.f64)) cosTheta)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2)) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 cosTheta) (neg.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 cosTheta)) (cbrt.f64 (pow.f64 cosTheta 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 cosTheta (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 0) (/.f64 1 (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))) (.f64 cosTheta (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 1 0) (.f64 cosTheta (sqrt.f64 (PI.f64))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))))))
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Outputs

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(/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (/.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 2/3) 0) (/.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (/.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 2/3))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 0) (/.f64 1 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) -1)) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))))))

simplify3.6s (4%)

Algorithm

1×

egglog

Counts

163 → 202

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64)))))) (.f64 -1 (.f64 (+.f64 (.f64 1/2 (sqrt.f64 (PI.f64))) (+.f64 (.f64 3/2 (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))) (pow.f64 cosTheta 4))))))
(/.f64 1 (+.f64 c 1))
(/.f64 1 (+.f64 c 1))
(/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))
(+.f64 (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)))))
(+.f64 (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 c 3) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2)))) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (+.f64 (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))
(/.f64 1 c)
(+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (/.f64 1 c))
(+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (+.f64 (/.f64 1 c) (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))))
(+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (+.f64 (/.f64 1 c) (+.f64 (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)) (.f64 -1 (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (.f64 (pow.f64 (/.f64 1 c) 4) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))))
(/.f64 1 c)
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (/.f64 1 c))
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)))))
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 4) (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))))))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (*.f64 -1/2 (/.f64 (pow.f64 cosTheta 2) (sqrt.f64 (PI.f64)))))) (/.f64 1 (sqrt.f64 (PI.f64))))
(.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta))
(.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2/3) cosTheta))
(.f64 (cbrt.f64 cosTheta) (.f64 (cbrt.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64))))
(.f64 (.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 cosTheta (cbrt.f64 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2/3))
(.f64 (cbrt.f64 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)) (neg.f64 (cbrt.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 2))))
(.f64 (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64)))) (cbrt.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(*.f64 cosTheta (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 cosTheta))
(.f64 (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2)) (cbrt.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64)))))
(*.f64 (neg.f64 cosTheta) (neg.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 cosTheta)) (cbrt.f64 (pow.f64 cosTheta 2)))
(.f64 -1 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta))
(.f64 1 (.f64 cosTheta (sqrt.f64 (PI.f64))))
(.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 1)
(-.f64 0 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta) -1)
(/.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 1)
(pow.f64 (cbrt.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3)
(pow.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 3) 1/3)
(pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 1)
(cbrt.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 3))
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 0) (/.f64 1 (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))) (.f64 cosTheta (sqrt.f64 (PI.f64))))
(if (!=.f64 1 0) (.f64 cosTheta (sqrt.f64 (PI.f64))) (.f64 cosTheta (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c)) -1)) (/.f64 1 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c)) 2))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c)) -1)) 2) (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c)) -1)))
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(.f64 -1 (/.f64 -1 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c))))
(.f64 (/.f64 -1 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c))) -1)
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(/.f64 (*.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) cosTheta) 1) (sqrt.f64 (PI.f64)))
(/.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))))) 1) (cbrt.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (cbrt.f64 cosTheta) (sqrt.f64 (PI.f64)))) 1) (cbrt.f64 (pow.f64 cosTheta 2)))
(/.f64 (*.f64 (pow.f64 cosTheta -1) (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (sqrt.f64 (PI.f64)))
(/.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))) (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) cosTheta) (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))))) (sqrt.f64 (PI.f64)))
(/.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64))))) (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 2/3)) (cbrt.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) cosTheta) (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 2/3)) (sqrt.f64 (PI.f64)))
(/.f64 (.f64 (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))))) (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))))) (cbrt.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64)))))) (neg.f64 (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2))))
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)) -1)
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 1)
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))) 3)
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 1)
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3))
(neg.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)))
(neg.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) (neg.f64 cosTheta)))
(neg.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) -1))
(neg.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)) 1))
(if (!=.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 0) (/.f64 1 (/.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))))
(if (!=.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (/.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))))
(if (!=.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 2/3) 0) (/.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (/.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 2/3))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))))
(if (!=.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) 0) (/.f64 1 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) -1)) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))

Outputs
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))
(-.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 (*.f64 (pow.f64 cosTheta 2) (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))
(-.f64 (-.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 (.f64 (pow.f64 cosTheta 2) (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 (pow.f64 cosTheta 3) (-.f64 (.f64 (sqrt.f64 (PI.f64)) -3/2) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) (pow.f64 (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1)) 2)))))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64)))))) (.f64 -1 (.f64 (+.f64 (.f64 1/2 (sqrt.f64 (PI.f64))) (+.f64 (.f64 3/2 (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))) (pow.f64 cosTheta 4))))))
(-.f64 (-.f64 (-.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 (pow.f64 cosTheta 3) (-.f64 (.f64 (sqrt.f64 (PI.f64)) -3/2) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) (pow.f64 (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1)) 2))))) (.f64 (fma.f64 1/2 (sqrt.f64 (PI.f64)) (-.f64 (.f64 (.f64 3/2 (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1))) (pow.f64 (sqrt.f64 (PI.f64)) 2)) (.f64 (sqrt.f64 (PI.f64)) (.f64 (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1)) (-.f64 (.f64 (sqrt.f64 (PI.f64)) -3/2) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) (pow.f64 (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1)) 2))))))) (pow.f64 cosTheta 4))) (.f64 (*.f64 (pow.f64 cosTheta 2) (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))
(/.f64 1 (+.f64 c 1))
(/.f64 1 (-.f64 c -1))
(/.f64 1 (+.f64 c 1))
(/.f64 1 (-.f64 c -1))
(/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))
(pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1)
(+.f64 (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)))))
(-.f64 (pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1) (/.f64 c (pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)))
(+.f64 (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))))
(+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 c 2) (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))) (neg.f64 c)) (pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)) (pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1))
(+.f64 (.f64 -1 (/.f64 (pow.f64 c 3) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2)))) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (+.f64 (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))
(-.f64 (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 c 2) (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))) (neg.f64 c)) (pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)) (pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1)) (/.f64 (pow.f64 c 3) (pow.f64 (pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) 2)))
(/.f64 1 c)
(pow.f64 c -1)
(+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (/.f64 1 c))
(-.f64 (pow.f64 c -1) (.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (pow.f64 c -1) 2)))
(+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (+.f64 (/.f64 1 c) (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))))
(+.f64 (-.f64 (pow.f64 c -1) (.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (pow.f64 c -1) 2))) (/.f64 (pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (pow.f64 c 3)))
(+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (+.f64 (/.f64 1 c) (+.f64 (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)) (.f64 -1 (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (.f64 (pow.f64 (/.f64 1 c) 4) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))))
(-.f64 (+.f64 (-.f64 (pow.f64 c -1) (.f64 (pow.f64 (pow.f64 c -1) 4) (pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 3))) (/.f64 (pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (pow.f64 c 3))) (.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (pow.f64 c -1) 2)))
(/.f64 1 c)
(pow.f64 c -1)
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(-.f64 (pow.f64 c -1) (.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (exp.f64 (pow.f64 cosTheta 2))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (pow.f64 c -1) 2)))
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)))))
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(/.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 2/3) (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))) (cbrt.f64 cosTheta))
(/.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) 2/3)) (.f64 (cbrt.f64 cosTheta) (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) cosTheta) 2))))
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(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (cbrt.f64 cosTheta) (sqrt.f64 (PI.f64)))) (cbrt.f64 (pow.f64 cosTheta 2)))
(/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) (.f64 (sqrt.f64 (PI.f64)) (*.f64 (cbrt.f64 cosTheta) (cbrt.f64 (pow.f64 cosTheta 2)))))
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(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 cosTheta))
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
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(/.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (pow.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) 2/3)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 (*.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) cosTheta) 1) (sqrt.f64 (PI.f64)))
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(/.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))))) 1) (cbrt.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
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(/.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))) (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) cosTheta) (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64))))) (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 2/3)) (cbrt.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) 2/3)) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) 2)))
(/.f64 (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) cosTheta) (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 2/3)) (sqrt.f64 (PI.f64)))
(/.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (pow.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) 2/3)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 (.f64 (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))))) (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))))) (cbrt.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64)))))) (neg.f64 (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2))))
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(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 1)
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))) 3)
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3) 1/3)
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
(pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 1)
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3))
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
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(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
(neg.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) (neg.f64 cosTheta)))
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
(neg.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) -1))
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
(neg.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)) 1))
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64)))
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(if (!=.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 2/3) 0) (/.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1)))) (/.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) 2/3))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))))
(if (!=.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) 2/3) 0) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (pow.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) 2/3))) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64))))
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(if (!=.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64))) 0) (/.f64 -1 (/.f64 -1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64))))) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64))))

eval411.0ms (0.5%)

Compiler: Compiled 20492 to 13748 computations (32.9% saved)

prune132.0ms (0.2%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	531	21	552
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	532	22	554

Error

0.0b

Counts

554 → 22

Alt Table

Click to see full alt table

Status	Error	Program
	41.9b	(if (!=.f64 (+.f64 1 (.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) cosTheta)) (+.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) cosTheta)) -1))) 0) (/.f64 (+.f64 1 (.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) cosTheta)) (+.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) cosTheta)) -1))) (-.f64 (pow.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) cosTheta)) 3) -1)) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) -1))
	1.6b	(if (!=.f64 (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64))) (-.f64 c -1))) 0) (pow.f64 (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64))) (-.f64 c -1))) -3) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64))) (-.f64 c -1)) -1))
	0.4b	(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2) cosTheta)) (+.f64 1 c)) -1)
	41.2b	(pow.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) 3) -1) 1/3)
	1.5b	(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)) 3)
	28.4b	(/.f64 (/.f64 1 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c)) 2))) (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c))))
	28.4b	(/.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c)))) (neg.f64 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c)) 2))))
	60.5b	(/.f64 1 (-.f64 c -1))
	0.4b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
	0.6b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
▶	0.3b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
	2.4b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
✓	0.5b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
▶	0.5b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
	2.4b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 1) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
	39.8b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 3)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
	0.5b	(/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))
▶	62.4b	(/.f64 1 c)
	1.1b	(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64)))))) (.f64 -1 (.f64 (+.f64 (.f64 1/2 (sqrt.f64 (PI.f64))) (+.f64 (.f64 3/2 (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))) (pow.f64 cosTheta 4))))))
	2.4b	(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
▶	39.9b	(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 3) -1))
▶	38.9b	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) -1) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 2)))

Compiler

Compiled 1623 to 1249 computations (23% saved)

localize46.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64)))
✓	0.1b	(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta)
✓	0.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 120 to 69 computations (42.5% saved)

series95.0ms (0.1%)

Counts

3 → 22

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	c	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	cosTheta	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	cosTheta	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
0.0ms	cosTheta	@	inf	(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta)
0.0ms	cosTheta	@	inf	(/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64)))

Compiler

Compiled 12400 to 8785 computations (29.2% saved)

rewrite1.5s (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

57×	`egg-rr`
53×	`egg-rr`
34×	`egg-rr`

Counts

3 → 144

Calls

Call 1

Inputs
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta)
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64)))

Inputs

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta)

(/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64)))

Outputs
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(neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1)) 2) (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1)) (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 -1 (fma.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1 (fma.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (.f64 cosTheta 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Outputs

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simplify3.7s (4.2%)

Algorithm

1×

egglog

Counts

166 → 216

Calls

Call 1

Inputs
(/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))
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(/.f64 1 c)
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(/.f64 1 c)
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(/.f64 1 (+.f64 c 1))
(/.f64 1 (+.f64 c 1))
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(*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (/.f64 1 (pow.f64 (sqrt.f64 (PI.f64)) 2/3)))
(*.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) -1))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64))))) (neg.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64))))) 2)))
(.f64 (.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (*.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (sqrt.f64 (sqrt.f64 (PI.f64))))))
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(.f64 (.f64 (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) 1) (*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) 1))
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(.f64 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))))) (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) -1)) (*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))))) (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) -1)))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 -1 (sqrt.f64 (sqrt.f64 (PI.f64))))) (*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 -1 (sqrt.f64 (sqrt.f64 (PI.f64))))))
(.f64 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))))) (/.f64 -1 (sqrt.f64 (sqrt.f64 (PI.f64))))) (*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))))) (/.f64 -1 (sqrt.f64 (sqrt.f64 (PI.f64))))))
(*.f64 (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))))) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64))))) 2))
(*.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (pow.f64 (sqrt.f64 (PI.f64)) -1))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64)))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 2)))
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(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 2)) (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 2/3) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))))
(*.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 -1 (sqrt.f64 (PI.f64))))
(*.f64 (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))) (neg.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 2))))
(*.f64 -1 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))) -1)
(*.f64 1 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 1)
(-.f64 (/.f64 0 (neg.f64 (sqrt.f64 (PI.f64)))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))))
(-.f64 0 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (cbrt.f64 (sqrt.f64 (PI.f64))))) (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2/3)))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (neg.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (neg.f64 (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2/3))
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))) -1)
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 1)
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64)))) 3)
(pow.f64 (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) 2)
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 1)
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 3) 1))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))) 3) -1))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 3))
(neg.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))))
(if (!=.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(if (!=.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 0) (/.f64 1 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(if (!=.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 2/3) 0) (/.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 2/3))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(if (!=.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 0) (/.f64 1 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) -1)) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(if (!=.f64 -1 0) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(if (!=.f64 1 0) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))

Outputs
(/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))
(pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1)
(+.f64 (/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))) (.f64 -1 (/.f64 c (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1)))))
(-.f64 (pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1) (/.f64 c (pow.f64 (+.f64 1 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (exp.f64 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)))
(+.f64 (/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (.f64 -1 (/.f64 c (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1))))))
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(/.f64 1 c)
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(/.f64 1 c)
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(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(*.f64 (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))) (neg.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 2))))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(*.f64 -1 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))) -1)
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(*.f64 1 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 1)
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(-.f64 (/.f64 0 (neg.f64 (sqrt.f64 (PI.f64)))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(-.f64 0 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (cbrt.f64 (sqrt.f64 (PI.f64))))) (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2/3)))
(/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (pow.f64 (sqrt.f64 (PI.f64)) 2/3)))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (neg.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (neg.f64 (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2/3))
(/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (pow.f64 (sqrt.f64 (PI.f64)) 2/3)))
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))) -1)
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 1)
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64)))) 3)
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(pow.f64 (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) 2)
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 3) 1/3)
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 1)
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 3) 1))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))) 3) -1))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 3))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(neg.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (neg.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(if (!=.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(if (!=.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2)))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2)))) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2)))))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))))
(if (!=.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 0) (/.f64 1 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(if (!=.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) 0) (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (-.f64 1 (.f64 cosTheta 2)))) -1) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64))))
(if (!=.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 2/3) 0) (/.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 2/3))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(if (!=.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) 2/3) 0) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2)))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) 2/3))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))))
(if (!=.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 0) (/.f64 1 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) -1)) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(if (!=.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) 0) (/.f64 -1 (/.f64 -1 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64))))
(if (!=.f64 -1 0) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(if (!=.f64 -1 0) (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))))
(if (!=.f64 1 0) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))))
(if (!=.f64 1 0) (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))))

localize3.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

localize44.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)
✓	0.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
✓	0.4b	(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta))
	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 128 to 61 computations (52.3% saved)

series116.0ms (0.1%)

Counts

3 → 24

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	cosTheta	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
0.0ms	cosTheta	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
0.0ms	c	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
0.0ms	cosTheta	@	-inf	(/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)
0.0ms	cosTheta	@	-inf	(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta))

Compiler

Compiled 12170 to 8855 computations (27.2% saved)

rewrite1.6s (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

62×	`egg-rr`
34×	`egg-rr`
32×	`egg-rr`

Counts

3 → 128

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)

Inputs

(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta))

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

(/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)

Outputs
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Outputs

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(#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) cosTheta) 1))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 0) (pow.f64 (/.f64 cosTheta (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) -1) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 cosTheta (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 2)) 0) (/.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) 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simplify3.6s (4.1%)

Algorithm

1×

egglog

Counts

152 → 202

Calls

Call 1

Inputs
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (*.f64 -1/2 (/.f64 (pow.f64 cosTheta 2) (sqrt.f64 (PI.f64)))))) (/.f64 1 (sqrt.f64 (PI.f64))))
(/.f64 1 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1))
(+.f64 (/.f64 1 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1)) (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))
(+.f64 (/.f64 1 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1)) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 c 3) (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)))) (+.f64 (/.f64 1 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1)) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))))
(/.f64 1 c)
(+.f64 (/.f64 1 c) (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 1 c) 2))))
(+.f64 (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)) (+.f64 (/.f64 1 c) (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 1 c) 2)))))
(+.f64 (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)) (+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 1 c) 2))) (.f64 -1 (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 1 c) 4)))))))
(/.f64 1 c)
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (/.f64 1 c))
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (/.f64 1 c)))
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(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
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(/.f64 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)) (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) 2)))
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(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)) 3)
(pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1) 1)
(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)
(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) 3) -1))
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(neg.f64 (.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1) -1))
(neg.f64 (.f64 (/.f64 1 (-.f64 -1 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (pow.f64 cosTheta 2)))))) 1))
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(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta)) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 2)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 2)) (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta)))
(*.f64 (cbrt.f64 (pow.f64 cosTheta -1)) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (cbrt.f64 (pow.f64 cosTheta 2))))
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (cbrt.f64 cosTheta)) (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (cbrt.f64 (pow.f64 cosTheta 2))))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta)) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 2) (pow.f64 cosTheta 2))))
(*.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 2)) cosTheta))
(*.f64 1 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta))
(*.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 1)
(*.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (pow.f64 cosTheta -1))
(*.f64 (pow.f64 cosTheta -1) (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))))
(*.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (cbrt.f64 cosTheta)) (/.f64 1 (cbrt.f64 (pow.f64 cosTheta 2))))
(*.f64 -1 (/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) cosTheta))
(*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) cosTheta))
(*.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 -1 cosTheta))
(-.f64 (/.f64 0 (neg.f64 cosTheta)) (/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) cosTheta))
(-.f64 0 (/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) cosTheta))
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 1)
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta)
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (neg.f64 cosTheta))
(/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (cbrt.f64 cosTheta)) (cbrt.f64 (pow.f64 cosTheta 2)))
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) cosTheta) -1)
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (cbrt.f64 cosTheta))) (neg.f64 (cbrt.f64 (pow.f64 cosTheta 2))))
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta)) 3)
(pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 1)
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 3) 1/3)
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 3))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 3) 1))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) cosTheta))
(neg.f64 (/.f64 (/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) cosTheta) 1))
(if (!=.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 0) (pow.f64 (/.f64 cosTheta (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) -1) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta))
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(if (!=.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 2)) 0) (/.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 cosTheta (cbrt.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 2)))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta))
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Outputs
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta)
(-.f64 (+.f64 (.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (*.f64 -1/2 (/.f64 (pow.f64 cosTheta 2) (sqrt.f64 (PI.f64)))))) (/.f64 1 (sqrt.f64 (PI.f64))))
(-.f64 (fma.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (/.f64 (.f64 -1/2 (.f64 cosTheta cosTheta)) (sqrt.f64 (PI.f64))))) (/.f64 1 (sqrt.f64 (PI.f64))))
(/.f64 1 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1))
(/.f64 1 (-.f64 (/.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) (pow.f64 (exp.f64 cosTheta) cosTheta)) (sqrt.f64 (PI.f64))) cosTheta) -1))
(+.f64 (/.f64 1 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1)) (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))
(-.f64 (/.f64 1 (-.f64 (/.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (pow.f64 (exp.f64 cosTheta) cosTheta)) (sqrt.f64 (PI.f64))) cosTheta) -1)) (/.f64 c (pow.f64 (-.f64 (/.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (pow.f64 (exp.f64 cosTheta) cosTheta)) (sqrt.f64 (PI.f64))) cosTheta) -1) 2)))
(+.f64 (/.f64 1 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1)) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))))))
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(/.f64 1 c)
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(/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (cbrt.f64 cosTheta)) (cbrt.f64 (.f64 cosTheta cosTheta)))
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta)) 3)
(/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta)
(pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 1)
(/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta)
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 3) 1/3)
(/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta)
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 3))
(/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta)
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 3) 1))
(/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta)
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) cosTheta))
(/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta)
(neg.f64 (/.f64 (/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) cosTheta) 1))
(/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta)
(if (!=.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 0) (pow.f64 (/.f64 cosTheta (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) -1) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta))
(if (!=.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) 0) (pow.f64 (/.f64 cosTheta (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1))) -1) (/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta))
(if (!=.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 cosTheta (sqrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta))
(if (!=.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1))) (/.f64 cosTheta (sqrt.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1))))) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta))
(if (!=.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 2)) 0) (/.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1)))) (/.f64 cosTheta (cbrt.f64 (pow.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) 2)))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta))
(if (!=.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) 2)) 0) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1))) (/.f64 cosTheta (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) 2)))) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta))
(if (!=.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) 0) (/.f64 1 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) -1)) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta))
(if (!=.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) 0) (pow.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) -1) -1) (/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta))
(if (!=.f64 1 0) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) cosTheta))
(if (!=.f64 1 0) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta))

localize77.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
✓	0.8b	(pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 3) -1)
	1.0b	(sqrt.f64 (PI.f64))
✓	38.8b	(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 3) -1))

Compiler

Compiled 137 to 92 computations (32.8% saved)

series712.0ms (0.8%)

Counts

2 → 33

Calls

12 calls:

Time	Variable		Point	Expression
16.0ms	cosTheta	@	-inf	(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 3) -1))
13.0ms	cosTheta	@	inf	(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 3) -1))
13.0ms	c	@	0	(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 3) -1))
7.0ms	cosTheta	@	0	(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 3) -1))
6.0ms	c	@	-inf	(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 3) -1))

Compiler

Compiled 93030 to 69570 computations (25.2% saved)

rewrite1.5s (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

46×	`egg-rr`
33×	`egg-rr`

Counts

2 → 79

Calls

Call 1

Inputs

(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 3) -1))

(pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 3) -1)

Outputs

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simplify3.4s (3.8%)

Algorithm

1×

egglog

Counts

112 → 152

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) 2)) 1/3) cosTheta)
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Outputs
(.f64 (pow.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) 2)) 1/3) cosTheta)
(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3)) cosTheta)
(+.f64 (.f64 -1/3 (/.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) 2) (.f64 (-.f64 (+.f64 (.f64 3 (/.f64 1 (pow.f64 (sqrt.f64 (PI.f64)) 2))) (+.f64 (.f64 2 (/.f64 c (pow.f64 (sqrt.f64 (PI.f64)) 2))) (/.f64 c (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (.f64 3 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) 2))))) (.f64 (pow.f64 cosTheta 2) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (pow.f64 (pow.f64 (pow.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) 2)) 1/3) 2) 1/3))) (.f64 (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) 2)) 1/3) cosTheta))
(fma.f64 -1/3 (/.f64 (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 4) (.f64 (-.f64 (.f64 3 (+.f64 (.f64 c (pow.f64 (sqrt.f64 (PI.f64)) -2)) (pow.f64 (sqrt.f64 (PI.f64)) -2))) (/.f64 3 (pow.f64 (sqrt.f64 (PI.f64)) 3))) (.f64 (.f64 cosTheta cosTheta) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) 3)))) (*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3)) cosTheta))
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localize75.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 2)
	0.3b	(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
	1.0b	(sqrt.f64 (PI.f64))
✓	38.8b	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) -1) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 2)))

Compiler

Compiled 197 to 131 computations (33.5% saved)

series407.0ms (0.5%)

Counts

2 → 33

Calls

12 calls:

Time	Variable		Point	Expression
16.0ms	cosTheta	@	inf	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) -1) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 2)))
9.0ms	cosTheta	@	0	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) -1) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 2)))
8.0ms	c	@	0	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) -1) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 2)))
8.0ms	cosTheta	@	-inf	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) -1) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 2)))
3.0ms	c	@	-inf	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) -1) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 2)))

Compiler

Compiled 57370 to 42890 computations (25.2% saved)

rewrite1.5s (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

48×	`egg-rr`
40×	`egg-rr`

Counts

2 → 88

Calls

Call 1

Inputs

(cbrt.f64 (/.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) -1) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 2)))

(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 2)

Outputs

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simplify3.6s (4.1%)

Algorithm

1×

egglog

Counts

121 → 165

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) 2)) 1/3) cosTheta)
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(+.f64 (*.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)) (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) c)) (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)))

Outputs
(.f64 (pow.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) 2)) 1/3) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
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(fma.f64 1/3 (.f64 (.f64 (.f64 cosTheta cosTheta) (-.f64 (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 4) (-.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 c -1))) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 4) (.f64 (.f64 2 (-.f64 (/.f64 (-.f64 c -1) (sqrt.f64 (PI.f64))) (pow.f64 (sqrt.f64 (PI.f64)) -2))) (sqrt.f64 (PI.f64)))))) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))
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(+.f64 (*.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)) (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) c)) (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)))
(pow.f64 (fma.f64 (exp.f64 (neg.f64 (.f64 cosTheta cosTheta))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 2)

eval975.0ms (1.1%)

Compiler: Compiled 61389 to 40917 computations (33.3% saved)

prune227.0ms (0.3%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	979	17	996
Fresh	14	2	16
Picked	1	0	1
Done	3	2	5
Total	997	21	1018

Error

Counts

1018 → 21

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(if (!=.f64 (.f64 (fma.f64 c c (-.f64 1 c)) cosTheta) 0) (/.f64 (.f64 (fma.f64 c c (-.f64 1 c)) cosTheta) (fma.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (fma.f64 c c (-.f64 1 c)) (+.f64 (.f64 (pow.f64 c 3) cosTheta) cosTheta))) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (-.f64 c -1)) -1))
	41.2b	(pow.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)) 3) -1) 1/3)
	1.5b	(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1)) 3)
	1.5b	(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)) -1)) 3)
▶	60.5b	(/.f64 1 (-.f64 c -1))
	0.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) 0) (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (/.f64 cosTheta (pow.f64 (sqrt.f64 (PI.f64)) -1))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
▶	0.8b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))) (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
▶	0.4b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
	0.8b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
	0.3b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
	2.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
	1.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 3)) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
✓	0.5b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
	2.4b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 1 cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
▶	1.5b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
	1.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
✓	62.4b	(/.f64 1 c)
	2.4b	(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
	39.8b	(cbrt.f64 (/.f64 1 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)) 3)))
	39.9b	(cbrt.f64 (/.f64 1 (pow.f64 (-.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (pow.f64 (exp.f64 cosTheta) cosTheta)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) -1) 3)))
	40.8b	(cbrt.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 cosTheta 3) (pow.f64 (sqrt.f64 (PI.f64)) 2))))

Compiler

Compiled 1072 to 849 computations (20.8% saved)

localize107.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))
✓	0.2b	(pow.f64 (fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (-.f64 c -1)) -1)
	0.3b	(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 304 to 198 computations (34.9% saved)

series67.0ms (0.1%)

Counts

2 → 20

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	cosTheta	@	inf	(pow.f64 (fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (-.f64 c -1)) -1)
1.0ms	cosTheta	@	-inf	(pow.f64 (fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (-.f64 c -1)) -1)
1.0ms	cosTheta	@	0	(pow.f64 (fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (-.f64 c -1)) -1)
0.0ms	c	@	0	(pow.f64 (fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (-.f64 c -1)) -1)
0.0ms	c	@	-inf	(pow.f64 (fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (-.f64 c -1)) -1)

Compiler

Compiled 10220 to 7285 computations (28.7% saved)

rewrite1.5s (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

69×	`egg-rr`
33×	`egg-rr`

Counts

2 → 102

Calls

Call 1

Inputs

(pow.f64 (fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (-.f64 c -1)) -1)

(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))

Outputs

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(2) ((x /.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1)) 2) 1) (cbrt.f64 (fma.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1)) 2) (cbrt.f64 (fma.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (fma.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 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simplify2.9s (3.3%)

Algorithm

1×

egglog

Counts

122 → 153

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64)))))) (.f64 -1 (.f64 (+.f64 (.f64 1/2 (sqrt.f64 (PI.f64))) (+.f64 (.f64 3/2 (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))) (pow.f64 cosTheta 4))))))
(/.f64 1 (+.f64 c 1))
(/.f64 1 (+.f64 c 1))
(/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))
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(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta))
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) cosTheta))
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) cosTheta) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2)) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 cosTheta -1) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) cosTheta) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (PI.f64))))
(.f64 -1 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)))
(*.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 1)
(*.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) (cbrt.f64 cosTheta)) (/.f64 1 (cbrt.f64 (pow.f64 cosTheta 2))))
(.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))))) (/.f64 1 (cbrt.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 2))))
(*.f64 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (PI.f64))) (/.f64 -1 cosTheta))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta) (pow.f64 (sqrt.f64 (PI.f64)) -1))
(*.f64 (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64))) (sqrt.f64 (fma.f64 -2 cosTheta 1)))
(*.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64))))
(-.f64 (/.f64 0 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)))
(-.f64 0 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (PI.f64))) (neg.f64 cosTheta))
(/.f64 (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) cosTheta) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 1)
(/.f64 (*.f64 (pow.f64 cosTheta -1) (neg.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)))) (neg.f64 (sqrt.f64 (PI.f64))))
(/.f64 (*.f64 (pow.f64 cosTheta -1) (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (PI.f64)))
(/.f64 (*.f64 (pow.f64 cosTheta -1) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (cbrt.f64 (sqrt.f64 (PI.f64))))) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2)))
(/.f64 (*.f64 (pow.f64 cosTheta -1) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(/.f64 (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (PI.f64))) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2))) cosTheta)
(/.f64 (*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) cosTheta) (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)))) (sqrt.f64 (PI.f64)))
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 2)) (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))) (cbrt.f64 cosTheta))
(/.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 2)) (cbrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)))) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64)))))
(/.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 2)) (neg.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))))) (cbrt.f64 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)))
(/.f64 (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (sqrt.f64 (fma.f64 -2 cosTheta 1))) cosTheta)
(/.f64 (*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)))) cosTheta)
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 cosTheta (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2))))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (neg.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) (cbrt.f64 cosTheta))) (neg.f64 (cbrt.f64 (pow.f64 cosTheta 2))))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta)) (neg.f64 (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) (cbrt.f64 cosTheta)) (cbrt.f64 (pow.f64 cosTheta 2)))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))))) (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2))) (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))))) (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)))) (cbrt.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))) (sqrt.f64 (fma.f64 -2 cosTheta 1))) (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64)))))) (neg.f64 (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2))))
(pow.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 3) 1/3)
(pow.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 1)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 3))
(neg.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)))
(neg.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) (neg.f64 cosTheta)))
(neg.f64 (*.f64 (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)))))
(neg.f64 (*.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) -1))
(neg.f64 (.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)) 1))
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))))
(neg.f64 (.f64 (/.f64 -1 (.f64 cosTheta (sqrt.f64 (PI.f64)))) (sqrt.f64 (fma.f64 -2 cosTheta 1))))
(if (!=.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 0) (pow.f64 (/.f64 1 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)) -1) (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2)) 0) (/.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2)))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 0) (pow.f64 (/.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) (sqrt.f64 (fma.f64 -2 cosTheta 1))) -1) (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta))

Outputs
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))
(-.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 (.f64 cosTheta cosTheta) (.f64 (-.f64 (-.f64 c -1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2))))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))
(-.f64 (fma.f64 (pow.f64 (neg.f64 cosTheta) 3) (-.f64 (.f64 -3/2 (sqrt.f64 (PI.f64))) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) (pow.f64 (-.f64 (-.f64 c -1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (.f64 (.f64 cosTheta cosTheta) (.f64 (-.f64 (-.f64 c -1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2))))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64)))))) (.f64 -1 (.f64 (+.f64 (.f64 1/2 (sqrt.f64 (PI.f64))) (+.f64 (.f64 3/2 (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))) (pow.f64 cosTheta 4))))))
(fma.f64 (neg.f64 (.f64 cosTheta cosTheta)) (.f64 (-.f64 (-.f64 c -1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)) (fma.f64 (sqrt.f64 (PI.f64)) cosTheta (neg.f64 (fma.f64 (-.f64 (.f64 -3/2 (sqrt.f64 (PI.f64))) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) (pow.f64 (-.f64 (-.f64 c -1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2))) (pow.f64 cosTheta 3) (.f64 (-.f64 (fma.f64 1/2 (sqrt.f64 (PI.f64)) (.f64 (.f64 3/2 (-.f64 (-.f64 c -1) (/.f64 1 (sqrt.f64 (PI.f64))))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (-.f64 (-.f64 c -1) (/.f64 1 (sqrt.f64 (PI.f64))))) (-.f64 (.f64 -3/2 (sqrt.f64 (PI.f64))) (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) (pow.f64 (-.f64 (-.f64 c -1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2))))) (pow.f64 cosTheta 4))))))
(/.f64 1 (+.f64 c 1))
(/.f64 1 (-.f64 c -1))
(/.f64 1 (+.f64 c 1))
(/.f64 1 (-.f64 c -1))
(/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))
(pow.f64 (fma.f64 (/.f64 (exp.f64 (neg.f64 (*.f64 cosTheta cosTheta))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta) 1) -1)
(+.f64 (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)))))
(-.f64 (pow.f64 (fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 cosTheta cosTheta))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta) 1) -1) (/.f64 c (pow.f64 (fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 cosTheta cosTheta))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta) 1) 2)))
(+.f64 (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))))
(+.f64 (/.f64 (+.f64 (/.f64 (.f64 c c) (fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 cosTheta cosTheta))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta) 1)) (neg.f64 c)) (pow.f64 (fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 cosTheta cosTheta))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta) 1) 2)) (pow.f64 (fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 cosTheta cosTheta))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta) 1) -1))
(+.f64 (.f64 -1 (/.f64 (pow.f64 c 3) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (pow.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) 2)))) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (+.f64 (.f64 -1 (/.f64 c (.f64 (+.f64 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 1) (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))
(-.f64 (+.f64 (/.f64 (+.f64 (/.f64 (.f64 c c) (fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 cosTheta cosTheta))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta) 1)) (neg.f64 c)) (pow.f64 (fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 cosTheta cosTheta))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta) 1) 2)) (pow.f64 (fma.f64 (/.f64 (exp.f64 (neg.f64 (.f64 cosTheta cosTheta))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta) 1) -1)) (/.f64 (pow.f64 c 3) (pow.f64 (pow.f64 (fma.f64 (/.f64 (exp.f64 (neg.f64 (*.f64 cosTheta cosTheta))) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta) 1) 2) 2)))
(/.f64 1 c)
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(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(/.f64 (*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)))) cosTheta)
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 cosTheta (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2))))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2)) cosTheta))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(/.f64 (neg.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) (cbrt.f64 cosTheta))) (neg.f64 (cbrt.f64 (pow.f64 cosTheta 2))))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) (.f64 (cbrt.f64 cosTheta) (cbrt.f64 (.f64 cosTheta cosTheta))))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) cosTheta)) (neg.f64 (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(/.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) (cbrt.f64 cosTheta)) (cbrt.f64 (pow.f64 cosTheta 2)))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) (.f64 (cbrt.f64 cosTheta) (cbrt.f64 (.f64 cosTheta cosTheta))))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))))) (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (.f64 (cbrt.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) cosTheta) 2))))
(/.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2))) (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(cbrt.f64 (/.f64 (.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2)) (pow.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) 2)))
(/.f64 (.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))))) (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)))) (cbrt.f64 (pow.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (.f64 (cbrt.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) cosTheta) 2))))
(/.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))) (sqrt.f64 (fma.f64 -2 cosTheta 1))) (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2)))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (.f64 (cbrt.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) cosTheta) 2))))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64)))))) (neg.f64 (cbrt.f64 (pow.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) 2))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (.f64 (cbrt.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) cosTheta) 2))))
(pow.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)) 3)
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(pow.f64 (pow.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 3) 1/3)
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(pow.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 1)
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 3))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(neg.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(neg.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) (neg.f64 cosTheta)))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(neg.f64 (*.f64 (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)))))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(neg.f64 (*.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) -1))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(neg.f64 (.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) cosTheta)) 1))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(neg.f64 (.f64 (/.f64 -1 (.f64 cosTheta (sqrt.f64 (PI.f64)))) (sqrt.f64 (fma.f64 -2 cosTheta 1))))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)
(if (!=.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 0) (pow.f64 (/.f64 1 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta)) -1) (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) 0) (/.f64 1 (pow.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta) -1)) (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2)) 0) (/.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2)))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2)) 0) (/.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) cosTheta) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2)))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 0) (pow.f64 (/.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) (sqrt.f64 (fma.f64 -2 cosTheta 1))) -1) (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 0) (pow.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) cosTheta) (sqrt.f64 (fma.f64 -2 cosTheta 1))) -1) (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) cosTheta) (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) cosTheta))

localize8.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 c -1))

Compiler

Compiled 13 to 10 computations (23.1% saved)

series6.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	c	@	0	(/.f64 1 (-.f64 c -1))
0.0ms	c	@	-inf	(/.f64 1 (-.f64 c -1))
0.0ms	c	@	inf	(/.f64 1 (-.f64 c -1))

Compiler

Compiled 745 to 615 computations (17.4% saved)

rewrite1.5s (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

70× egg-rr

Counts

1 → 70

Calls

Call 1

Inputs
(/.f64 1 (-.f64 c -1))

Outputs

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simplify2.2s (2.5%)

Algorithm

1×

egglog

Counts

82 → 103

Calls

Call 1

Inputs
1
(+.f64 (*.f64 -1 c) 1)
(+.f64 (*.f64 -1 c) (+.f64 1 (pow.f64 c 2)))
(+.f64 (.f64 -1 (pow.f64 c 3)) (+.f64 (.f64 -1 c) (+.f64 1 (pow.f64 c 2))))
(/.f64 1 c)
(+.f64 (/.f64 1 c) (*.f64 -1 (pow.f64 (/.f64 1 c) 2)))
(+.f64 (pow.f64 (/.f64 1 c) 3) (+.f64 (/.f64 1 c) (*.f64 -1 (pow.f64 (/.f64 1 c) 2))))
(+.f64 (pow.f64 (/.f64 1 c) 3) (+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (pow.f64 (/.f64 1 c) 2)) (.f64 -1 (pow.f64 (/.f64 1 c) 4)))))
(/.f64 1 c)
(+.f64 (/.f64 1 c) (*.f64 -1 (pow.f64 (/.f64 -1 c) 2)))
(+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (pow.f64 (/.f64 -1 c) 2)) (.f64 -1 (pow.f64 (/.f64 -1 c) 3))))
(+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (pow.f64 (/.f64 -1 c) 2)) (+.f64 (.f64 -1 (pow.f64 (/.f64 -1 c) 4)) (*.f64 -1 (pow.f64 (/.f64 -1 c) 3)))))
(*.f64 (/.f64 -1 (+.f64 1 (pow.f64 c 3))) (/.f64 -1 (/.f64 -1 (-.f64 c (fma.f64 c c 1)))))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c)))) 2) (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2)) 2)) (cbrt.f64 (+.f64 1 c))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2)) (cbrt.f64 (cbrt.f64 (+.f64 1 c)))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c)))) 2))
(.f64 (.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c)))) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2)) 2)))
(*.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c))) (cbrt.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2)) (cbrt.f64 (/.f64 -1 (-.f64 -1 c))))
(*.f64 1 (/.f64 -1 (-.f64 -1 c)))
(*.f64 (/.f64 -1 (-.f64 -1 c)) 1)
(*.f64 (/.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c)))) (cbrt.f64 (+.f64 1 c))) (/.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c)))) 2) (cbrt.f64 (+.f64 1 c))))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c)))) 2) (/.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c))) (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 c) 2)) 2))))
(*.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c)))) (/.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c)))) 2) (cbrt.f64 (pow.f64 (+.f64 1 c) 2))))
(*.f64 (/.f64 1 (+.f64 1 (pow.f64 c 3))) (pow.f64 (/.f64 -1 (-.f64 c (fma.f64 c c 1))) -1))
(*.f64 -1 (/.f64 1 (-.f64 -1 c)))
(*.f64 (/.f64 1 (-.f64 -1 c)) -1)
(*.f64 (/.f64 -1 (cbrt.f64 (pow.f64 (+.f64 1 c) 2))) (cbrt.f64 (/.f64 1 (-.f64 -1 c))))
(*.f64 (cbrt.f64 (/.f64 1 (-.f64 -1 c))) (/.f64 -1 (cbrt.f64 (pow.f64 (+.f64 1 c) 2))))
(-.f64 (/.f64 0 (-.f64 -1 c)) (/.f64 1 (-.f64 -1 c)))
(-.f64 (/.f64 0 (+.f64 1 c)) (/.f64 1 (-.f64 -1 c)))
(-.f64 0 (/.f64 1 (-.f64 -1 c)))
(/.f64 (/.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c))) (cbrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 c) 2)))) (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 c) 2)) 2)))
(/.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c))) (cbrt.f64 (pow.f64 (+.f64 1 c) 2)))
(/.f64 (cbrt.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2)) (cbrt.f64 (+.f64 1 c)))
(/.f64 (/.f64 -1 (-.f64 -1 c)) 1)
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2)) -1) (cbrt.f64 (-.f64 -1 c)))
(/.f64 (cbrt.f64 (/.f64 1 (-.f64 -1 c))) (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 c) 2))))
(/.f64 (/.f64 1 (-.f64 -1 c)) -1)
(/.f64 (cbrt.f64 (/.f64 1 (-.f64 -1 c))) (*.f64 (cbrt.f64 (pow.f64 (+.f64 1 c) 2)) -1))
(/.f64 -1 (-.f64 -1 c))
(/.f64 (cbrt.f64 (/.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c))) (pow.f64 (+.f64 1 c) 2))) (cbrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 c) 2))))
(/.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2) (cbrt.f64 (+.f64 1 c)))) (cbrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 c) 2))))
(/.f64 (/.f64 -1 (cbrt.f64 (pow.f64 (+.f64 1 c) 2))) (cbrt.f64 (-.f64 -1 c)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2) -1)) (cbrt.f64 (-.f64 -1 c)))
(/.f64 1 (+.f64 1 c))
(/.f64 (/.f64 1 (+.f64 1 (pow.f64 c 3))) (/.f64 -1 (-.f64 c (fma.f64 c c 1))))
(pow.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c))) 3)
(pow.f64 (/.f64 -1 (-.f64 -1 c)) 1)
(pow.f64 (+.f64 1 c) -1)
(cbrt.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 3))
(neg.f64 (/.f64 1 (-.f64 -1 c)))
(neg.f64 (-.f64 (/.f64 1 (-.f64 -1 c)) (/.f64 0 (-.f64 -1 c))))
(neg.f64 (-.f64 (/.f64 1 (-.f64 -1 c)) 0))
(neg.f64 (-.f64 (/.f64 1 (-.f64 -1 c)) (/.f64 0 (+.f64 1 c))))
(if (!=.f64 (+.f64 1 c) 0) (/.f64 -1 (-.f64 -1 c)) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 -1 0) (/.f64 -1 (-.f64 -1 c)) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 (/.f64 -1 (-.f64 -1 c)) 0) (pow.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) -1) -1) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 (cbrt.f64 (+.f64 1 c)) 0) (pow.f64 (cbrt.f64 (+.f64 1 c)) -3) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 (pow.f64 (+.f64 1 c) 3) 0) (pow.f64 (pow.f64 (+.f64 1 c) 3) -1/3) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c)))) 2) 0) (/.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c)))) (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 c) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c)))) 2))) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 c))) 0) (/.f64 1 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 c) 2)) (cbrt.f64 (/.f64 -1 (-.f64 -1 c))))) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 (-.f64 (fma.f64 c c 1) c) 0) (/.f64 (-.f64 (fma.f64 c c 1) c) (+.f64 1 (pow.f64 c 3))) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 (-.f64 c (fma.f64 c c 1)) 0) (*.f64 (/.f64 1 (-.f64 -1 (pow.f64 c 3))) (-.f64 c (fma.f64 c c 1))) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 1 0) (/.f64 -1 (-.f64 -1 c)) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 3) 0) (/.f64 1 (pow.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 3) -1/3)) (/.f64 -1 (-.f64 -1 c)))
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(if (!=.f64 (/.f64 0 (-.f64 -1 c)) 0) (/.f64 (-.f64 (pow.f64 (/.f64 0 (-.f64 -1 c)) 3) (pow.f64 (/.f64 1 (-.f64 -1 c)) 3)) (+.f64 (.f64 (/.f64 0 (-.f64 -1 c)) (/.f64 0 (-.f64 -1 c))) (+.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2) (.f64 (/.f64 0 (-.f64 -1 c)) (/.f64 1 (-.f64 -1 c)))))) (/.f64 -1 (-.f64 -1 c)))
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(+.f64 (/.f64 0 (-.f64 -1 c)) (/.f64 -1 (-.f64 -1 c)))
(+.f64 0 (/.f64 -1 (-.f64 -1 c)))
(+.f64 (/.f64 0 (+.f64 1 c)) (/.f64 -1 (-.f64 -1 c)))

Outputs
1
(+.f64 (*.f64 -1 c) 1)
(-.f64 1 c)
(+.f64 (*.f64 -1 c) (+.f64 1 (pow.f64 c 2)))
(-.f64 (fma.f64 c c 1) c)
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(-.f64 (-.f64 (fma.f64 c c 1) c) (pow.f64 c 3))
(/.f64 1 c)
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(-.f64 (-.f64 (/.f64 1 c) (/.f64 (/.f64 1 c) c)) (pow.f64 (/.f64 -1 c) 3))
(+.f64 (pow.f64 (/.f64 1 c) 3) (+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (pow.f64 (/.f64 1 c) 2)) (.f64 -1 (pow.f64 (/.f64 1 c) 4)))))
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(if (!=.f64 (+.f64 (.f64 (/.f64 0 (+.f64 1 c)) (/.f64 0 (+.f64 1 c))) (+.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2) (.f64 (/.f64 0 (+.f64 1 c)) (/.f64 1 (-.f64 -1 c))))) 0) (/.f64 (-.f64 (pow.f64 (/.f64 0 (+.f64 1 c)) 3) (pow.f64 (/.f64 1 (-.f64 -1 c)) 3)) (+.f64 (.f64 (/.f64 0 (+.f64 1 c)) (/.f64 0 (+.f64 1 c))) (+.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2) (.f64 (/.f64 0 (+.f64 1 c)) (/.f64 1 (-.f64 -1 c)))))) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 (pow.f64 (/.f64 1 (-.f64 -1 c)) 2) 0) (/.f64 (pow.f64 (/.f64 1 (-.f64 -1 c)) 2) (/.f64 1 (-.f64 c -1))) (/.f64 1 (-.f64 c -1)))
(if (!=.f64 (/.f64 0 (-.f64 -1 c)) 0) (/.f64 (-.f64 (pow.f64 (/.f64 0 (-.f64 -1 c)) 3) (pow.f64 (/.f64 1 (-.f64 -1 c)) 3)) (+.f64 (.f64 (/.f64 0 (-.f64 -1 c)) (/.f64 0 (-.f64 -1 c))) (+.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2) (.f64 (/.f64 0 (-.f64 -1 c)) (/.f64 1 (-.f64 -1 c)))))) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 0 0) (/.f64 (pow.f64 (/.f64 1 (-.f64 -1 c)) 2) (/.f64 1 (-.f64 c -1))) (/.f64 1 (-.f64 c -1)))
(if (!=.f64 0 0) (/.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 3) (+.f64 0 (+.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2) (*.f64 0 (/.f64 1 (-.f64 -1 c)))))) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 0 0) (/.f64 (pow.f64 (/.f64 1 (-.f64 -1 c)) 2) (/.f64 1 (-.f64 c -1))) (/.f64 1 (-.f64 c -1)))
(if (!=.f64 (/.f64 0 (+.f64 1 c)) 0) (/.f64 (-.f64 (pow.f64 (/.f64 0 (+.f64 1 c)) 3) (pow.f64 (/.f64 1 (-.f64 -1 c)) 3)) (+.f64 (.f64 (/.f64 0 (+.f64 1 c)) (/.f64 0 (+.f64 1 c))) (+.f64 (pow.f64 (/.f64 -1 (-.f64 -1 c)) 2) (.f64 (/.f64 0 (+.f64 1 c)) (/.f64 1 (-.f64 -1 c)))))) (/.f64 -1 (-.f64 -1 c)))
(if (!=.f64 0 0) (/.f64 (pow.f64 (/.f64 1 (-.f64 -1 c)) 2) (/.f64 1 (-.f64 c -1))) (/.f64 1 (-.f64 c -1)))
(+.f64 (/.f64 0 (-.f64 -1 c)) (/.f64 -1 (-.f64 -1 c)))
(/.f64 1 (-.f64 c -1))
(+.f64 0 (/.f64 -1 (-.f64 -1 c)))
(/.f64 1 (-.f64 c -1))
(+.f64 (/.f64 0 (+.f64 1 c)) (/.f64 -1 (-.f64 -1 c)))
(/.f64 1 (-.f64 c -1))

localize34.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))
✓	0.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
✓	0.4b	(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1))
	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 102 to 57 computations (44.1% saved)

series80.0ms (0.1%)

Counts

3 → 18

Calls

12 calls:

Time	Variable		Point	Expression
9.0ms	c	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	cosTheta	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	cosTheta	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	cosTheta	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	c	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Compiler

Compiled 9645 to 7140 computations (26% saved)

rewrite1.5s (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

99×	`egg-rr`
44×	`egg-rr`
31×	`egg-rr`

Counts

3 → 174

Calls

Call 1

Inputs

(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1))

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))

Outputs

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simplify4.1s (4.7%)

Algorithm

1×

egglog

Counts

192 → 238

Calls

Call 1

Inputs
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
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(if (!=.f64 (-.f64 (+.f64 1 (pow.f64 (fma.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (+.f64 -1 (pow.f64 cosTheta -1)) c) 2)) (fma.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (+.f64 -1 (pow.f64 cosTheta -1)) c)) 0) (*.f64 (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (+.f64 -1 (pow.f64 cosTheta -1)) c) 3) 1)) (-.f64 (+.f64 1 (pow.f64 (fma.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (+.f64 -1 (pow.f64 cosTheta -1)) c) 2)) (fma.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (+.f64 -1 (pow.f64 cosTheta -1)) c))) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (+.f64 1 c)) -1))
(if (!=.f64 1 0) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (+.f64 1 c)) -1) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (+.f64 1 c)) -1))
(*.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (exp.f64 (pow.f64 cosTheta 2))) (pow.f64 (sqrt.f64 (PI.f64)) -1))
(*.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))))
(*.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (exp.f64 (pow.f64 cosTheta 2))))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1)) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -2)) (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (exp.f64 (pow.f64 cosTheta 2)))))
(.f64 (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))) (.f64 (pow.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) 2/3) (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64)))))
(*.f64 (/.f64 (-.f64 1 (pow.f64 cosTheta -1)) (exp.f64 (pow.f64 cosTheta 2))) (/.f64 -1 (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (exp.f64 (pow.f64 cosTheta 2))))
(*.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (+.f64 -1 (pow.f64 cosTheta -1)))
(*.f64 (cbrt.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2)))) (cbrt.f64 (pow.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) 2)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) 2)) (cbrt.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2)))))
(.f64 (sqrt.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))) (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64)))) (/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) 2)) (exp.f64 (pow.f64 cosTheta 2))))
(.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (cbrt.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) 2)))
(.f64 (.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))))) (pow.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) 2/3))
(.f64 (.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (sqrt.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))))) (sqrt.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))))
(*.f64 (/.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) -1) -1)
(*.f64 1 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))))
(*.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) 1)
(/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (/.f64 (sqrt.f64 (PI.f64)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2)))
(/.f64 (/.f64 (-.f64 1 (pow.f64 cosTheta -1)) (exp.f64 (pow.f64 cosTheta 2))) (neg.f64 (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (/.f64 1 (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (pow.f64 cosTheta 3) -1)) (exp.f64 (pow.f64 cosTheta 2))) (*.f64 (sqrt.f64 (PI.f64)) (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) 1) cosTheta) 1)))
(/.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 cosTheta -1)) (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) -1)
(/.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) 1)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2)))) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) 3) 1/3)
(pow.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) 1)
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) 3) 1))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) 3))
(neg.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 cosTheta -1)) (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))))
(if (!=.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) 0) (/.f64 1 (pow.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) -1)) (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))))
(if (!=.f64 -1 0) (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))))
(if (!=.f64 1 0) (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))))
(+.f64 (.f64 -1 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))) (.f64 (pow.f64 cosTheta -1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))))
(+.f64 (.f64 (pow.f64 cosTheta -1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))) (.f64 -1 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))))
(+.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) cosTheta) (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))) (.f64 (/.f64 -1 (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))))
(+.f64 (.f64 (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))) (.f64 (/.f64 -1 (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))))
(+.f64 (.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) -1) (.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (pow.f64 cosTheta -1)))
(+.f64 (.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (pow.f64 cosTheta -1)) (.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) -1))
(+.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) cosTheta)) (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 -1 (sqrt.f64 (PI.f64)))))
(+.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))) (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 -1 (sqrt.f64 (PI.f64)))))

Outputs
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) cosTheta)
(/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))))
(pow.f64 (+.f64 (/.f64 (-.f64 (pow.f64 cosTheta -1) 1) (*.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) 1) -1)
(+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))))) (+.f64 (.f64 -1 (/.f64 c (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))) 2))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))))))
(+.f64 (/.f64 (pow.f64 c 2) (pow.f64 (+.f64 (/.f64 (-.f64 (pow.f64 cosTheta -1) 1) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) 1) 3)) (-.f64 (pow.f64 (+.f64 (/.f64 (-.f64 (pow.f64 cosTheta -1) 1) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) 1) -1) (/.f64 c (pow.f64 (+.f64 (/.f64 (-.f64 (pow.f64 cosTheta -1) 1) (*.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) 1) 2))))
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(/.f64 1 c)
(pow.f64 c -1)
(+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))))))
(-.f64 (pow.f64 c -1) (.f64 (+.f64 (/.f64 (-.f64 (pow.f64 cosTheta -1) 1) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) 1) (pow.f64 (pow.f64 c -1) 2)))
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(+.f64 (.f64 -1 (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))) 2) (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 1 c) 4)))) (+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))))) (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))) 2)))))
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(/.f64 1 c)
(pow.f64 c -1)
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(-.f64 (pow.f64 c -1) (.f64 (+.f64 (/.f64 (-.f64 (pow.f64 cosTheta -1) 1) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) 1) (pow.f64 (pow.f64 c -1) 2)))
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(+.f64 (pow.f64 c -1) (+.f64 (.f64 (+.f64 (/.f64 (-.f64 1 (pow.f64 cosTheta -1)) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) -1) (pow.f64 (pow.f64 c -1) 2)) (/.f64 (pow.f64 (+.f64 (/.f64 (-.f64 (pow.f64 cosTheta -1) 1) (*.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) 1) 2) (pow.f64 c 3))))
(+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 4) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))) 2) (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64))))))) (+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 -1 c) 2))) (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (exp.f64 (*.f64 -1 (pow.f64 cosTheta 2))) (-.f64 (/.f64 1 cosTheta) 1)) (sqrt.f64 (PI.f64)))) 2))))))
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(/.f64 (-.f64 (pow.f64 cosTheta -1) 1) (*.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64))))
(+.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))) (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 -1 (sqrt.f64 (PI.f64)))))
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localize72.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))) (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
✓	0.5b	(/.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))
✓	0.5b	(/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))
	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 233 to 150 computations (35.6% saved)

series91.0ms (0.1%)

Counts

3 → 26

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	cosTheta	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))) (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	cosTheta	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))) (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	cosTheta	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))) (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	c	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))) (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	c	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))) (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))

Compiler

Compiled 15105 to 10040 computations (33.5% saved)

rewrite1.5s (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

68×	`egg-rr`
41×	`egg-rr`
32×	`egg-rr`

Counts

3 → 141

Calls

Call 1

Inputs

(/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))

(/.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))) (/.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Outputs

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(+.f64 1 c)) -1))))))

simplify3.4s (3.8%)

Algorithm

1×

egglog

Counts

167 → 193

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (*.f64 -1/2 (/.f64 (pow.f64 cosTheta 2) (sqrt.f64 (PI.f64)))))) (/.f64 1 (sqrt.f64 (PI.f64))))
(/.f64 1 (+.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (/.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))) 1))
(+.f64 (/.f64 1 (+.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (/.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))) 1)) (.f64 -1 (/.f64 c (pow.f64 (+.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (/.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)))) 1) 2))))
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(/.f64 1 c)
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(if (!=.f64 (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 1 c))) 0) (pow.f64 (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 1 c))) (neg.f64 3)) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 1 c)) -1))
(if (!=.f64 (-.f64 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (pow.f64 cosTheta 2)))) 2)) (+.f64 c (/.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (pow.f64 cosTheta 2))))) 0) (.f64 (/.f64 1 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (pow.f64 cosTheta 2)))) 3))) (-.f64 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (pow.f64 cosTheta 2)))) 2)) (+.f64 c (/.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (pow.f64 cosTheta 2)))))) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 1 c)) -1))

Outputs
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (*.f64 -1/2 (/.f64 (pow.f64 cosTheta 2) (sqrt.f64 (PI.f64)))))) (/.f64 1 (sqrt.f64 (PI.f64))))
(fma.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64))) (-.f64 (fma.f64 -1/2 (/.f64 (pow.f64 cosTheta 2) (sqrt.f64 (PI.f64))) (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) -1)))
(/.f64 1 (+.f64 (.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (/.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))) 1))
(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) 1) -1)
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(/.f64 1 c)
(pow.f64 c -1)
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(/.f64 1 c)
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(if (!=.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (-.f64 c -1)) 0) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (-.f64 c -1)) -1) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (-.f64 c -1)) -1))
(if (!=.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 1 c)) -1) 0) (pow.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 1 c)) -1) -1) -1) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 1 c)) -1))
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(if (!=.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (-.f64 c -1)) 3) 0) (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (-.f64 c -1)) 3) -1/3) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (-.f64 c -1)) -1))
(if (!=.f64 (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 1 c))) 0) (pow.f64 (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 1 c))) (neg.f64 3)) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 1 c)) -1))
(if (!=.f64 (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (-.f64 c -1))) 0) (pow.f64 (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (-.f64 c -1))) -3) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (-.f64 c -1)) -1))
(if (!=.f64 (-.f64 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (pow.f64 cosTheta 2)))) 2)) (+.f64 c (/.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (pow.f64 cosTheta 2))))) 0) (.f64 (/.f64 1 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (pow.f64 cosTheta 2)))) 3))) (-.f64 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (pow.f64 cosTheta 2)))) 2)) (+.f64 c (/.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (pow.f64 cosTheta 2)))))) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (+.f64 1 c)) -1))
(if (!=.f64 (-.f64 (-.f64 (pow.f64 (fma.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) c) 2) -1) (fma.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) c)) 0) (/.f64 (-.f64 (-.f64 (pow.f64 (fma.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) c) 2) -1) (fma.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) c)) (-.f64 (pow.f64 (fma.f64 (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) c) 3) -1)) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 cosTheta -1))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta)) (-.f64 c -1)) -1))

localize81.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)
✓	0.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
✓	0.3b	(/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta))
	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 148 to 70 computations (52.7% saved)

series108.0ms (0.1%)

Counts

3 → 20

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	c	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
2.0ms	cosTheta	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
2.0ms	cosTheta	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	c	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	cosTheta	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))

Compiler

Compiled 11945 to 8845 computations (26% saved)

rewrite1.5s (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

65×	`egg-rr`
35×	`egg-rr`
29×	`egg-rr`

Counts

3 → 129

Calls

Call 1

Inputs

(/.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta))

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)

Outputs

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simplify3.5s (4%)

Algorithm

1×

egglog

Counts

149 → 191

Calls

Call 1

Inputs
(/.f64 1 (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2) cosTheta))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 (pow.f64 cosTheta 2) (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2))) (+.f64 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2) cosTheta)) (*.f64 -1/2 (/.f64 cosTheta (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2))))) (/.f64 1 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2)))
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(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1)) 3)
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(pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1)
(cbrt.f64 (/.f64 1 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 3)))
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(.f64 -1 (.f64 (neg.f64 cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64)))))
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(.f64 (cbrt.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (cbrt.f64 (*.f64 (pow.f64 cosTheta 2) (sqrt.f64 (PI.f64)))))
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(.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) 1)
(.f64 (.f64 cosTheta (cbrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64))))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 cosTheta (sqrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))))
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(/.f64 (*.f64 (neg.f64 cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64)))) -1)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) 3) 1/3)
(pow.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) 3)
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(if (!=.f64 1 0) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta))

Outputs
(/.f64 1 (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2) cosTheta))
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(if (!=.f64 (.f64 (-.f64 (+.f64 1 (pow.f64 c 2)) c) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) 0) (.f64 (/.f64 1 (+.f64 (.f64 (+.f64 1 (pow.f64 c 3)) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (.f64 (-.f64 (+.f64 1 (pow.f64 c 2)) c) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))))) (.f64 (-.f64 (+.f64 1 (pow.f64 c 2)) c) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta))) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1))
(if (!=.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (.f64 cosTheta (+.f64 (.f64 c c) (-.f64 1 c)))) 0) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (.f64 cosTheta (+.f64 (.f64 c c) (-.f64 1 c)))) (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (.f64 c c) (-.f64 1 c)) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (+.f64 (.f64 (pow.f64 c 3) cosTheta) cosTheta)))) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (.f64 cosTheta cosTheta))) (-.f64 c -1)) -1))
(if (!=.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) (-.f64 (+.f64 1 (pow.f64 c 2)) c)) 0) (.f64 (/.f64 1 (+.f64 (.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2))) (-.f64 (+.f64 1 (pow.f64 c 2)) c)) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 (pow.f64 c 3))))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) (-.f64 (+.f64 1 (pow.f64 c 2)) c))) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1))
(if (!=.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (.f64 cosTheta (+.f64 (.f64 c c) (-.f64 1 c)))) 0) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (.f64 cosTheta (+.f64 (.f64 c c) (-.f64 1 c)))) (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (.f64 c c) (-.f64 1 c)) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (+.f64 (.f64 (pow.f64 c 3) cosTheta) cosTheta)))) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (.f64 cosTheta cosTheta))) (-.f64 c -1)) -1))
(if (!=.f64 (-.f64 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))) 2)) (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2))))) 0) (.f64 (/.f64 1 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))) 3))) (-.f64 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))) 2)) (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))))) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1))
(if (!=.f64 (+.f64 1 (-.f64 (pow.f64 (+.f64 c (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))) 2) (+.f64 c (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) 0) (/.f64 (+.f64 1 (-.f64 (pow.f64 (+.f64 c (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))) 2) (+.f64 c (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))))) (-.f64 (pow.f64 (+.f64 c (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))) 3) -1)) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (.f64 cosTheta cosTheta))) (-.f64 c -1)) -1))
(.f64 -1 (.f64 (neg.f64 cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64)))))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) cosTheta))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) cosTheta) (cbrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (cbrt.f64 (*.f64 (pow.f64 cosTheta 2) (sqrt.f64 (PI.f64)))))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (neg.f64 cosTheta) (neg.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))) (neg.f64 cosTheta))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))) cosTheta))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 cosTheta) (.f64 (cbrt.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (sqrt.f64 (PI.f64)))))
(.f64 (cbrt.f64 cosTheta) (.f64 (cbrt.f64 (*.f64 cosTheta cosTheta)) (sqrt.f64 (sqrt.f64 (PI.f64)))))
(.f64 (cbrt.f64 (.f64 (pow.f64 cosTheta 2) (sqrt.f64 (PI.f64)))) (cbrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) 1)
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 cosTheta (cbrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64))))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))) cosTheta))
(.f64 (.f64 cosTheta (sqrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 cosTheta)) (cbrt.f64 (pow.f64 cosTheta 2)))
(.f64 (.f64 (cbrt.f64 cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (*.f64 cosTheta cosTheta)))
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(.f64 1 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (.f64 (neg.f64 cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64))))) (neg.f64 (pow.f64 (cbrt.f64 (*.f64 (neg.f64 cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64))))) 2)))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (neg.f64 (cbrt.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta))) (neg.f64 (cbrt.f64 (*.f64 (pow.f64 cosTheta 2) (sqrt.f64 (PI.f64))))))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (neg.f64 (cbrt.f64 (.f64 (neg.f64 cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64)))))) (pow.f64 (cbrt.f64 (*.f64 (neg.f64 cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64))))) 2))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(-.f64 0 (*.f64 (neg.f64 cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64)))))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) 1)
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(/.f64 (*.f64 (neg.f64 cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64)))) -1)
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) 3) 1/3)
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(pow.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) 1)
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) 3)
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) 3))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) 3) 1))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(neg.f64 (*.f64 (neg.f64 cosTheta) (sqrt.f64 (sqrt.f64 (PI.f64)))))
(*.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))
(if (!=.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) 0) (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1/2) cosTheta) -1) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 (.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64)))) 0) (/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1/2) cosTheta)) (.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64)))))
(if (!=.f64 1 0) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta))
(if (!=.f64 1 0) (.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64)))))

eval973.0ms (1.1%)

Compiler: Compiled 56597 to 36794 computations (35% saved)

prune296.0ms (0.3%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	1136	5	1141
Fresh	7	7	14
Picked	1	0	1
Done	3	3	6
Total	1147	15	1162

Error

Counts

1162 → 15

Alt Table

Click to see full alt table

Status	Error	Program
	41.2b	(pow.f64 (/.f64 1 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 3)) 1/3)
✓	60.5b	(/.f64 1 (-.f64 c -1))
▶	0.8b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
▶	0.3b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
▶	2.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
✓	0.5b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
	2.4b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 1 cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
✓	1.5b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
▶	1.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
▶	60.5b	(-.f64 1 c)
	2.2b	(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2) cosTheta)
	2.4b	(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
	40.9b	(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (+.f64 1 c)) 3) -1))
	39.9b	(cbrt.f64 (/.f64 1 (pow.f64 (-.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (pow.f64 (exp.f64 cosTheta) cosTheta)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) -1) 3)))
	60.5b	1

Compiler

Compiled 491 to 406 computations (17.3% saved)

localize41.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))
✓	0.1b	(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta)
✓	0.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 118 to 67 computations (43.2% saved)

series96.0ms (0.1%)

Counts

3 → 22

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	c	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
0.0ms	cosTheta	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
0.0ms	cosTheta	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
0.0ms	cosTheta	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
0.0ms	c	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Compiler

Compiled 12400 to 8785 computations (29.2% saved)

rewrite1.5s (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

53×	`egg-rr`
50×	`egg-rr`
34×	`egg-rr`

Counts

3 → 137

Calls

Call 1

Inputs

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta)

(/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))

Outputs

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simplify3.4s (3.9%)

Algorithm

1×

egglog

Counts

159 → 194

Calls

Call 1

Inputs
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(if (!=.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))
(if (!=.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 0) (/.f64 1 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (fma.f64 -2 cosTheta 1)))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))
(if (!=.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2/3) 0) (/.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2/3))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))
(if (!=.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) 0) (/.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) -1)) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))
(if (!=.f64 1 0) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))

Outputs
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(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
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(.f64 (.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (sqrt.f64 (PI.f64)))) 1) (*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (sqrt.f64 (PI.f64)))) 1))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(.f64 (.f64 -1 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (*.f64 -1 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (sqrt.f64 (PI.f64))))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(.f64 (.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (*.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (sqrt.f64 (PI.f64))))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(*.f64 (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (neg.f64 (sqrt.f64 (PI.f64)))))) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (neg.f64 (sqrt.f64 (PI.f64))))) 2))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (pow.f64 (sqrt.f64 (PI.f64)) -1))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) 2)))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2/3) (pow.f64 (sqrt.f64 (PI.f64)) 2/3)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) 2)) (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(*.f64 (neg.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 -1 (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2/3) (sqrt.f64 (PI.f64))))
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2/3)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (sqrt.f64 (fma.f64 -2 cosTheta 1)))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(*.f64 (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))) (neg.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) 2))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(*.f64 -1 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (neg.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(*.f64 1 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (neg.f64 (sqrt.f64 (PI.f64)))) -1)
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) 1)
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(-.f64 (/.f64 0 (neg.f64 (sqrt.f64 (PI.f64)))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (neg.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(-.f64 0 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (neg.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (neg.f64 (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (cbrt.f64 (sqrt.f64 (PI.f64))))) (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2/3)))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (pow.f64 (sqrt.f64 (PI.f64)) 2/3)))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (sqrt.f64 (PI.f64))))) (neg.f64 (sqrt.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2/3))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (pow.f64 (sqrt.f64 (PI.f64)) 2/3)))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (neg.f64 (sqrt.f64 (PI.f64)))) -1)
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) 1)
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))) 3)
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) 3) 1/3)
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(pow.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (sqrt.f64 (sqrt.f64 (PI.f64)))) 2)
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) 1)
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (neg.f64 (sqrt.f64 (PI.f64)))) 3) -1))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) 3) 1))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) 3))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(neg.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (neg.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))
(if (!=.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))
(if (!=.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 0) (/.f64 1 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (fma.f64 -2 cosTheta 1)))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))
(if (!=.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 0) (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (fma.f64 -2 cosTheta 1))) -1) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))
(if (!=.f64 (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2/3) 0) (/.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) 2/3))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))
(if (!=.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) 0) (/.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) -1)) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))
(if (!=.f64 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) 0) (pow.f64 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64)))) -1) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))
(if (!=.f64 1 0) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (fma.f64 -2 cosTheta 1)) (sqrt.f64 (PI.f64))))

localize3.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))
✓	0.1b	(/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta)
✓	0.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 78 to 35 computations (55.1% saved)

series46.0ms (0.1%)

Counts

3 → 32

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	cosTheta	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	c	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	cosTheta	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	cosTheta	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
0.0ms	c	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))

Compiler

Compiled 6665 to 4600 computations (31% saved)

rewrite1.5s (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

47×	`egg-rr`
46×	`egg-rr`
33×	`egg-rr`

Counts

3 → 126

Calls

Call 1

Inputs

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

(/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta)

(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))

Outputs

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(PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (neg.f64 cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) 0) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 0) (/.f64 1 (pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) -1)) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 1 0) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))))))

simplify3.4s (3.8%)

Algorithm

1×

egglog

Counts

158 → 186

Calls

Call 1

Inputs
(/.f64 1 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))
(+.f64 (.f64 -1 (/.f64 c (pow.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (/.f64 1 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))))
(+.f64 (.f64 -1 (/.f64 c (pow.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (+.f64 (.f64 -1 (/.f64 (pow.f64 c 3) (pow.f64 (pow.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) 2))) (+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (/.f64 1 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))
(/.f64 1 c)
(+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))))
(+.f64 (.f64 (pow.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (pow.f64 (/.f64 1 c) 3)) (+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))
(+.f64 (.f64 (pow.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (pow.f64 (/.f64 1 c) 3)) (+.f64 (.f64 -1 (.f64 (pow.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 1 c) 4)))) (+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))))))
(/.f64 1 c)
(+.f64 (/.f64 1 c) (.f64 -1 (.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))))
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(+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (.f64 -1 (.f64 (pow.f64 (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (.f64 (pow.f64 (/.f64 -1 c) 4) (+.f64 1 (/.f64 (exp.f64 (.f64 -1 (pow.f64 cosTheta 2))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)))))))))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (+.f64 c 1) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))
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(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (+.f64 c 1) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 (+.f64 c 1) (pow.f64 (sqrt.f64 (PI.f64)) 2)) (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (+.f64 c 1) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (+.f64 c 1) 2) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (.f64 -1 (sqrt.f64 (PI.f64)))))))) (pow.f64 cosTheta 4))) (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (+.f64 c 1) 2) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (.f64 -1 (sqrt.f64 (PI.f64)))))))))
(/.f64 1 (+.f64 c 1))
(/.f64 1 (+.f64 c 1))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
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(.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 (+.f64 c (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64)))))))) (cbrt.f64 (pow.f64 (/.f64 -1 (-.f64 -1 (+.f64 c (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))))) 2)))
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(.f64 -1 (/.f64 -1 (+.f64 (+.f64 c 1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64)))))))
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(-.f64 0 (/.f64 -1 (+.f64 (+.f64 c 1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))))
(/.f64 (cbrt.f64 (pow.f64 (/.f64 -1 (-.f64 -1 (+.f64 c (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64))))))) 2)) (cbrt.f64 (+.f64 (+.f64 c 1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64)))))))
(/.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 (+.f64 c (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64)))))))) (cbrt.f64 (pow.f64 (+.f64 (+.f64 c 1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64))))) 2)))
(/.f64 (neg.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 (+.f64 c (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64))))))))) (neg.f64 (cbrt.f64 (pow.f64 (+.f64 (+.f64 c 1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64))))) 2))))
(/.f64 -1 (/.f64 (+.f64 (+.f64 c 1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))) -1))
(/.f64 -1 (/.f64 (-.f64 -1 (+.f64 c (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))) 1))
(/.f64 -1 (-.f64 -1 (+.f64 c (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))))
(/.f64 1 (+.f64 (+.f64 c 1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))))
(/.f64 (/.f64 -1 (-.f64 -1 (+.f64 c (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))))) 1)
(pow.f64 (+.f64 (+.f64 c 1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))) -1)
(pow.f64 (cbrt.f64 (/.f64 -1 (-.f64 -1 (+.f64 c (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))))) 3)
(pow.f64 (pow.f64 (/.f64 -1 (-.f64 -1 (+.f64 c (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))))) 3) 1/3)
(pow.f64 (/.f64 -1 (-.f64 -1 (+.f64 c (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))))) 1)
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(neg.f64 (/.f64 -1 (+.f64 (+.f64 c 1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))))
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(if (!=.f64 (pow.f64 (+.f64 (+.f64 c 1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64))))) 3) 0) (pow.f64 (pow.f64 (+.f64 (+.f64 c 1) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64))))) 3) -1/3) (/.f64 -1 (-.f64 -1 (+.f64 c (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))))))
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(pow.f64 (cbrt.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))) 3)
(pow.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3) 1/3)
(pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 1)
(cbrt.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3) 1))
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Outputs
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(pow.f64 (+.f64 (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64))) 1) -1)
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(-.f64 (+.f64 (/.f64 (pow.f64 c 2) (pow.f64 (+.f64 (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64))) 1) 3)) (pow.f64 (+.f64 (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64))) 1) -1)) (/.f64 c (pow.f64 (+.f64 (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64))) 1) 2)))
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(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) cosTheta) (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))))) (pow.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) 2/3))
(.f64 (exp.f64 (neg.f64 (.f64 (pow.f64 cosTheta 2) 2/3))) (/.f64 (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))
(.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))))) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) cosTheta) 2)))
(/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64))) 2))) (cbrt.f64 (.f64 cosTheta (sqrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (/.f64 (pow.f64 cosTheta -1) (exp.f64 (pow.f64 cosTheta 2))))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 (neg.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64))) (/.f64 -1 cosTheta))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (cbrt.f64 cosTheta)) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (cbrt.f64 (pow.f64 cosTheta 2))))
(/.f64 (/.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (cbrt.f64 cosTheta)) (exp.f64 (pow.f64 cosTheta 2))) (cbrt.f64 (pow.f64 cosTheta 2)))
(*.f64 (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (cbrt.f64 cosTheta)) (/.f64 1 (cbrt.f64 (pow.f64 cosTheta 2))))
(/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 (.f64 (cbrt.f64 (pow.f64 cosTheta 2)) (cbrt.f64 cosTheta)) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (pow.f64 cosTheta -1))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(.f64 1 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64)))))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) 1)
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta)
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (neg.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64))) (neg.f64 cosTheta))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (*.f64 cosTheta (exp.f64 (pow.f64 cosTheta 2))))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (/.f64 (*.f64 cosTheta (exp.f64 (pow.f64 cosTheta 2))) 1))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 -1 (sqrt.f64 (PI.f64))) (/.f64 (neg.f64 cosTheta) (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) cosTheta) (/.f64 1 (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))) (*.f64 (neg.f64 cosTheta) (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1)) (.f64 (.f64 cosTheta (exp.f64 (pow.f64 cosTheta 2))) (pow.f64 (sqrt.f64 (PI.f64)) 2/3)))
(/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2/3) (.f64 cosTheta (exp.f64 (pow.f64 cosTheta 2)))))
(/.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) -1) (.f64 (.f64 cosTheta (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1/2) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (.f64 cosTheta (exp.f64 (pow.f64 cosTheta 2)))))
(/.f64 (/.f64 -1 (sqrt.f64 (PI.f64))) (neg.f64 (*.f64 cosTheta (exp.f64 (pow.f64 cosTheta 2)))))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (cbrt.f64 cosTheta)) (cbrt.f64 (pow.f64 cosTheta 2)))
(/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 (.f64 (cbrt.f64 (pow.f64 cosTheta 2)) (cbrt.f64 cosTheta)) (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) cosTheta) (exp.f64 (pow.f64 cosTheta 2)))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (cbrt.f64 cosTheta))) (neg.f64 (cbrt.f64 (pow.f64 cosTheta 2))))
(/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 (.f64 (cbrt.f64 (pow.f64 cosTheta 2)) (cbrt.f64 cosTheta)) (sqrt.f64 (PI.f64))))
(/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 -1 (.f64 (.f64 cosTheta (exp.f64 (pow.f64 cosTheta 2))) (neg.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (neg.f64 cosTheta)) -1)
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 1 (/.f64 (*.f64 cosTheta (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2)))))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 1 (.f64 (.f64 cosTheta (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 1 (.f64 (.f64 cosTheta (sqrt.f64 (PI.f64))) (exp.f64 (pow.f64 cosTheta 2))))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 1)
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(pow.f64 (cbrt.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64))))) 3)
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(pow.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3) 1/3)
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 1)
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(cbrt.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) 3) 1))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(neg.f64 (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (neg.f64 cosTheta)))
(/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))
(if (!=.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) 0) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64)))))
(if (!=.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) 0) (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64))) (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64))))
(if (!=.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) 0) (/.f64 1 (pow.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) -1)) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))))
(if (!=.f64 (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64))) 0) (pow.f64 (/.f64 1 (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64)))) -1) (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64))))
(if (!=.f64 1 0) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (.f64 cosTheta (sqrt.f64 (PI.f64)))))
(if (!=.f64 1 0) (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64))) (/.f64 (/.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) cosTheta) (sqrt.f64 (PI.f64))))

localize50.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 -1/2 cosTheta) (/.f64 1 cosTheta))
✓	0.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1))
	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 133 to 80 computations (39.8% saved)

series70.0ms (0.1%)

Counts

3 → 18

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	cosTheta	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
2.0ms	cosTheta	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	c	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	c	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	c	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))

Compiler

Compiled 10300 to 7735 computations (24.9% saved)

rewrite1.5s (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

119×	`egg-rr`
33×	`egg-rr`
32×	`egg-rr`

Counts

3 → 184

Calls

Call 1

Inputs

(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (*.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1))

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (*.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

(+.f64 (*.f64 -1/2 cosTheta) (/.f64 1 cosTheta))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 3)) (/.f64 1 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (+.f64 1 (+.f64 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 2) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 (-.f64 1 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))) (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1))) (/.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) 2)) (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (pow.f64 (sqrt.f64 (PI.f64)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) 2)) (cbrt.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1)) (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 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(#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 1 0) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 -1 0) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/2 cosTheta) (pow.f64 cosTheta -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 cosTheta -1) (*.f64 -1/2 cosTheta))))))

simplify4.3s (4.9%)

Algorithm

1×

egglog

Counts

202 → 242

Calls

Call 1

Inputs
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(*.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64))))
(*.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64))))
(/.f64 1 c)
(+.f64 (/.f64 1 c) (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (*.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 1 c) 2))))
(+.f64 (/.f64 1 c) (+.f64 (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) 2)) (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (*.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 1 c) 2)))))
(+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) 2) (pow.f64 (/.f64 1 c) 4)))) (+.f64 (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) 2)) (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 1 c) 2))))))
(/.f64 1 c)
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (*.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 -1 c) 2))) (/.f64 1 c))
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 -1 c) 2))) (+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) 2)))))
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) 2) (pow.f64 (/.f64 -1 c) 4)))) (+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 -1 c) 2))) (+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (*.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) 2))))))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 -1 (.f64 (+.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 3/2 (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))) (pow.f64 cosTheta 4))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (*.f64 -3/2 (sqrt.f64 (PI.f64)))))))))
(/.f64 1 cosTheta)
(*.f64 -1/2 cosTheta)
(*.f64 -1/2 cosTheta)
(*.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) 1)
(.f64 (-.f64 1 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 3)) (/.f64 1 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) (+.f64 1 (+.f64 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 2) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))))))
(*.f64 -1 (/.f64 (-.f64 1 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))) (sqrt.f64 (PI.f64))))
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(fma.f64 cosTheta -1/2 (pow.f64 cosTheta -1))
(pow.f64 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 3) 1/3)
(pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 1)
(pow.f64 (cbrt.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))) 3)
(cbrt.f64 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 3))
(neg.f64 (neg.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))))
(if (!=.f64 (.f64 -1/2 cosTheta) 0) (/.f64 (+.f64 (.f64 (pow.f64 cosTheta 3) -1/8) (pow.f64 (pow.f64 cosTheta -1) 3)) (-.f64 (*.f64 (pow.f64 cosTheta 2) 1/4) (/.f64 (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta)) cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta)) 0) (/.f64 (fma.f64 1/4 (pow.f64 cosTheta 2) (/.f64 -1 (pow.f64 cosTheta 2))) (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (.f64 -1/2 cosTheta) 0) (.f64 cosTheta (*.f64 -1/2 (+.f64 1 (/.f64 -2 (pow.f64 cosTheta 2))))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (-.f64 (.f64 (pow.f64 cosTheta 2) 1/4) (/.f64 (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta)) cosTheta)) 0) (/.f64 (+.f64 (.f64 (pow.f64 cosTheta 3) -1/8) (pow.f64 (pow.f64 cosTheta -1) 3)) (-.f64 (*.f64 (pow.f64 cosTheta 2) 1/4) (/.f64 (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta)) cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (+.f64 (.f64 (pow.f64 cosTheta 3) -1/8) (pow.f64 (pow.f64 cosTheta -1) 3)) (-.f64 (.f64 (pow.f64 cosTheta 2) 1/4) (/.f64 (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta)) cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (-.f64 (pow.f64 cosTheta -1) (*.f64 -1/2 cosTheta)) 0) (/.f64 (fma.f64 1/4 (pow.f64 cosTheta 2) (/.f64 -1 (pow.f64 cosTheta 2))) (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (pow.f64 cosTheta -1) 0) (.f64 (pow.f64 cosTheta -1) (+.f64 1 (/.f64 cosTheta (.f64 (pow.f64 cosTheta -1) -2)))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 0) (/.f64 1 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) -1)) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 1 0) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 -1 0) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(+.f64 (*.f64 -1/2 cosTheta) (pow.f64 cosTheta -1))
(+.f64 (pow.f64 cosTheta -1) (*.f64 -1/2 cosTheta))

Outputs
(/.f64 1 (*.f64 (sqrt.f64 (PI.f64)) cosTheta))
(/.f64 (pow.f64 cosTheta -1) (sqrt.f64 (PI.f64)))
(*.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64))))
(/.f64 cosTheta (/.f64 (sqrt.f64 (PI.f64)) -1/2))
(*.f64 -1/2 (/.f64 cosTheta (sqrt.f64 (PI.f64))))
(/.f64 cosTheta (/.f64 (sqrt.f64 (PI.f64)) -1/2))
(/.f64 1 c)
(pow.f64 c -1)
(+.f64 (/.f64 1 c) (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (*.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 1 c) 2))))
(-.f64 (pow.f64 c -1) (.f64 (+.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) (pow.f64 (pow.f64 c -1) 2)))
(+.f64 (/.f64 1 c) (+.f64 (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) 2)) (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (*.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 1 c) 2)))))
(+.f64 (-.f64 (pow.f64 c -1) (.f64 (+.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) (pow.f64 (pow.f64 c -1) 2))) (/.f64 (pow.f64 (+.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (*.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) 2) (pow.f64 c 3)))
(+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) 2) (pow.f64 (/.f64 1 c) 4)))) (+.f64 (.f64 (pow.f64 (/.f64 1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) 2)) (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 1 c) 2))))))
(-.f64 (+.f64 (-.f64 (pow.f64 c -1) (.f64 (+.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) (pow.f64 (pow.f64 c -1) 2))) (/.f64 (pow.f64 (+.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) 2) (pow.f64 c 3))) (.f64 (pow.f64 (+.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (*.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) 3) (pow.f64 (/.f64 -1 c) 4)))
(/.f64 1 c)
(pow.f64 c -1)
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (*.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 -1 c) 2))) (/.f64 1 c))
(-.f64 (pow.f64 c -1) (.f64 (+.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) (pow.f64 (pow.f64 c -1) 2)))
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 -1 c) 2))) (+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) 2)))))
(+.f64 (-.f64 (pow.f64 c -1) (.f64 (+.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) (pow.f64 (pow.f64 c -1) 2))) (/.f64 (pow.f64 (+.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (*.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) 2) (pow.f64 c 3)))
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) 2) (pow.f64 (/.f64 -1 c) 4)))) (+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) (pow.f64 (/.f64 -1 c) 2))) (+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (exp.f64 (*.f64 -1 (pow.f64 cosTheta 2)))) (sqrt.f64 (PI.f64)))) 2))))))
(-.f64 (+.f64 (-.f64 (pow.f64 c -1) (.f64 (+.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) (pow.f64 (pow.f64 c -1) 2))) (/.f64 (pow.f64 (+.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) 2) (pow.f64 c 3))) (.f64 (pow.f64 (+.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (*.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) 3) (pow.f64 (/.f64 -1 c) 4)))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))
(-.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 (*.f64 (pow.f64 cosTheta 2) (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))
(-.f64 (-.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 (.f64 (pow.f64 cosTheta 2) (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 (pow.f64 cosTheta 3) (-.f64 (.f64 (sqrt.f64 (PI.f64)) -3/2) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) (pow.f64 (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1)) 2)))))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 -1 (.f64 (+.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 3/2 (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))) (pow.f64 cosTheta 4))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (*.f64 -3/2 (sqrt.f64 (PI.f64)))))))))
(-.f64 (-.f64 (-.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 (pow.f64 cosTheta 3) (-.f64 (.f64 (sqrt.f64 (PI.f64)) -3/2) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) (pow.f64 (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1)) 2))))) (.f64 (-.f64 (+.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 3/2 (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1))) (-.f64 (.f64 (sqrt.f64 (PI.f64)) -3/2) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 3) (pow.f64 (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1)) 2))))) (pow.f64 cosTheta 4))) (.f64 (*.f64 (pow.f64 cosTheta 2) (-.f64 (-.f64 c -1) (pow.f64 (sqrt.f64 (PI.f64)) -1))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))
(/.f64 1 cosTheta)
(pow.f64 cosTheta -1)
(*.f64 -1/2 cosTheta)
(*.f64 -1/2 cosTheta)
(*.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) 1)
(/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))
(.f64 (-.f64 1 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 3)) (/.f64 1 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) (+.f64 1 (+.f64 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 2) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))))))
(/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))
(*.f64 -1 (/.f64 (-.f64 1 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))) (sqrt.f64 (PI.f64))))
(/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1))) (/.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) 2)) (sqrt.f64 (PI.f64))))
(/.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) 3)) (sqrt.f64 (PI.f64)))
(*.f64 1 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))))
(/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)))
(/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))
(*.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (pow.f64 (sqrt.f64 (PI.f64)) -1))
(/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) 2)))
(/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) 2)) (cbrt.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))))
(/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1)) (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2))))
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1)) (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1))) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2)))
(*.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))) (cbrt.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) 2) (pow.f64 (sqrt.f64 (PI.f64)) 2))))
(cbrt.f64 (*.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) (/.f64 (pow.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) 2) (pow.f64 (sqrt.f64 (PI.f64)) 2))))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) -1) (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (/.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) 2)) (sqrt.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) 3)) (sqrt.f64 (PI.f64)))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1)) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -2)) (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1))))
(.f64 (cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (pow.f64 (sqrt.f64 (PI.f64)) -2))) (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)))
(*.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -2)))
(/.f64 (*.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) -2))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (cbrt.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)))) (cbrt.f64 (pow.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) 2)))
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) (cbrt.f64 (pow.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) 3)))
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(if (!=.f64 1 0) (pow.f64 (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))) (-.f64 c -1)) -1) (pow.f64 (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))) (-.f64 c -1)) -1))
(if (!=.f64 (pow.f64 (fma.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1) 0) (/.f64 1 (pow.f64 (pow.f64 (fma.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1) -1)) (pow.f64 (fma.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1))
(if (!=.f64 (pow.f64 (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))) (-.f64 c -1)) -1) 0) (pow.f64 (/.f64 1 (pow.f64 (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))) (-.f64 c -1)) -1)) -1) (pow.f64 (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (*.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))) (-.f64 c -1)) -1))
(if (!=.f64 (cbrt.f64 (fma.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1))) 0) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1))) (neg.f64 3)) (pow.f64 (fma.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1))
(if (!=.f64 (cbrt.f64 (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))) (-.f64 c -1))) 0) (pow.f64 (cbrt.f64 (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))) (-.f64 c -1))) -3) (pow.f64 (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (*.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))) (-.f64 c -1)) -1))
(if (!=.f64 (pow.f64 (fma.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) 3) 0) (pow.f64 (pow.f64 (fma.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) 3) (neg.f64 1/3)) (pow.f64 (fma.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1))
(if (!=.f64 (pow.f64 (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))) (-.f64 c -1)) 3) 0) (pow.f64 (pow.f64 (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))) (-.f64 c -1)) 3) -1/3) (pow.f64 (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (*.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))) (-.f64 c -1)) -1))
(if (!=.f64 (-.f64 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))) 2)) (+.f64 c (/.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))))) 0) (*.f64 (/.f64 1 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))) 3))) (-.f64 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))) 2)) (+.f64 c (/.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64)))))) (pow.f64 (fma.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (sqrt.f64 (PI.f64))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1))
(if (!=.f64 (+.f64 1 (.f64 (+.f64 c (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) (+.f64 -1 (+.f64 c (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))))))) 0) (/.f64 (+.f64 1 (.f64 (+.f64 c (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) (+.f64 -1 (+.f64 c (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))))))) (-.f64 (pow.f64 (+.f64 c (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2))))) 3) -1)) (pow.f64 (+.f64 (/.f64 (+.f64 (pow.f64 cosTheta -1) (fma.f64 cosTheta -1/2 -1)) (.f64 (sqrt.f64 (PI.f64)) (exp.f64 (pow.f64 cosTheta 2)))) (-.f64 c -1)) -1))
(*.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 1)
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(*.f64 1 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(*.f64 (/.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) -1) -1)
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(.f64 (+.f64 (cbrt.f64 (pow.f64 (pow.f64 cosTheta -1) 2)) (-.f64 (cbrt.f64 (.f64 (pow.f64 cosTheta 2) 1/4)) (.f64 (cbrt.f64 (pow.f64 cosTheta -1)) (cbrt.f64 (.f64 -1/2 cosTheta))))) (+.f64 (cbrt.f64 (pow.f64 cosTheta -1)) (cbrt.f64 (*.f64 -1/2 cosTheta))))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(.f64 (+.f64 (cbrt.f64 (.f64 (pow.f64 cosTheta 2) 1/4)) (-.f64 (cbrt.f64 (pow.f64 (pow.f64 cosTheta -1) 2)) (.f64 (cbrt.f64 (.f64 -1/2 cosTheta)) (cbrt.f64 (pow.f64 cosTheta -1))))) (+.f64 (cbrt.f64 (*.f64 -1/2 cosTheta)) (cbrt.f64 (pow.f64 cosTheta -1))))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(*.f64 (cbrt.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))) (cbrt.f64 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 2)))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 2)) (cbrt.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(-.f64 (*.f64 -1/2 cosTheta) (/.f64 -1 cosTheta))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(/.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 1)
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(/.f64 (neg.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))) -1)
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(fma.f64 (cbrt.f64 (pow.f64 cosTheta -1)) (cbrt.f64 (pow.f64 (pow.f64 cosTheta -1) 2)) (*.f64 -1/2 cosTheta))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(fma.f64 (cbrt.f64 (.f64 -1/2 cosTheta)) (cbrt.f64 (.f64 (pow.f64 cosTheta 2) 1/4)) (pow.f64 cosTheta -1))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(fma.f64 1 (pow.f64 cosTheta -1) (*.f64 -1/2 cosTheta))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(fma.f64 1 (*.f64 -1/2 cosTheta) (pow.f64 cosTheta -1))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(fma.f64 cosTheta -1/2 (pow.f64 cosTheta -1))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(pow.f64 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 3) 1/3)
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 1)
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(pow.f64 (cbrt.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))) 3)
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(cbrt.f64 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 3))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(neg.f64 (neg.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(if (!=.f64 (.f64 -1/2 cosTheta) 0) (/.f64 (+.f64 (.f64 (pow.f64 cosTheta 3) -1/8) (pow.f64 (pow.f64 cosTheta -1) 3)) (-.f64 (*.f64 (pow.f64 cosTheta 2) 1/4) (/.f64 (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta)) cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (.f64 -1/2 cosTheta) 0) (/.f64 (fma.f64 (pow.f64 cosTheta 3) -1/8 (/.f64 1 (pow.f64 cosTheta 3))) (fma.f64 (pow.f64 cosTheta 2) 1/4 (/.f64 (-.f64 (pow.f64 cosTheta -1) (.f64 -1/2 cosTheta)) cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta)) 0) (/.f64 (fma.f64 1/4 (pow.f64 cosTheta 2) (/.f64 -1 (pow.f64 cosTheta 2))) (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (.f64 -1/2 cosTheta) 0) (.f64 cosTheta (*.f64 -1/2 (+.f64 1 (/.f64 -2 (pow.f64 cosTheta 2))))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (.f64 -1/2 cosTheta) 0) (.f64 (*.f64 -1/2 cosTheta) (+.f64 1 (/.f64 -2 (pow.f64 cosTheta 2)))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (-.f64 (.f64 (pow.f64 cosTheta 2) 1/4) (/.f64 (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta)) cosTheta)) 0) (/.f64 (+.f64 (.f64 (pow.f64 cosTheta 3) -1/8) (pow.f64 (pow.f64 cosTheta -1) 3)) (-.f64 (*.f64 (pow.f64 cosTheta 2) 1/4) (/.f64 (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta)) cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (fma.f64 (pow.f64 cosTheta 2) 1/4 (/.f64 (-.f64 (pow.f64 cosTheta -1) (.f64 -1/2 cosTheta)) cosTheta)) 0) (/.f64 (fma.f64 (pow.f64 cosTheta 3) -1/8 (/.f64 1 (pow.f64 cosTheta 3))) (fma.f64 (pow.f64 cosTheta 2) 1/4 (/.f64 (-.f64 (pow.f64 cosTheta -1) (.f64 -1/2 cosTheta)) cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (+.f64 (.f64 (pow.f64 cosTheta 3) -1/8) (pow.f64 (pow.f64 cosTheta -1) 3)) (-.f64 (.f64 (pow.f64 cosTheta 2) 1/4) (/.f64 (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta)) cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (fma.f64 (pow.f64 cosTheta 3) -1/8 (/.f64 1 (pow.f64 cosTheta 3))) (fma.f64 (pow.f64 cosTheta 2) 1/4 (/.f64 (-.f64 (pow.f64 cosTheta -1) (*.f64 -1/2 cosTheta)) cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (-.f64 (pow.f64 cosTheta -1) (*.f64 -1/2 cosTheta)) 0) (/.f64 (fma.f64 1/4 (pow.f64 cosTheta 2) (/.f64 -1 (pow.f64 cosTheta 2))) (fma.f64 -1/2 cosTheta (/.f64 -1 cosTheta))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (pow.f64 cosTheta -1) 0) (.f64 (pow.f64 cosTheta -1) (+.f64 1 (/.f64 cosTheta (.f64 (pow.f64 cosTheta -1) -2)))) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (pow.f64 cosTheta -1) 0) (/.f64 (+.f64 1 (/.f64 cosTheta (/.f64 -2 cosTheta))) cosTheta) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) 0) (/.f64 1 (pow.f64 (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) -1)) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 1 0) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(if (!=.f64 -1 0) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)) (fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1)))
(+.f64 (*.f64 -1/2 cosTheta) (pow.f64 cosTheta -1))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))
(+.f64 (pow.f64 cosTheta -1) (*.f64 -1/2 cosTheta))
(fma.f64 -1/2 cosTheta (pow.f64 cosTheta -1))

localize46.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta)
✓	0.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
	0.5b	(/.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))
	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 118 to 68 computations (42.4% saved)

series74.0ms (0.1%)

Counts

2 → 22

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	c	@	0	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	cosTheta	@	-inf	(/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta)
1.0ms	c	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
1.0ms	c	@	inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
0.0ms	cosTheta	@	-inf	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Compiler

Compiled 9890 to 7440 computations (24.8% saved)

rewrite1.5s (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

37×	`egg-rr`
35×	`egg-rr`

Counts

2 → 72

Calls

Call 1

Inputs

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

(/.f64 (sqrt.f64 (-.f64 (*.f64 cosTheta -2) -1)) cosTheta)

Outputs

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(/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta) 1))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 0) (pow.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) -1) -1) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) (/.f64 cosTheta (sqrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) 0) (pow.f64 (/.f64 cosTheta (sqrt.f64 (fma.f64 cosTheta -2 1))) -1) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) 2)) 0) (/.f64 (cbrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) (/.f64 cosTheta (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) 2)))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 1 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta))))))

simplify2.5s (2.8%)

Algorithm

1×

egglog

Counts

94 → 118

Calls

Call 1

Inputs
(/.f64 1 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))
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(+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (+.f64 (.f64 -1 (/.f64 c (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))))
(+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (+.f64 (.f64 -1 (/.f64 c (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (+.f64 (/.f64 1 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)))) (.f64 -1 (/.f64 (pow.f64 c 3) (pow.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) 2))))))
(/.f64 1 c)
(+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))))
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(+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 1 c) 4)))) (+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (pow.f64 (/.f64 1 c) 3)))))
(/.f64 1 c)
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (/.f64 1 c))
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2)))))
(+.f64 (.f64 -1 (.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 2))) (+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 -1 c) 3) (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (.f64 -1 (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (pow.f64 (/.f64 -1 c) 4)))))))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
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(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))
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(/.f64 1 (+.f64 c 1))
(/.f64 1 (+.f64 c 1))
(/.f64 1 cosTheta)
(-.f64 (/.f64 1 cosTheta) 1)
(-.f64 (+.f64 (*.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)
(-.f64 (+.f64 (.f64 -1/2 cosTheta) (+.f64 (/.f64 1 cosTheta) (.f64 -1/2 (pow.f64 cosTheta 2)))) 1)
(.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)))) (/.f64 -1 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 2))))
(.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1)) (/.f64 1 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 2))))
(.f64 1 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1))
(.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1) 1)
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1) 2)) (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1)))
(.f64 -1 (/.f64 1 (-.f64 -1 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))))))
(.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1)) (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1) 2)))
(.f64 (/.f64 1 (-.f64 -1 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))))) -1)
(-.f64 (/.f64 0 (-.f64 -1 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))))) (/.f64 1 (-.f64 -1 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))))))
(-.f64 (/.f64 0 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c))) (/.f64 1 (-.f64 -1 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))))))
(-.f64 0 (/.f64 1 (-.f64 -1 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))))))
(/.f64 1 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)))
(/.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1) 1)
(/.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)))) (neg.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 2))))
(/.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1)) (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 2)))
(/.f64 -1 (-.f64 -1 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2))))))
(/.f64 (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1) 2)) (cbrt.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c))))
(/.f64 -1 (.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 2)) (cbrt.f64 (-.f64 -1 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2))))))))
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(neg.f64 (.f64 (/.f64 1 (-.f64 -1 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))))) 1))
(if (!=.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 0) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1))
(if (!=.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1) 0) (pow.f64 (pow.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1) -1) -1) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1))
(if (!=.f64 -1 0) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1))
(if (!=.f64 1 0) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1))
(if (!=.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 3) 0) (pow.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 3) (neg.f64 1/3)) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1))
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(if (!=.f64 (-.f64 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))) 2)) (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2))))) 0) (.f64 (/.f64 1 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))) 3))) (-.f64 (+.f64 1 (pow.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))) 2)) (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (pow.f64 cosTheta 2)))))) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1))
(if (!=.f64 (.f64 (-.f64 1 (-.f64 c (pow.f64 c 2))) (sqrt.f64 (PI.f64))) 0) (.f64 (/.f64 1 (+.f64 (.f64 (+.f64 1 (pow.f64 c 3)) (sqrt.f64 (PI.f64))) (.f64 (-.f64 1 (-.f64 c (pow.f64 c 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (exp.f64 (pow.f64 cosTheta 2))) cosTheta)))) (.f64 (-.f64 1 (-.f64 c (pow.f64 c 2))) (sqrt.f64 (PI.f64)))) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1))
(if (!=.f64 (.f64 (sqrt.f64 (PI.f64)) (-.f64 1 (-.f64 c (pow.f64 c 2)))) 0) (.f64 (/.f64 1 (+.f64 (.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (exp.f64 (pow.f64 cosTheta 2))) cosTheta) (-.f64 1 (-.f64 c (pow.f64 c 2)))) (.f64 (sqrt.f64 (PI.f64)) (+.f64 1 (pow.f64 c 3))))) (.f64 (sqrt.f64 (PI.f64)) (-.f64 1 (-.f64 c (pow.f64 c 2))))) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) -1))
(*.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) (/.f64 -1 cosTheta))
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) (cbrt.f64 cosTheta)) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) (cbrt.f64 (pow.f64 cosTheta 2))))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta)) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) 2) (pow.f64 cosTheta 2))))
(*.f64 (cbrt.f64 (pow.f64 cosTheta -1)) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (cbrt.f64 (pow.f64 cosTheta 2))))
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) 2)) cosTheta))
(*.f64 1 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 1)
(*.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta)) (neg.f64 (pow.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta)) 2)))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta)) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 2)))
(*.f64 (neg.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta))) (pow.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta)) 2))
(*.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (pow.f64 cosTheta -1))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (cbrt.f64 cosTheta)) (/.f64 1 (cbrt.f64 (pow.f64 cosTheta 2))))
(*.f64 -1 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta))
(*.f64 (pow.f64 cosTheta -1) (sqrt.f64 (fma.f64 cosTheta -2 1)))
(*.f64 (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta))) (neg.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 2))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 2)) (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta)))
(-.f64 (/.f64 0 (neg.f64 cosTheta)) (/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta))
(-.f64 0 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) (neg.f64 cosTheta))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 1)
(/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (cbrt.f64 cosTheta)) (cbrt.f64 (pow.f64 cosTheta 2)))
(/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta)
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta) -1)
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (cbrt.f64 cosTheta))) (neg.f64 (cbrt.f64 (pow.f64 cosTheta 2))))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 1)
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta)) 3)
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 3) 1/3)
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 3))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 3) 1))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta))
(neg.f64 (/.f64 (/.f64 (neg.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) cosTheta) 1))
(if (!=.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) 0) (pow.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) -1) -1) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta))
(if (!=.f64 (sqrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) 0) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) (/.f64 cosTheta (sqrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta))
(if (!=.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) 0) (pow.f64 (/.f64 cosTheta (sqrt.f64 (fma.f64 cosTheta -2 1))) -1) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta))
(if (!=.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) 2)) 0) (/.f64 (cbrt.f64 (sqrt.f64 (fma.f64 cosTheta -2 1))) (/.f64 cosTheta (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) 2)))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta))
(if (!=.f64 1 0) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) cosTheta))

Outputs
(/.f64 1 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))
(/.f64 1 (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1))
(+.f64 (.f64 -1 (/.f64 c (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)))))
(-.f64 (/.f64 1 (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1)) (/.f64 c (pow.f64 (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1) 2)))
(+.f64 (/.f64 (pow.f64 c 2) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (+.f64 (.f64 -1 (/.f64 c (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2))) (/.f64 1 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))))
(+.f64 (/.f64 (.f64 c c) (pow.f64 (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1) 3)) (-.f64 (/.f64 1 (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1)) (/.f64 c (pow.f64 (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1) 2))))
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(+.f64 (/.f64 (.f64 c c) (pow.f64 (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1) 3)) (-.f64 (-.f64 (/.f64 1 (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1)) (/.f64 c (pow.f64 (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1) 2))) (/.f64 (pow.f64 c 3) (pow.f64 (pow.f64 (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1) 2) 2))))
(/.f64 1 c)
(+.f64 (/.f64 1 c) (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))))
(-.f64 (/.f64 1 c) (.f64 (/.f64 (/.f64 1 c) c) (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1)))
(+.f64 (/.f64 1 c) (+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 1 c) 2) (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))))) (.f64 (pow.f64 (+.f64 1 (/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -2 cosTheta))) (exp.f64 (.f64 -1 (pow.f64 cosTheta 2)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) 2) (pow.f64 (/.f64 1 c) 3))))
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(+.f64 (-.f64 (/.f64 1 c) (.f64 (pow.f64 (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1) 3) (pow.f64 (/.f64 1 c) 4))) (-.f64 (/.f64 (pow.f64 (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1) 2) (pow.f64 c 3)) (.f64 (/.f64 (/.f64 1 c) c) (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1))))
(/.f64 1 c)
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(-.f64 (/.f64 1 c) (.f64 (/.f64 (/.f64 1 c) c) (-.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (pow.f64 (exp.f64 cosTheta) cosTheta) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) -1)))
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eval512.0ms (0.6%)

Compiler: Compiled 34916 to 22160 computations (36.5% saved)

prune270.0ms (0.3%)

Pruning

17 alts after pruning (9 fresh and 8 done)

	Pruned	Kept	Total
New	956	2	958
Fresh	0	7	7
Picked	0	1	1
Done	0	7	7
Total	956	17	973

Error

Counts

973 → 17

Alt Table

Click to see full alt table

Status	Error	Program
	41.2b	(pow.f64 (/.f64 1 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 3)) 1/3)
✓	60.5b	(/.f64 1 (-.f64 c -1))
✓	0.8b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
✓	0.3b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
✓	2.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
	1.8b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (/.f64 1 cosTheta) 1) (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
	1.5b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
✓	0.5b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
	2.4b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 1 cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
✓	1.5b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
✓	1.2b	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
✓	60.5b	(-.f64 1 c)
	2.2b	(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2) cosTheta)
	2.4b	(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
	40.9b	(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (+.f64 1 c)) 3) -1))
	39.9b	(cbrt.f64 (/.f64 1 (pow.f64 (-.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (pow.f64 (exp.f64 cosTheta) cosTheta)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) -1) 3)))
	60.5b	1

Compiler

Compiled 324 to 267 computations (17.6% saved)

regimes141.0ms (0.2%)

Counts

47 → 1

Calls

Call 1

Inputs
1
(-.f64 1 c)
(/.f64 1 c)
(/.f64 1 (-.f64 c -1))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 1 cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (/.f64 1 cosTheta) 1) (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 1) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))) (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(cbrt.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 cosTheta 3) (pow.f64 (sqrt.f64 (PI.f64)) 2))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 3)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 3)) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(cbrt.f64 (/.f64 1 (pow.f64 (-.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (pow.f64 (exp.f64 cosTheta) cosTheta)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) -1) 3)))
(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) 0) (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (/.f64 cosTheta (pow.f64 (sqrt.f64 (PI.f64)) -1))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (+.f64 1 c)) 3) -1))
(cbrt.f64 (/.f64 1 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)) 3)))
(pow.f64 (/.f64 1 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 3)) 1/3)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 3) -1))
(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)) -1)) 3)
(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)) 3)
(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1)) 3)
(pow.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)) 3) -1) 1/3)
(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2) cosTheta)) (+.f64 1 c)) -1)
(pow.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) 3) -1) 1/3)
(if (!=.f64 (.f64 (fma.f64 c c (-.f64 1 c)) cosTheta) 0) (/.f64 (.f64 (fma.f64 c c (-.f64 1 c)) cosTheta) (fma.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (fma.f64 c c (-.f64 1 c)) (+.f64 (.f64 (pow.f64 c 3) cosTheta) cosTheta))) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (-.f64 c -1)) -1))
(if (!=.f64 (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64))) (-.f64 c -1))) 0) (pow.f64 (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64))) (-.f64 c -1))) -3) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 2 cosTheta))) cosTheta) (sqrt.f64 (PI.f64))) (-.f64 c -1)) -1))
(cbrt.f64 (/.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) -1) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 2)))
(/.f64 (/.f64 1 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c)) 2))) (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c))))
(/.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c)))) (neg.f64 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 cosTheta (sqrt.f64 (PI.f64)))) (+.f64 1 c)) 2))))
(if (!=.f64 (+.f64 1 (.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) cosTheta)) (+.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) cosTheta)) -1))) 0) (/.f64 (+.f64 1 (.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) cosTheta)) (+.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) cosTheta)) -1))) (-.f64 (pow.f64 (+.f64 c (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (exp.f64 (pow.f64 cosTheta 2)) (sqrt.f64 (PI.f64)))) cosTheta)) 3) -1)) (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) -1))
(+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 2) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2)))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) cosTheta) (+.f64 (.f64 -1 (.f64 (pow.f64 cosTheta 3) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64)))))) (.f64 -1 (.f64 (+.f64 (.f64 1/2 (sqrt.f64 (PI.f64))) (+.f64 (.f64 3/2 (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) 2))) (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) (+.f64 (.f64 -1 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (pow.f64 (-.f64 (+.f64 c 1) (/.f64 1 (sqrt.f64 (PI.f64)))) 2)))) (.f64 -3/2 (sqrt.f64 (PI.f64))))))))) (pow.f64 cosTheta 4))))))

Outputs

(if (!=.f64 (*.f64 (fma.f64 c c (-.f64 1 c)) cosTheta) 0) (/.f64 (*.f64 (fma.f64 c c (-.f64 1 c)) cosTheta) (fma.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (exp.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) (fma.f64 c c (-.f64 1 c)) (+.f64 (*.f64 (pow.f64 c 3) cosTheta) cosTheta))) (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (-.f64 c -1)) -1))

Calls

6 calls:

21.0ms	(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))
20.0ms	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
20.0ms	(+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta))))
20.0ms	c
20.0ms	cosTheta

Results

Error	Segments	Branch
0.2b	1	`cosTheta`
0.2b	1	`c`
0.2b	1	`(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))`
0.2b	1	`(+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta))))`
0.2b	1	`(+.f64 1 c)`
0.2b	1	`(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))`

Compiler

Compiled 1464 to 964 computations (34.2% saved)

regimes106.0ms (0.1%)

Counts

40 → 1

Calls

Call 1

Inputs
1
(-.f64 1 c)
(/.f64 1 c)
(/.f64 1 (-.f64 c -1))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 1 cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (/.f64 1 cosTheta) 1) (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 1) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))) (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(cbrt.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 cosTheta 3) (pow.f64 (sqrt.f64 (PI.f64)) 2))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 3)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 3)) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(cbrt.f64 (/.f64 1 (pow.f64 (-.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (pow.f64 (exp.f64 cosTheta) cosTheta)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) -1) 3)))
(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) 0) (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (/.f64 cosTheta (pow.f64 (sqrt.f64 (PI.f64)) -1))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (+.f64 -1 (pow.f64 cosTheta -1)) (sqrt.f64 (PI.f64))) (+.f64 1 c)) 3) -1))
(cbrt.f64 (/.f64 1 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)) 3)))
(pow.f64 (/.f64 1 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 1 c)) 3)) 1/3)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 cosTheta (sqrt.f64 (sqrt.f64 (PI.f64))))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (-.f64 c -1)) 3) -1))
(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)) -1)) 3)
(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)) 3)
(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (*.f64 cosTheta (sqrt.f64 (PI.f64)))) (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (+.f64 c 1)) -1)) 3)
(pow.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (sqrt.f64 (PI.f64))) cosTheta) (+.f64 1 c)) 3) -1) 1/3)
(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2) cosTheta)) (+.f64 1 c)) -1)
(pow.f64 (pow.f64 (pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) 3) -1) 1/3)

Outputs

(/.f64 1 (+.f64 (+.f64 1 c) (*.f64 (if (!=.f64 (pow.f64 (sqrt.f64 (PI.f64)) -1) 0) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (/.f64 cosTheta (pow.f64 (sqrt.f64 (PI.f64)) -1))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 cosTheta 2))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Calls

6 calls:

18.0ms	(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))
17.0ms	(+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta))))
17.0ms	c
17.0ms	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
16.0ms	cosTheta

Results

Error	Segments	Branch
0.2b	1	`cosTheta`
0.2b	1	`c`
0.2b	1	`(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))`
0.2b	1	`(+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta))))`
0.2b	1	`(+.f64 1 c)`
0.2b	1	`(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))`

Compiler

Compiled 939 to 603 computations (35.8% saved)

regimes74.0ms (0.1%)

Counts

27 → 1

Calls

Call 1

Inputs
1
(-.f64 1 c)
(/.f64 1 c)
(/.f64 1 (-.f64 c -1))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 1 cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (/.f64 1 cosTheta) 1) (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 1) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 1 (+.f64 cosTheta cosTheta))) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (if (!=.f64 (/.f64 1 cosTheta) 0) (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 cosTheta))) (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) cosTheta) (sqrt.f64 (PI.f64)))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 1 (/.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (sqrt.f64 (-.f64 1 (.f64 2 cosTheta)))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(cbrt.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 cosTheta 3) (pow.f64 (sqrt.f64 (PI.f64)) 2))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (.f64 (sqrt.f64 (PI.f64)) cosTheta)) 3)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (neg.f64 (fma.f64 2 cosTheta -1))) (sqrt.f64 (PI.f64))) 3)) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(cbrt.f64 (/.f64 1 (pow.f64 (-.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 cosTheta -2 1)) (pow.f64 (exp.f64 cosTheta) cosTheta)) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) -1) 3)))
(pow.f64 (fma.f64 (exp.f64 (neg.f64 (pow.f64 cosTheta 2))) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 cosTheta 2 -1))) (*.f64 (sqrt.f64 (PI.f64)) cosTheta)) (+.f64 1 c)) -1)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 cosTheta -2) -1)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) cosTheta)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))

Outputs
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 cosTheta 2))) (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Calls

6 calls:

13.0ms	(+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta))))
12.0ms	c
12.0ms	(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))
12.0ms	(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
12.0ms	cosTheta

Results

Error	Segments	Branch
0.3b	1	`cosTheta`
0.3b	1	`c`
0.3b	1	`(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))`
0.3b	1	`(+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta))))`
0.3b	1	`(+.f64 1 c)`
0.3b	1	`(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (-.f64 (-.f64 1 cosTheta) cosTheta)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))`

Compiler

Compiled 596 to 370 computations (37.9% saved)

regimes22.0ms (0%)

Counts

14 → 1

Calls

Call 1

Inputs
1
(-.f64 1 c)
(/.f64 1 c)
(/.f64 1 (-.f64 c -1))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 1 cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (/.f64 1 cosTheta) 1) (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 1) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Outputs
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1)) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))

Calls

3 calls:

8.0ms	c
7.0ms	cosTheta
2.0ms	(+.f64 1 c)

Results

Error	Segments	Branch
1.2b	1	`cosTheta`
1.2b	1	`c`
1.2b	1	`(+.f64 1 c)`

Compiler

Compiled 205 to 123 computations (40% saved)

regimes19.0ms (0%)

Counts

11 → 1

Calls

Call 1

Inputs
1
(-.f64 1 c)
(/.f64 1 c)
(/.f64 1 (-.f64 c -1))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 1 cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (/.f64 1 cosTheta) 1) (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Outputs
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (+.f64 (.f64 -1/2 cosTheta) (/.f64 1 cosTheta)) 1) (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Calls

3 calls:

7.0ms	cosTheta
6.0ms	c
2.0ms	(+.f64 1 c)

Results

Error	Segments	Branch
1.5b	1	`cosTheta`
1.5b	1	`c`
1.5b	1	`(+.f64 1 c)`

Compiler

Compiled 151 to 91 computations (39.7% saved)

regimes17.0ms (0%)

Counts

10 → 1

Calls

Call 1

Inputs
1
(-.f64 1 c)
(/.f64 1 c)
(/.f64 1 (-.f64 c -1))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 1 cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (/.f64 1 cosTheta) 1) (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Outputs
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (-.f64 (/.f64 1 cosTheta) 1)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Calls

3 calls:

6.0ms	c
6.0ms	cosTheta
2.0ms	(+.f64 1 c)

Results

Error	Segments	Branch
1.5b	1	`cosTheta`
1.5b	1	`c`
1.5b	1	`(+.f64 1 c)`

Compiler

Compiled 127 to 77 computations (39.4% saved)

regimes17.0ms (0%)

Counts

9 → 1

Calls

Call 1

Inputs
1
(-.f64 1 c)
(/.f64 1 c)
(/.f64 1 (-.f64 c -1))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 1 cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (/.f64 1 cosTheta) 1) (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))

Outputs
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (-.f64 (/.f64 1 cosTheta) 1) (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))

Calls

3 calls:

7.0ms	c
5.0ms	cosTheta
2.0ms	(+.f64 1 c)

Results

Error	Segments	Branch
1.8b	1	`cosTheta`
1.8b	1	`c`
1.8b	1	`(+.f64 1 c)`

Compiler

Compiled 105 to 64 computations (39% saved)

regimes14.0ms (0%)

Counts

8 → 1

Calls

Call 1

Inputs
1
(-.f64 1 c)
(/.f64 1 c)
(/.f64 1 (-.f64 c -1))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 1 cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Outputs
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (PI.f64))) cosTheta) (exp.f64 (.f64 (neg.f64 cosTheta) cosTheta)))))

Calls

3 calls:

5.0ms	c
5.0ms	cosTheta
2.0ms	(+.f64 1 c)

Results

Error	Segments	Branch
2.2b	1	`cosTheta`
2.2b	1	`c`
2.2b	1	`(+.f64 1 c)`

Compiler

Compiled 85 to 53 computations (37.6% saved)

regimes13.0ms (0%)

Counts

6 → 1

Calls

Call 1

Inputs
1
(-.f64 1 c)
(/.f64 1 c)
(/.f64 1 (-.f64 c -1))
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)
(/.f64 1 (+.f64 (+.f64 1 c) (.f64 (/.f64 1 (.f64 (sqrt.f64 (PI.f64)) cosTheta)) (exp.f64 (*.f64 (neg.f64 cosTheta) cosTheta)))))

Outputs
(*.f64 (sqrt.f64 (PI.f64)) cosTheta)

Calls

3 calls:

5.0ms	cosTheta
4.0ms	c
2.0ms	(+.f64 1 c)

Results

Error	Segments	Branch
2.4b	1	`cosTheta`
2.4b	1	`c`
2.4b	1	`(+.f64 1 c)`

Compiler

Compiled 47 to 33 computations (29.8% saved)

regimes8.0ms (0%)

Accuracy

Total -2.0b remaining (-3.2%)

Threshold costs -2.0b (-3.2%)

Counts

4 → 1

Calls

Call 1

Inputs
1
(-.f64 1 c)
(/.f64 1 c)
(/.f64 1 (-.f64 c -1))

Outputs
1

Calls

2 calls:

4.0ms	c
4.0ms	cosTheta

Results

Error	Segments	Branch
60.5b	1	`cosTheta`
60.5b	1	`c`

Compiler

Compiled 20 to 15 computations (25% saved)

simplify6.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 271 to 210 computations (22.5% saved)

soundness0.0ms (0%)

end104.0ms (0.1%)

Compiler: Compiled 253 to 156 computations (38.3% saved)