Metrics for Migdal et al, Equation (64)

analyze0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 21 to 14 computations (33.3% saved)

sample1.1s (11.1%)

Memory

30.9MiB live, 2 057.6MiB allocated

Samples

870.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 603.0ms

ival-mult: 216.0ms (35.8% of total)

ival-cos: 207.0ms (34.3% of total)

ival-sqrt: 65.0ms (10.8% of total)

ival-div: 62.0ms (10.3% of total)

ival-add: 38.0ms (6.3% of total)

ival-true: 6.0ms (1% of total)

exact: 6.0ms (1% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

preprocess139.0ms (1.3%)

Memory

18.6MiB live, 57.0MiB allocated

Algorithm

1×	egg-herbie

Rules

1 520×	`times-frac`
1 254×	`distribute-lft-in`
1 236×	`distribute-rgt-in`
946×	`div-sub`
714×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	120
1	130	120
2	373	120
3	1018	120
4	2414	120
5	4784	120
6	5686	120
7	6500	120
8	6573	120
9	6589	120
10	6760	120
11	6878	120
12	6890	120
13	6890	120
14	6890	120
0	12	19
0	20	13
1	33	13
2	58	13
3	88	13
4	100	13
0	100	12

Stop Event

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

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Outputs

(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))

(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))

Symmetry

(abs th)

(abs a2)

(abs a1)

(sort a1 a2)

explain150.0ms (1.4%)

Memory

-11.3MiB live, 315.4MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`a1`
-	-	`(*.f64 a1 a1)`
-	-	`(sqrt.f64 #s(literal 2 binary64))`
-	-	`th`
-	-	`#s(literal 2 binary64)`
-	-	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
-	-	`(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))`
-	-	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
-	-	`(*.f64 a2 a2)`
-	-	`(cos.f64 th)`
-	-	`(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))`
-	-	`a2`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

57.0ms

512×

valid

Compiler

Compiled 160 to 52 computations (67.5% saved)

Precisions

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

ival-mult: 13.0ms (37.6% of total)

ival-cos: 12.0ms (34.7% of total)

ival-sqrt: 4.0ms (11.6% of total)

ival-div: 3.0ms (8.7% of total)

ival-add: 2.0ms (5.8% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Compiler

Compiled 22 to 12 computations (45.5% saved)

simplify8.0ms (0.1%)

Memory

-29.3MiB live, 9.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(cos.f64 th)
✓	cost-diff	0	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
✓	cost-diff	8192	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Rules

100×	`lower-*.f32`
92×	`lower-*.f64`
60×	`lower-fma.f64`
60×	`lower-fma.f32`
48×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	56
0	20	50
1	33	50
2	58	50
3	88	50
4	100	50
0	100	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 a1 a1)
a1
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
(*.f64 a2 a2)
a2

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
(/.f64 (.f64 a1 (.f64 (cos.f64 th) a1)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 a1 a1)
a1
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
(/.f64 (.f64 a2 (.f64 (cos.f64 th) a2)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 a2 a2)
a2

localize41.0ms (0.4%)

Memory

-0.5MiB live, 81.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
✓	accuracy	99.7%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
✓	accuracy	99.7%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
✓	accuracy	98.9%	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

27.0ms

256×

valid

Compiler

Compiled 58 to 14 computations (75.9% saved)

Precisions

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

ival-cos: 7.0ms (40.5% of total)

ival-mult: 5.0ms (28.9% of total)

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

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

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

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.1%)

Memory

23.5MiB live, 23.5MiB allocated

Counts

5 → 108

Calls

Call 1

Inputs
#<alt (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))>
#<alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))>
#<alt (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (cos.f64 th)>
#<alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))>

Outputs
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (+ (* -1/2 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))) (/ (pow a1 2) (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))))) (/ (pow a1 2) (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))) (* 1/24 (/ (pow a1 2) (sqrt 2))))))) (/ (pow a1 2) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (/ 1 (sqrt 2))>
#<alt (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2)))>
#<alt (+ (* (pow th 2) (- (* 1/24 (/ (pow th 2) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))>
#<alt (+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/720 (/ (pow th 2) (sqrt 2))) (* 1/24 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow th 2)))>
#<alt (+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))>
#<alt (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (+ (* -1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))))) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2))))))) (/ (pow a2 2) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>

Calls

27 calls:

Time	Variable		Point	Expression
2.0ms	th	@	inf	(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
2.0ms	th	@	-inf	(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
2.0ms	th	@	-inf	(/ (cos th) (sqrt 2))
1.0ms	a1	@	0	(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
1.0ms	th	@	0	(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

simplify800.0ms (7.7%)

Memory

-29.3MiB live, 1 018.9MiB allocated

Algorithm

1×	egg-herbie

Rules

34 694×	`lower-fma.f64`
34 694×	`lower-fma.f32`
6 426×	`lower-*.f64`
6 426×	`lower-*.f32`
4 620×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	111	1498
1	343	1366
2	1205	1262
3	3898	1233
0	8422	1172

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

Inputs
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(+ (* -1/2 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))) (/ (pow a1 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))))) (/ (pow a1 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))) (* 1/24 (/ (pow a1 2) (sqrt 2))))))) (/ (pow a1 2) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ 1 (sqrt 2))
(+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2)))
(+ (* (pow th 2) (- (* 1/24 (/ (pow th 2) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/720 (/ (pow th 2) (sqrt 2))) (* 1/24 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
1
(+ 1 (* -1/2 (pow th 2)))
(+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))
(+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(/ (pow a2 2) (sqrt 2))
(+ (* -1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))))) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2))))))) (/ (pow a2 2) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))

Outputs
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 th (.f64 th (.f64 (.f64 (/.f64 (.f64 th th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (.f64 a2 a2) (.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (.f64 a2 a2) (.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (.f64 a2 a2) (.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (.f64 a2 a2) (.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (.f64 a2 a2) (.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (.f64 a2 a2) (.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))) (/ (pow a1 2) (sqrt 2)))
(.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))))) (/ (pow a1 2) (sqrt 2)))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))) (* 1/24 (/ (pow a1 2) (sqrt 2))))))) (/ (pow a1 2) (sqrt 2)))
(fma.f64 (.f64 th th) (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 th (.f64 th (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/ 1 (sqrt 2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2)))
(.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow th 2) (- (* 1/24 (/ (pow th 2) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(fma.f64 (/.f64 (.f64 th th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/720 (/ (pow th 2) (sqrt 2))) (* 1/24 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(fma.f64 (.f64 th th) (/.f64 (.f64 th (.f64 th (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow th 2)))
(fma.f64 th (*.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))
(fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))
(fma.f64 (.f64 th th) (fma.f64 th (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (/ (pow a2 2) (sqrt 2)))
(.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))))) (/ (pow a2 2) (sqrt 2)))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2))))))) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 th th)) (fma.f64 th (.f64 th (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))

rewrite420.0ms (4.1%)

Memory

28.3MiB live, 432.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 176×	`lower-fma.f64`
6 176×	`lower-fma.f32`
4 662×	`lower-*.f32`
4 654×	`lower-*.f64`
2 804×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	44
0	20	38
1	58	38
2	411	38
3	7331	38
0	8434	37

Stop Event

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

Counts

5 → 327

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))

Outputs
(+.f64 (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (.f64 (.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(fma.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2) (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (neg.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 a1 (/.f64 (.f64 (cos.f64 th) a1) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 a1 a1) (/.f64 (.f64 (.f64 a1 a1) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) #s(literal 2 binary64))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (neg.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (neg.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (.f64 a2 a2)) (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (.f64 a1 a1)) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a2 (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a1) (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a1) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (.f64 a1 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (neg.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) #s(literal 2 binary64)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (neg.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) #s(literal 2 binary64)) (/.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (neg.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (.f64 a1 a1) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) #s(literal 2 binary64))) (/.f64 (.f64 a1 a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (neg.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (.f64 (.f64 a1 a1) (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (neg.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64)) (.f64 (cos.f64 th) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64)))))
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(.f64 (/.f64 (.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (.f64 (cos.f64 th) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (.f64 a2 a2))))) #s(literal 2 binary64))
(.f64 (/.f64 (.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) (-.f64 (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))))))) (fma.f64 (.f64 (.f64 a2 a2) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th))))) #s(literal 1/2 binary64))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (.f64 a1 a1))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (.f64 a1 a1))) #s(literal 1 binary64)))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (.f64 a1 a1)))))
(/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
(/.f64 (.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (.f64 a1 a1) #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (cos.f64 th))))
(/.f64 (.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (cos.f64 th))))
(/.f64 (neg.f64 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (cos.f64 th))))
(/.f64 (neg.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (.f64 a1 a1))) #s(literal -1 binary64))
(.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
(.f64 a1 (/.f64 (.f64 (cos.f64 th) a1) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)))
(.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (*.f64 a1 a1)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.f64 (/.f64 (.f64 (cos.f64 th) a1) (sqrt.f64 #s(literal 2 binary64))) a1)
(.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (*.f64 a1 a1) (neg.f64 (cos.f64 th))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a1 (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (cos.f64 th))
(.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.f64 (.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a1 a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (.f64 a1 a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (.f64 (cos.f64 th) a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (.f64 a1 a1) #s(literal -1 binary64)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 (.f64 a1 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (cos.f64 th)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
(/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (cos.f64 th))))
(/.f64 (*.f64 (neg.f64 (cos.f64 th)) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(/.f64 (/.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -1 binary64))
(*.f64 (cos.f64 th) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 (neg.f64 (cos.f64 th)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (cos.f64 th)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -1/2 binary64)))
(cos.f64 th)
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 th)))
(neg.f64 (neg.f64 (cos.f64 th)))
(*.f64 (cos.f64 th) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 th))
(*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 th)))
(neg.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (.f64 a2 a2))) #s(literal 1 binary64)))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (.f64 a2 a2)))))
(/.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (cos.f64 th))))
(/.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
(/.f64 (.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (.f64 a2 a2) #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (cos.f64 th))))
(/.f64 (.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(/.f64 (/.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th))) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (.f64 a2 a2))) #s(literal -1 binary64))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
(.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.f64 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a2)
(.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (*.f64 a2 a2) (neg.f64 (cos.f64 th))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.f64 (.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (.f64 (cos.f64 th) a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (.f64 a2 a2) #s(literal -1 binary64)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))

eval82.0ms (0.8%)

Memory: -17.0MiB live, 99.7MiB allocated
Compiler: Compiled 14 708 to 1 018 computations (93.1% saved)

prune128.0ms (1.2%)

Memory

-18.9MiB live, 146.2MiB allocated

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	471	19	490
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	472	19	491

Accuracy

100.0%

Counts

491 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	99.5%	(/.f64 (/.f64 (fma.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
	99.6%	(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
	17.7%	(/.f64 (.f64 (fma.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))))) (cos.f64 th)) (.f64 (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
	99.6%	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
	98.9%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
	98.9%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))))
	41.5%	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) #s(approx (* (/ (cos th) (sqrt 2)) (* a2 a2)) (fma.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 th th)) (fma.f64 th (.f64 th (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
	99.6%	(.f64 (fma.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (.f64 a1 a1)))) #s(literal 1/2 binary64))
▶	99.6%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
▶	99.6%	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
▶	99.5%	(.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
▶	65.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
▶	49.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
	61.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
	60.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))

Compiler

Compiled 818 to 494 computations (39.6% saved)

simplify329.0ms (3.2%)

Memory

18.9MiB live, 334.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 a1 a1)
✓	cost-diff	0	(/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	1344	(.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th)))
✓	cost-diff	0	(cos.f64 th)
✓	cost-diff	0	(neg.f64 (cos.f64 th))
✓	cost-diff	192	(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	cost-diff	256	(.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
✓	cost-diff	0	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 a2 a2)
✓	cost-diff	0	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	cost-diff	0	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	1344	(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(*.f64 a2 a2)
✓	cost-diff	0	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	cost-diff	0	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))

Rules

5 748×	`lower-fma.f32`
5 742×	`lower-fma.f64`
2 710×	`lower-*.f32`
2 694×	`lower-*.f64`
1 682×	`unsub-neg`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	292
0	58	266
1	110	265
2	272	265
3	764	265
4	2273	250
5	5321	250
0	8062	250

Stop Event

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

Calls

Call 1

Inputs
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(cos.f64 th)
th
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
a1
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 a2 a2)
a2
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(neg.f64 (cos.f64 th))
(cos.f64 th)
th
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal -1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th)))
(*.f64 a1 a1)
a1
(.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
a2
(/.f64 a2 (*.f64 a1 a1))
#s(literal 1 binary64)
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

Outputs
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 a1 a1 (*.f64 a2 a2))
(fma.f64 a2 a2 (*.f64 a1 a1))
a1
(*.f64 a2 a2)
a2
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(cos.f64 th)
th
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
a1
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 a2 a2)
a2
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 a1 a1 (*.f64 a2 a2))
(fma.f64 a2 a2 (*.f64 a1 a1))
a1
(*.f64 a2 a2)
a2
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 (cos.f64 th))
(cos.f64 th)
th
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(neg.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal -1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 a1 a1 (*.f64 a2 a2))
(fma.f64 a2 a2 (*.f64 a1 a1))
a1
(*.f64 a2 a2)
a2
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(*.f64 a1 a1)
a1
(.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))
(.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
a2
(/.f64 a2 (*.f64 a1 a1))
#s(literal 1 binary64)
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

localize330.0ms (3.2%)

Memory

1.5MiB live, 239.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	95.1%	(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
✓	accuracy	85.0%	(/.f64 a2 (*.f64 a1 a1))
✓	accuracy	59.4%	(.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th)))
✓	accuracy	100.0%	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	accuracy	99.8%	(.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
✓	accuracy	99.6%	(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	accuracy	98.4%	(/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(cos.f64 th)
✓	accuracy	100.0%	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	accuracy	99.7%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	98.9%	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.7%	(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.4%	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	66.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	100.0%	(cos.f64 th)
✓	accuracy	100.0%	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	accuracy	99.8%	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
✓	accuracy	99.7%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))

Samples

136.0ms

256×

valid

Compiler

Compiled 275 to 34 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 17.0ms (35.4% of total)

ival-add: 12.0ms (25% of total)

ival-div: 10.0ms (20.8% of total)

ival-cos: 6.0ms (12.5% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series53.0ms (0.5%)

Memory

23.6MiB live, 62.0MiB allocated

Counts

22 → 480

Calls

Call 1

Inputs
#<alt (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))>
#<alt (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 a1 a1 (*.f64 a2 a2))>
#<alt (*.f64 a2 a2)>
#<alt (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))>
#<alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))>
#<alt (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))>
#<alt (neg.f64 (cos.f64 th))>
#<alt (cos.f64 th)>
#<alt (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th)))>
#<alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 a1 a1)>
#<alt (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 a2 (*.f64 a1 a1))>
#<alt (fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))>

Outputs
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))>
#<alt (+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
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#<alt (- (* (pow th 2) (+ 1/2 (* -1/24 (pow th 2)))) 1)>
#<alt (- (* (pow th 2) (+ 1/2 (* (pow th 2) (- (* 1/720 (pow th 2)) 1/24)))) 1)>
#<alt (* -1 (cos th))>
#<alt (* -1 (cos th))>
#<alt (* -1 (cos th))>
#<alt (* -1 (cos th))>
#<alt (* -1 (cos th))>
#<alt (* -1 (cos th))>
#<alt (* -1 (cos th))>
#<alt (* -1 (cos th))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow th 2)))>
#<alt (+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))>
#<alt (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (* (pow a2 2) (cos th))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (* (pow a1 2) (cos th))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (cos th))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (cos th))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (+ (* -1/2 (* (pow a1 2) (* (pow th 2) (+ 1 (/ (pow a2 2) (pow a1 2)))))) (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))))>
#<alt (+ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (* (pow th 2) (+ (* -1/2 (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))) (* 1/24 (* (pow a1 2) (* (pow th 2) (+ 1 (/ (pow a2 2) (pow a1 2)))))))))>
#<alt (+ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (* (pow th 2) (+ (* -1/2 (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))) (* (pow th 2) (+ (* -1/720 (* (pow a1 2) (* (pow th 2) (+ 1 (/ (pow a2 2) (pow a1 2)))))) (* 1/24 (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))))))))>
#<alt (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2)))))>
#<alt (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2)))))>
#<alt (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2)))))>
#<alt (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2)))))>
#<alt (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2)))))>
#<alt (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2)))))>
#<alt (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2)))))>
#<alt (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2)))))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2))>
#<alt (+ (* -1/2 (/ (* (pow a1 2) (* (pow th 2) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))) (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2))) (* 1/24 (/ (* (pow a1 2) (* (pow th 2) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))))) (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a1 2) (* (pow th 2) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))) (* 1/24 (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2))))))) (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))>
#<alt (/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))>
#<alt (/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))>
#<alt (/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))>
#<alt (/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))>
#<alt (/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))>
#<alt (/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))>
#<alt (/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt (/ a2 (pow a1 2))>
#<alt 1>
#<alt (+ 1 (/ (pow a2 2) (pow a1 2)))>
#<alt (+ 1 (/ (pow a2 2) (pow a1 2)))>
#<alt (+ 1 (/ (pow a2 2) (pow a1 2)))>
#<alt (/ (pow a2 2) (pow a1 2))>
#<alt (* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))>
#<alt (* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))>
#<alt (* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))>
#<alt (/ (pow a2 2) (pow a1 2))>
#<alt (* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))>
#<alt (* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))>
#<alt (* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))>
#<alt (/ (pow a2 2) (pow a1 2))>
#<alt (/ (+ (pow a1 2) (pow a2 2)) (pow a1 2))>
#<alt (/ (+ (pow a1 2) (pow a2 2)) (pow a1 2))>
#<alt (/ (+ (pow a1 2) (pow a2 2)) (pow a1 2))>
#<alt 1>
#<alt (+ 1 (/ (pow a2 2) (pow a1 2)))>
#<alt (+ 1 (/ (pow a2 2) (pow a1 2)))>
#<alt (+ 1 (/ (pow a2 2) (pow a1 2)))>
#<alt 1>
#<alt (+ 1 (/ (pow a2 2) (pow a1 2)))>
#<alt (+ 1 (/ (pow a2 2) (pow a1 2)))>
#<alt (+ 1 (/ (pow a2 2) (pow a1 2)))>

Calls

120 calls:

Time	Variable		Point	Expression
27.0ms	th	@	0	(neg (cos th))
1.0ms	th	@	inf	(* (* a1 a1) (* (+ (* a2 (/ a2 (* a1 a1))) 1) (cos th)))
1.0ms	th	@	0	(* (* a1 a1) (* (+ (* a2 (/ a2 (* a1 a1))) 1) (cos th)))
1.0ms	a2	@	inf	(* (* a1 a1) (* (+ (* a2 (/ a2 (* a1 a1))) 1) (cos th)))
1.0ms	th	@	inf	(* (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (cos th))

simplify661.0ms (6.4%)

Memory

-29.9MiB live, 846.3MiB allocated

Algorithm

1×	egg-herbie

Rules

16 784×	`lower-fma.f64`
16 784×	`lower-fma.f32`
5 998×	`lower-*.f64`
5 998×	`lower-*.f32`
2 950×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	189	6278
1	613	5324
2	2232	5104
3	5867	4894
0	8600	4520

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 480

Calls

Call 1

Inputs
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
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1
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(* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2))
(+ (* -1/2 (/ (* (pow a1 2) (* (pow th 2) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))) (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2))) (* 1/24 (/ (* (pow a1 2) (* (pow th 2) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))))) (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a1 2) (* (pow th 2) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))) (* 1/24 (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2))))))) (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2)))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
(/ a2 (pow a1 2))
1
(+ 1 (/ (pow a2 2) (pow a1 2)))
(+ 1 (/ (pow a2 2) (pow a1 2)))
(+ 1 (/ (pow a2 2) (pow a1 2)))
(/ (pow a2 2) (pow a1 2))
(* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))
(* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))
(* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))
(/ (pow a2 2) (pow a1 2))
(* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))
(* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))
(* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))
(/ (pow a2 2) (pow a1 2))
(/ (+ (pow a1 2) (pow a2 2)) (pow a1 2))
(/ (+ (pow a1 2) (pow a2 2)) (pow a1 2))
(/ (+ (pow a1 2) (pow a2 2)) (pow a1 2))
1
(+ 1 (/ (pow a2 2) (pow a1 2)))
(+ 1 (/ (pow a2 2) (pow a1 2)))
(+ 1 (/ (pow a2 2) (pow a1 2)))
1
(+ 1 (/ (pow a2 2) (pow a1 2)))
(+ 1 (/ (pow a2 2) (pow a1 2)))
(+ 1 (/ (pow a2 2) (pow a1 2)))

Outputs
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 (/.f64 (.f64 th th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 (.f64 th th) (.f64 (.f64 (.f64 th th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
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(fma.f64 (/.f64 (.f64 th th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow th 2) (+ (* -1/2 (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a1 2) (* (pow th 2) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))) (* 1/24 (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2))))))) (/ (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2)))) (sqrt 2)))
(fma.f64 (.f64 th th) (.f64 (.f64 (.f64 th th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (* (cos th) (+ 1 (/ (pow a2 2) (pow a1 2))))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
(/ a2 (pow a1 2))
(/.f64 a2 (*.f64 a1 a1))
1
#s(literal 1 binary64)
(+ 1 (/ (pow a2 2) (pow a1 2)))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(+ 1 (/ (pow a2 2) (pow a1 2)))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(+ 1 (/ (pow a2 2) (pow a1 2)))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(/ (pow a2 2) (pow a1 2))
(/.f64 (.f64 a2 a2) (.f64 a1 a1))
(* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(/ (pow a2 2) (pow a1 2))
(/.f64 (.f64 a2 a2) (.f64 a1 a1))
(* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(* (pow a2 2) (+ (/ 1 (pow a1 2)) (/ 1 (pow a2 2))))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(/ (pow a2 2) (pow a1 2))
(/.f64 (.f64 a2 a2) (.f64 a1 a1))
(/ (+ (pow a1 2) (pow a2 2)) (pow a1 2))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 a1 a1))
(/ (+ (pow a1 2) (pow a2 2)) (pow a1 2))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 a1 a1))
(/ (+ (pow a1 2) (pow a2 2)) (pow a1 2))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 a1 a1))
1
#s(literal 1 binary64)
(+ 1 (/ (pow a2 2) (pow a1 2)))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(+ 1 (/ (pow a2 2) (pow a1 2)))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(+ 1 (/ (pow a2 2) (pow a1 2)))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (/ (pow a2 2) (pow a1 2)))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(+ 1 (/ (pow a2 2) (pow a1 2)))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(+ 1 (/ (pow a2 2) (pow a1 2)))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))

rewrite384.0ms (3.7%)

Memory

22.5MiB live, 933.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 526×	`lower-/.f32`
5 512×	`lower-/.f64`
4 608×	`lower-*.f32`
4 592×	`lower-*.f64`
4 314×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	225
0	58	208
1	201	207
2	1532	203
0	8749	203

Stop Event

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

Counts

22 → 1 568

Calls

Call 1

Inputs
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 a1 a1 (*.f64 a2 a2))
(*.f64 a2 a2)
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(neg.f64 (cos.f64 th))
(cos.f64 th)
(.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 a1 a1)
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 a2 (*.f64 a1 a1))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))

Outputs
(+.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (.f64 (cos.f64 th) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (.f64 (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th))) (.f64 (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th))))
(-.f64 #s(literal 0 binary64) (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) (.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) #s(literal 1/2 binary64))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) (.f64 #s(literal 1/2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
(-.f64 (/.f64 (/.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (/.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(-.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) (.f64 #s(literal 1/2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))))) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) (.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) #s(literal 1/2 binary64))) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))))
(fma.f64 a1 (/.f64 (.f64 (cos.f64 th) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (cos.f64 th) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (cos.f64 th) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (cos.f64 th) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a1 (/.f64 #s(literal 1 binary64) (cos.f64 th))) (.f64 (cos.f64 th) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (neg.f64 (cos.f64 th)) (/.f64 (*.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th)) (.f64 (/.f64 (*.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a1) (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a1 a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 a2 a2) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
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(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 a2 a2)) #s(literal -1 binary64)) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
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(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
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(neg.f64 (/.f64 a1 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 (neg.f64 a1) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
(/.f64 (neg.f64 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 a1)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 a1 #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (*.f64 a1 #s(literal 1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 a1))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 a1 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 a1) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1)
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(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
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(-.f64 #s(literal 0 binary64) (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
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(-.f64 (/.f64 (/.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (/.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(-.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) (.f64 #s(literal 1/2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))))) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) th)))) (.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) #s(literal 1/2 binary64))) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))))
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(fma.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
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(fma.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (cos.f64 th) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (cos.f64 th) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
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(fma.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (neg.f64 (cos.f64 th)) (/.f64 (*.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th)) (.f64 (/.f64 (*.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th))))
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(fma.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
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(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 (neg.f64 (cos.f64 th)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
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(pow.f64 (/.f64 a1 (/.f64 a2 a1)) #s(literal -1 binary64))
(.f64 a2 (/.f64 #s(literal 1 binary64) (.f64 a1 a1)))
(.f64 #s(literal 1 binary64) (/.f64 a2 (.f64 a1 a1)))
(.f64 (neg.f64 a2) (/.f64 #s(literal 1 binary64) (.f64 a1 (neg.f64 a1))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 a1 a1)) a2)
(.f64 (/.f64 #s(literal 1 binary64) (.f64 a1 a1)) (pow.f64 (/.f64 #s(literal 1 binary64) a2) #s(literal -1 binary64)))
(*.f64 (/.f64 a2 a1) (/.f64 #s(literal 1 binary64) a1))
(*.f64 (/.f64 #s(literal 1 binary64) a1) (/.f64 a2 a1))
(*.f64 (/.f64 #s(literal -1 binary64) a1) (/.f64 a2 (neg.f64 a1)))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (.f64 a1 a1)))
(+.f64 (/.f64 (.f64 a2 a2) (.f64 a1 a1)) #s(literal 1 binary64))
(-.f64 (/.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(fma.f64 a2 (.f64 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (.f64 a1 a1)) #s(literal 1 binary64))
(fma.f64 (/.f64 a2 (*.f64 a1 a1)) a2 #s(literal 1 binary64))
(fma.f64 (/.f64 a2 (.f64 a1 a1)) (.f64 a2 #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 a2 (*.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a2)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (.f64 a1 a1)) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 a2 a2) (.f64 a1 a1)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 a1 a1)) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)) #s(literal 1 binary64))
(fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) a1) (/.f64 (*.f64 a2 a2) a1) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) a1) (/.f64 a2 (/.f64 a1 a2)) #s(literal 1 binary64))
(fma.f64 (/.f64 (*.f64 a2 a2) a1) (/.f64 #s(literal 1 binary64) a1) #s(literal 1 binary64))
(fma.f64 (/.f64 a2 (neg.f64 a1)) (/.f64 (neg.f64 a2) a1) #s(literal 1 binary64))
(fma.f64 (/.f64 a2 #s(literal -1 binary64)) (/.f64 (neg.f64 a2) (*.f64 a1 a1)) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 a2) #s(literal -1 binary64)) (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) a1) (/.f64 (*.f64 a2 a2) (neg.f64 a1)) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 a2) a1) (/.f64 a2 (neg.f64 a1)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (.f64 a1 a1)))) (fma.f64 (.f64 a2 (.f64 a2 a2)) (/.f64 (.f64 a2 (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (*.f64 a1 a1))))) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal -1 binary64)) (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (*.f64 a1 a1)))) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (.f64 a1 a1)))) (fma.f64 (.f64 a2 (.f64 a2 a2)) (/.f64 (.f64 a2 (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (*.f64 a1 a1))))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal -1 binary64)) (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (*.f64 a1 a1)))) #s(literal -1 binary64))))
(/.f64 (fma.f64 (.f64 a2 (.f64 a2 a2)) (/.f64 (.f64 a2 (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) #s(literal 1 binary64)) (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(/.f64 (fma.f64 (.f64 a2 (.f64 a2 a2)) (/.f64 (.f64 a2 (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (/.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a2 a2)) (.f64 a2 a2)) (*.f64 a1 a1))))
(/.f64 (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) #s(literal -1 binary64)) (fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 a2 (.f64 a2 a2)) (/.f64 (.f64 a2 (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) #s(literal 1 binary64))) (neg.f64 (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(/.f64 (neg.f64 (fma.f64 (.f64 a2 (.f64 a2 a2)) (/.f64 (.f64 a2 (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (/.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a2 a2)) (.f64 a2 a2)) (*.f64 a1 a1)))))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) #s(literal -1 binary64))) (neg.f64 (fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (.f64 a1 a1))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal -1 binary64))) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal -1 binary64)) (fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 a2 (.f64 a2 a2)) (/.f64 (.f64 a2 (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (*.f64 a1 a1)))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))))) (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(pow.f64 (/.f64 (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (.f64 a1 a1)))) (fma.f64 (.f64 a2 (.f64 a2 a2)) (/.f64 (.f64 a2 (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (*.f64 a1 a1))))) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal -1 binary64)) (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (*.f64 a1 a1)))) #s(literal -1 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 a2 (.f64 a2 a2)) (/.f64 (.f64 a2 (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(.f64 (+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal -1 binary64))))

eval286.0ms (2.8%)

Memory: 27.3MiB live, 560.8MiB allocated
Compiler: Compiled 56 382 to 3 221 computations (94.3% saved)

prune228.0ms (2.2%)

Memory

-14.6MiB live, 441.4MiB allocated

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	2 273	25	2 298
Fresh	11	3	14
Picked	5	0	5
Done	0	0	0
Total	2 289	28	2 317

Accuracy

100.0%

Counts

2 317 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	99.6%	(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	98.9%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
	98.9%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))))
	60.2%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	60.4%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 th (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	65.8%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	98.9%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
	98.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (cos.f64 th) (/.f64 #s(literal 1 binary64) (fma.f64 a1 a1 (.f64 a2 a2)))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
	99.6%	(.f64 (neg.f64 (cos.f64 th)) (/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) #s(literal 2 binary64)))
	98.8%	(.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
▶	65.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	65.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
	30.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
▶	61.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	65.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))) #s(literal 2 binary64)))
	65.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
	52.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
	65.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
	51.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	35.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) #s(approx (cos th) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
	42.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 #s(approx (+ ( a2 (/ a2 (* a1 a1))) 1) (/.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
	61.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (* (* a1 a1) (* (+ (* a2 (/ a2 (* a1 a1))) 1) (cos th))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
	65.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
▶	15.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 1 070 to 632 computations (40.9% saved)

simplify185.0ms (1.8%)

Memory

4.5MiB live, 402.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 a2 a2)
✓	cost-diff	0	#s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))
✓	cost-diff	0	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
✓	cost-diff	64	(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
✓	cost-diff	960	(fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
✓	cost-diff	1472	(/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
✓	cost-diff	1600	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
✓	cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	64	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	64	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	1280	(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(*.f64 a1 a1)
✓	cost-diff	0	#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	64	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
✓	cost-diff	0	(*.f64 a2 a2)
✓	cost-diff	0	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	cost-diff	448	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))

Rules

5 064×	`lower-*.f32`
5 054×	`lower-*.f64`
2 754×	`lower-fma.f32`
2 748×	`lower-fma.f64`
2 718×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	313
0	60	274
1	94	270
2	136	270
3	170	268
4	194	268
5	244	268
6	349	268
7	544	268
8	1444	250
9	2463	250
10	3555	250
11	3723	250
12	3837	250
13	3951	250
14	4152	250
15	6993	250
0	8133	249

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(cos.f64 th)
th
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 a1 a1)
a1
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
a2
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 a1 a1)
a1
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
(/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(*.f64 a2 a2)
a2
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
a1
(*.f64 (sqrt.f64 #s(literal 2 binary64)) a1)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))
(*.f64 a2 a2)
a2
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(cos.f64 th)
th

Outputs
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(cos.f64 th)
th
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(*.f64 a1 a1)
a1
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(.f64 a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
a2
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(*.f64 a1 a1)
a1
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 (/.f64 a2 a1) a1))
(*.f64 a2 a2)
a2
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
a1
(*.f64 (sqrt.f64 #s(literal 2 binary64)) a1)
(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(/.f64 #s(literal 2 binary64) a1)
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(.f64 (.f64 (cos.f64 th) #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))
(*.f64 a2 a2)
a2
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(cos.f64 th)
th

localize124.0ms (1.2%)

Memory

-34.0MiB live, 225.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 th)
✓	accuracy	99.8%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
✓	accuracy	99.7%	(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.3%	#s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))
✓	accuracy	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
✓	accuracy	86.7%	(/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
✓	accuracy	86.2%	(fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
✓	accuracy	66.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
✓	accuracy	99.8%	(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.7%	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.4%	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	66.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.7%	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	66.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	17.1%	#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(cos.f64 th)
✓	accuracy	100.0%	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	accuracy	99.7%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
✓	accuracy	99.6%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))

Samples

67.0ms

256×

valid

Compiler

Compiled 249 to 33 computations (86.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-div: 19.0ms (39.9% of total)

ival-mult: 14.0ms (29.4% of total)

ival-add: 6.0ms (12.6% of total)

ival-cos: 6.0ms (12.6% of total)

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

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

exact: 0.0ms (0% of total)

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

series18.0ms (0.2%)

Memory

-1.6MiB live, 37.0MiB allocated

Counts

20 → 432

Calls

Call 1

Inputs
#<alt (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))>
#<alt (fma.f64 a1 a1 (*.f64 a2 a2))>
#<alt (*.f64 a2 a2)>
#<alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))>
#<alt (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))>
#<alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 a1 a1)>
#<alt (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))>
#<alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))>
#<alt (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))>
#<alt (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1))>
#<alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))>
#<alt (/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))>
#<alt #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))>
#<alt (cos.f64 th)>
#<alt (sqrt.f64 #s(literal 2 binary64))>

Outputs
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))>
#<alt (+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (pow a2 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (sqrt 2)>
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#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))>
#<alt (+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (pow a2 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow th 2)))>
#<alt (+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))>
#<alt (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>

Calls

108 calls:

Time	Variable		Point	Expression
1.0ms	a2	@	0	(/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1)))
1.0ms	a1	@	0	(/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1)))
1.0ms	a1	@	-inf	(/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1)))
1.0ms	a2	@	inf	(/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1)))
1.0ms	a1	@	inf	(/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1)))

simplify353.0ms (3.4%)

Memory

24.5MiB live, 615.8MiB allocated

Algorithm

1×	egg-herbie

Rules

13 004×	`lower-fma.f64`
13 004×	`lower-fma.f32`
4 234×	`lower-*.f64`
4 234×	`lower-*.f32`
2 876×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	148	5641
1	482	4816
2	1754	4497
3	4978	4490
4	7903	4490
0	8069	4158

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 432

Calls

Call 1

Inputs
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(pow a2 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(+ (sqrt 2) (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(+ (sqrt 2) (* (pow th 2) (- (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/720 (sqrt 2)) (+ (* 1/48 (sqrt 2)) (* 1/2 (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(/ (pow a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* a1 (sqrt 2))
(+ (* a1 (sqrt 2)) (/ (* (pow a2 2) (sqrt 2)) a1))
(+ (* a1 (sqrt 2)) (/ (* (pow a2 2) (sqrt 2)) a1))
(+ (* a1 (sqrt 2)) (/ (* (pow a2 2) (sqrt 2)) a1))
(/ (* (pow a2 2) (sqrt 2)) a1)
(* (pow a2 2) (+ (/ (sqrt 2) a1) (/ (* a1 (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (/ (sqrt 2) a1) (/ (* a1 (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (/ (sqrt 2) a1) (/ (* a1 (sqrt 2)) (pow a2 2))))
(/ (* (pow a2 2) (sqrt 2)) a1)
(* (pow a2 2) (+ (/ (sqrt 2) a1) (/ (* a1 (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (/ (sqrt 2) a1) (/ (* a1 (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (/ (sqrt 2) a1) (/ (* a1 (sqrt 2)) (pow a2 2))))
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) a1)
(/ (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) a1)
(/ (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) a1)
(* a1 (sqrt 2))
(* a1 (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* a1 (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* a1 (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* a1 (sqrt 2))
(* -1 (* a1 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))))
(* -1 (* a1 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))))
(* -1 (* a1 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(pow a2 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
1
(+ 1 (* -1/2 (pow th 2)))
(+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))
(+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)

Outputs
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
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(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 th (/.f64 (.f64 th (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 (.f64 th th) (.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 (.f64 th th) (fma.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (.f64 th th)) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(pow a2 2)
(*.f64 a2 a2)
(+ (pow a1 2) (pow a2 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow a1 2)
(*.f64 a1 a1)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(fma.f64 a2 a2 (*.f64 a1 a1))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(fma.f64 a2 a2 (*.f64 a1 a1))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow a1 2)
(*.f64 a1 a1)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(fma.f64 a2 a2 (*.f64 a1 a1))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(fma.f64 a2 a2 (*.f64 a1 a1))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow a1 2)
(*.f64 a1 a1)
(+ (pow a1 2) (pow a2 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow a2 2)
(*.f64 a2 a2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(fma.f64 a2 a2 (*.f64 a1 a1))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(fma.f64 a2 a2 (*.f64 a1 a1))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow a2 2)
(*.f64 a2 a2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(fma.f64 a2 a2 (*.f64 a1 a1))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(fma.f64 a2 a2 (*.f64 a1 a1))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(fma.f64 a2 a2 (*.f64 a1 a1))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow th 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))
(+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))
(fma.f64 (.f64 th th) (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))
(fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)

rewrite345.0ms (3.3%)

Memory

29.0MiB live, 659.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 268×	`lower-fma.f32`
6 262×	`lower-fma.f64`
5 840×	`lower-/.f32`
5 826×	`lower-/.f64`
4 550×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	265
0	60	242
1	219	222
2	1762	222
0	8491	222

Stop Event

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

Counts

20 → 793

Calls

Call 1

Inputs
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(fma.f64 a1 a1 (*.f64 a2 a2))
(*.f64 a2 a2)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 a1 a1)
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
#s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))
(cos.f64 th)
(sqrt.f64 #s(literal 2 binary64))

Outputs
(+.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (/.f64 (.f64 (pow.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
(-.f64 (/.f64 (/.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (/.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (/.f64 (.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))))
(fma.f64 a1 (/.f64 (.f64 (cos.f64 th) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (cos.f64 th) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) #s(literal 1 binary64)) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a1 (/.f64 #s(literal 1 binary64) (cos.f64 th))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (cos.f64 th) #s(literal 1 binary64)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a1) (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (.f64 a1 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 a1 a1))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (neg.f64 (.f64 (.f64 a2 a2) (cos.f64 th))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (cos.f64 th) #s(literal 1 binary64)) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (cos.f64 th) #s(literal 1 binary64)) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 a1 #s(literal 1 binary64)) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a2 (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 a1 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 a1 a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a1 a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a2 #s(literal 1 binary64)) (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 a2 a2) #s(literal -1 binary64)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 a1 (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a1 (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (/.f64 a1 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) #s(literal -1 binary64)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a2 (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 a2 (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 (neg.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.f64 (fma.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (.f64 (pow.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) #s(literal 2 binary64)) #s(literal 1/2 binary64) (-.f64 (.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1))))) (fma.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) #s(literal 2 binary64)) #s(literal 1/2 binary64) (-.f64 (.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (cos.f64 th))) #s(literal 1/2 binary64)))) (+.f64 (pow.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 a2 a2) (cos.f64 th))))))
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(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (cos.f64 th) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (neg.f64 (cos.f64 th)) (fma.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (*.f64 a1 a1))))))))
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(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (fma.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (*.f64 a1 a1))))) (neg.f64 (cos.f64 th)))))
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(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (/.f64 (.f64 (.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2)))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 (.f64 a1 a1)))))) (neg.f64 (neg.f64 (+.f64 (/.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 a1 a1)) (-.f64 (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 a1 a1)) (.f64 #s(literal 2 binary64) (.f64 a1 a1))))) (neg.f64 (neg.f64 (-.f64 (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (/.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 a1 a1)))) (neg.f64 (-.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (*.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (/.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 a1 a1)) (-.f64 (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (-.f64 (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (/.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 a1 a1)) (-.f64 (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (/.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 a1 a1)) (-.f64 (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (-.f64 (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (-.f64 (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (/.f64 (/.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 a1 a1)) (-.f64 (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (-.f64 (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (/.f64 (.f64 (.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2)))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 (.f64 a1 a1)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 a1 a1)) (-.f64 (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))))
(.f64 (fma.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (/.f64 (.f64 (.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2)))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 (.f64 a1 a1)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (.f64 a1 a1) (/.f64 (-.f64 (.f64 (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) a1))))
(.f64 #s(literal 1 binary64) (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (-.f64 (/.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 a1 a1)) (.f64 #s(literal 2 binary64) (.f64 a1 a1))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (/.f64 (.f64 (.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2)))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (/.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 a1 a1)) (-.f64 (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))))))
(.f64 (neg.f64 (-.f64 (/.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 a1 a1)) (.f64 #s(literal 2 binary64) (.f64 a1 a1)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
(.f64 (-.f64 (.f64 #s(literal 2 binary64) (.f64 a1 a1)) (/.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 a1 a1))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 (neg.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 (neg.f64 (neg.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) #s(literal -1 binary64))
(.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))))
(.f64 (neg.f64 (neg.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))))
(/.f64 (neg.f64 (cos.f64 th)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (cos.f64 th)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (neg.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2))) (.f64 (cos.f64 th) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))) (cos.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2))) (.f64 #s(literal 1 binary64) (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))))
(/.f64 (neg.f64 (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (cos.f64 th) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))
(/.f64 (.f64 (cos.f64 th) (neg.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (neg.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))) (cos.f64 th)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (cos.f64 th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))
(/.f64 (neg.f64 (neg.f64 (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (cos.f64 th) (neg.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (cos.f64 th) #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 (neg.f64 (.f64 (neg.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))) (cos.f64 th))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (cos.f64 th))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))) #s(literal -1 binary64))
(.f64 (cos.f64 th) (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) (/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (cos.f64 th) (/.f64 #s(literal 1 binary64) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(.f64 (.f64 (cos.f64 th) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 (.f64 (cos.f64 th) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (.f64 (cos.f64 th) #s(literal 1 binary64)) (/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (cos.f64 th) (neg.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (.f64 (neg.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (cos.f64 th)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (cos.f64 th)) (/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (cos.f64 th) #s(literal -1 binary64)) (/.f64 (neg.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (neg.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))) #s(literal -1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))
(cos.f64 th)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

eval169.0ms (1.6%)

Memory: 12.2MiB live, 354.1MiB allocated
Compiler: Compiled 30 396 to 2 067 computations (93.2% saved)

prune181.0ms (1.7%)

Memory

-21.9MiB live, 341.7MiB allocated

Pruning

45 alts after pruning (42 fresh and 3 done)

	Pruned	Kept	Total
New	1 374	32	1 406
Fresh	13	10	23
Picked	2	3	5
Done	0	0	0
Total	1 389	45	1 434

Accuracy

100.0%

Counts

1 434 → 45

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
	99.6%	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
▶	57.0%	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
	28.2%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (-.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	99.6%	(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	98.2%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))))
	98.9%	(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	98.1%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
	60.2%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	65.8%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	98.9%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	59.6%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	59.7%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	61.1%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
	98.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (cos.f64 th) (/.f64 #s(literal 1 binary64) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
	98.8%	(.f64 (.f64 (cos.f64 th) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
	99.6%	(.f64 (neg.f64 (cos.f64 th)) (/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) #s(literal 2 binary64)))
	98.8%	(.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
	33.2%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (fma.f64 th (/.f64 (.f64 th (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1)))))
	65.9%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
▶	98.9%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
✓	65.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	65.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	65.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	65.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2 (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	61.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a1))))
	65.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))) #s(literal 2 binary64)))
	65.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
	51.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	35.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) #s(approx (cos th) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
▶	60.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	61.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 (/.f64 a2 a1) a1))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	61.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (* (* a1 a1) (* (+ (* a2 (/ a2 (* a1 a1))) 1) (cos th))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
	60.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) a1) (/.f64 (/.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
	65.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))))))
	60.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
	65.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2))))))
	65.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
	61.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) a1))
	65.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
✓	15.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	15.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	15.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
▶	15.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
	15.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))

Compiler

Compiled 1 686 to 1 007 computations (40.3% saved)

simplify61.0ms (0.6%)

Memory

16.2MiB live, 53.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 a2 (cos.f64 th))
✓	cost-diff	0	(.f64 a2 (.f64 a2 (cos.f64 th)))
✓	cost-diff	0	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	#s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1))
✓	cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
✓	cost-diff	768	(/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
✓	cost-diff	1600	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
✓	cost-diff	0	#s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64))))
✓	cost-diff	0	(*.f64 a2 a2)
✓	cost-diff	0	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	cost-diff	0	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
✓	cost-diff	0	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
✓	cost-diff	0	#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
✓	cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
✓	cost-diff	0	(*.f64 a2 a2)
✓	cost-diff	0	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	cost-diff	384	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))

Rules

728×	`lower-*.f32`
710×	`lower-*.f64`
462×	`lower-/.f32`
444×	`lower-/.f64`
406×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	374
0	81	360
1	139	344
2	201	344
3	384	335
4	468	335
5	587	335
6	687	327
7	765	327
8	866	327
9	924	327
10	1003	327
11	1095	327
12	1140	327
13	1161	327
14	1161	327
0	1161	324

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
#s(literal 1 binary64)
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
a1
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
#s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64))
(*.f64 th th)
th
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
(/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
#s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1))
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
a2
(*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
a1
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 a2 (.f64 a2 (cos.f64 th)))
a2
(*.f64 a2 (cos.f64 th))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

Outputs
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
#s(literal 1 binary64)
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
a1
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 th (*.f64 th #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
#s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 th (.f64 th #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 th (.f64 th #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 th (*.f64 th #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 th th)
th
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 #s(approx (+ ( (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 a1 #s(literal 1/2 binary64))))
(/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(.f64 #s(approx (+ ( (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 a1 #s(literal 1/2 binary64)))
#s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1))
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
a2
(*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
a1
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(/.f64 #s(literal 2 binary64) a1)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 a2 (.f64 a2 (cos.f64 th)))
a2
(*.f64 a2 (cos.f64 th))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

localize147.0ms (1.4%)

Memory

16.0MiB live, 169.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 a2 (.f64 a2 (cos.f64 th)))
✓	accuracy	99.7%	(*.f64 a2 (cos.f64 th))
✓	accuracy	99.7%	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.3%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.1%	#s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1))
✓	accuracy	86.7%	(/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
✓	accuracy	86.0%	(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
✓	accuracy	66.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
✓	accuracy	99.8%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓	accuracy	99.7%	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
✓	accuracy	99.7%	(fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	accuracy	49.5%	#s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64))))
✓	accuracy	99.8%	(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
✓	accuracy	99.4%	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	66.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
✓	accuracy	17.1%	#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
✓	accuracy	100.0%	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	accuracy	99.7%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	99.0%	(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	98.9%	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

83.0ms

256×

valid

Compiler

Compiled 276 to 42 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-mult: 26.0ms (43% of total)

ival-div: 15.0ms (24.8% of total)

ival-add: 11.0ms (18.2% of total)

ival-cos: 6.0ms (9.9% of total)

ival-sqrt: 2.0ms (3.3% of total)

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

exact: 0.0ms (0% of total)

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

series24.0ms (0.2%)

Memory

-14.8MiB live, 22.5MiB allocated

Counts

22 → 480

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (fma.f64 a1 a1 (*.f64 a2 a2))>
#<alt (*.f64 a2 a2)>
#<alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))>
#<alt #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))>
#<alt (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)>
#<alt (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))>
#<alt #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64))))>
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))>
#<alt (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))>
#<alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))>
#<alt #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1))>
#<alt #s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 a2 (.f64 a2 (cos.f64 th)))>
#<alt (*.f64 a2 (cos.f64 th))>
#<alt (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64))>
#<alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))>
#<alt (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)>

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))>
#<alt (+ (sqrt 2) (* (pow th 2) (- (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/720 (sqrt 2)) (+ (* 1/48 (sqrt 2)) (* 1/2 (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))>
#<alt (+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (pow a2 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
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#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (+ (* -1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))))) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2))))))) (/ (pow a2 2) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (pow a2 2)>
#<alt (+ (* -1/2 (* (pow a2 2) (pow th 2))) (pow a2 2))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (pow a2 2)) (* 1/24 (* (pow a2 2) (pow th 2))))) (pow a2 2))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (pow a2 2)) (* (pow th 2) (+ (* -1/720 (* (pow a2 2) (pow th 2))) (* 1/24 (pow a2 2)))))) (pow a2 2))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt a2>
#<alt (+ a2 (* -1/2 (* a2 (pow th 2))))>
#<alt (+ a2 (* (pow th 2) (+ (* -1/2 a2) (* 1/24 (* a2 (pow th 2))))))>
#<alt (+ a2 (* (pow th 2) (+ (* -1/2 a2) (* (pow th 2) (+ (* -1/720 (* a2 (pow th 2))) (* 1/24 a2))))))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (* a2 (cos th))>
#<alt (/ 1 (sqrt 2))>
#<alt (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2)))>
#<alt (+ (* (pow th 2) (- (* 1/24 (/ (pow th 2) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))>
#<alt (+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/720 (/ (pow th 2) (sqrt 2))) (* 1/24 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt 1>
#<alt (+ 1 (* 1/2 (pow th 2)))>
#<alt (+ 1 (* 1/2 (pow th 2)))>
#<alt (+ 1 (* 1/2 (pow th 2)))>
#<alt (* 1/2 (pow th 2))>
#<alt (* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))>
#<alt (* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))>
#<alt (* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))>
#<alt (* 1/2 (pow th 2))>
#<alt (* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))>
#<alt (* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))>
#<alt (* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))>
#<alt (* 1/2 (* (pow th 2) (sqrt 2)))>
#<alt (* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))>
#<alt (* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))>
#<alt (* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))>
#<alt (* 1/2 (* (pow th 2) (sqrt 2)))>
#<alt (* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))>
#<alt (* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))>
#<alt (* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>
#<alt (/ (* (pow a2 2) (sqrt 2)) a1)>

Calls

120 calls:

Time	Variable		Point	Expression
6.0ms	th	@	inf	(* (sqrt 2) (+ (* (* th th) 1/2) 1))
5.0ms	th	@	0	(* a2 (cos th))
0.0ms	th	@	inf	(+ (* (* th th) 1/2) 1)
0.0ms	a2	@	0	(* a2 (cos th))
0.0ms	a2	@	inf	(* a2 (* a2 (cos th)))

simplify414.0ms (4%)

Memory

-10.9MiB live, 544.8MiB allocated

Algorithm

1×	egg-herbie

Rules

15 540×	`lower-fma.f64`
15 540×	`lower-fma.f32`
5 110×	`lower-*.f64`
5 110×	`lower-*.f32`
3 566×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	204	6059
1	666	5216
2	2335	4910
3	5567	4902
0	8120	4586

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 479

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(+ (sqrt 2) (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(+ (sqrt 2) (* (pow th 2) (- (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/720 (sqrt 2)) (+ (* 1/48 (sqrt 2)) (* 1/2 (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(pow a2 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(+ (sqrt 2) (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(+ (sqrt 2) (* (pow th 2) (- (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/720 (sqrt 2)) (+ (* 1/48 (sqrt 2)) (* 1/2 (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow (sqrt 2) 2) a1)
(/ (pow a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* a1 (sqrt 2))
(+ (* a1 (sqrt 2)) (/ (* (pow a2 2) (sqrt 2)) a1))
(+ (* a1 (sqrt 2)) (/ (* (pow a2 2) (sqrt 2)) a1))
(+ (* a1 (sqrt 2)) (/ (* (pow a2 2) (sqrt 2)) a1))
(/ (* (pow a2 2) (sqrt 2)) a1)
(* (pow a2 2) (+ (/ (sqrt 2) a1) (/ (* a1 (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (/ (sqrt 2) a1) (/ (* a1 (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (/ (sqrt 2) a1) (/ (* a1 (sqrt 2)) (pow a2 2))))
(/ (* (pow a2 2) (sqrt 2)) a1)
(* (pow a2 2) (+ (/ (sqrt 2) a1) (/ (* a1 (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (/ (sqrt 2) a1) (/ (* a1 (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (/ (sqrt 2) a1) (/ (* a1 (sqrt 2)) (pow a2 2))))
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) a1)
(/ (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) a1)
(/ (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) a1)
(* a1 (sqrt 2))
(* a1 (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* a1 (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* a1 (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* a1 (sqrt 2))
(* -1 (* a1 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))))
(* -1 (* a1 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))))
(* -1 (* a1 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(+ (* -1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))))) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2))))))) (/ (pow a2 2) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(pow a2 2)
(+ (* -1/2 (* (pow a2 2) (pow th 2))) (pow a2 2))
(+ (* (pow th 2) (+ (* -1/2 (pow a2 2)) (* 1/24 (* (pow a2 2) (pow th 2))))) (pow a2 2))
(+ (* (pow th 2) (+ (* -1/2 (pow a2 2)) (* (pow th 2) (+ (* -1/720 (* (pow a2 2) (pow th 2))) (* 1/24 (pow a2 2)))))) (pow a2 2))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* (pow a2 2) (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
a2
(+ a2 (* -1/2 (* a2 (pow th 2))))
(+ a2 (* (pow th 2) (+ (* -1/2 a2) (* 1/24 (* a2 (pow th 2))))))
(+ a2 (* (pow th 2) (+ (* -1/2 a2) (* (pow th 2) (+ (* -1/720 (* a2 (pow th 2))) (* 1/24 a2))))))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(/ 1 (sqrt 2))
(+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2)))
(+ (* (pow th 2) (- (* 1/24 (/ (pow th 2) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/720 (/ (pow th 2) (sqrt 2))) (* 1/24 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
1
(+ 1 (* 1/2 (pow th 2)))
(+ 1 (* 1/2 (pow th 2)))
(+ 1 (* 1/2 (pow th 2)))
(* 1/2 (pow th 2))
(* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))
(* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))
(* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))
(* 1/2 (pow th 2))
(* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))
(* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))
(* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(* 1/2 (* (pow th 2) (sqrt 2)))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(* 1/2 (* (pow th 2) (sqrt 2)))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)))
(+ (sqrt 2) (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(fma.f64 (.f64 th th) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (*.f64 th th) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow th 2) (- (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/720 (sqrt 2)) (+ (* 1/48 (sqrt 2)) (* 1/2 (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (.f64 (.f64 th th) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 61/720 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (*.f64 th th) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
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(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (/ (pow a2 2) (sqrt 2)))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))))) (/ (pow a2 2) (sqrt 2)))
(fma.f64 (.f64 th th) (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2))))))) (/ (pow a2 2) (sqrt 2)))
(fma.f64 th (.f64 th (.f64 (.f64 th th) (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(pow a2 2)
(*.f64 a2 a2)
(+ (* -1/2 (* (pow a2 2) (pow th 2))) (pow a2 2))
(.f64 (.f64 a2 a2) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(+ (* (pow th 2) (+ (* -1/2 (pow a2 2)) (* 1/24 (* (pow a2 2) (pow th 2))))) (pow a2 2))
(fma.f64 (.f64 th (.f64 th (.f64 a2 a2))) (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 a2 a2))
(+ (* (pow th 2) (+ (* -1/2 (pow a2 2)) (* (pow th 2) (+ (* -1/720 (* (pow a2 2) (pow th 2))) (* 1/24 (pow a2 2)))))) (pow a2 2))
(fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (.f64 (.f64 a2 a2) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 a2 a2))) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
a2
(+ a2 (* -1/2 (* a2 (pow th 2))))
(fma.f64 th (.f64 th (.f64 #s(literal -1/2 binary64) a2)) a2)
(+ a2 (* (pow th 2) (+ (* -1/2 a2) (* 1/24 (* a2 (pow th 2))))))
(fma.f64 (.f64 (.f64 th th) a2) (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) a2)
(+ a2 (* (pow th 2) (+ (* -1/2 a2) (* (pow th 2) (+ (* -1/720 (* a2 (pow th 2))) (* 1/24 a2))))))
(fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (.f64 a2 (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) a2)) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(/ 1 (sqrt 2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2)))
(fma.f64 (*.f64 th th) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow th 2) (- (* 1/24 (/ (pow th 2) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(fma.f64 (.f64 th th) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/720 (/ (pow th 2) (sqrt 2))) (* 1/24 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(fma.f64 (.f64 th th) (fma.f64 (/.f64 (.f64 th th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow th 2)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64))
(+ 1 (* 1/2 (pow th 2)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64))
(+ 1 (* 1/2 (pow th 2)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64))
(* 1/2 (pow th 2))
(.f64 #s(literal 1/2 binary64) (.f64 th th))
(* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64))
(* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64))
(* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64))
(* 1/2 (pow th 2))
(.f64 #s(literal 1/2 binary64) (.f64 th th))
(* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64))
(* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64))
(* (pow th 2) (+ 1/2 (/ 1 (pow th 2))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)))
(* 1/2 (* (pow th 2) (sqrt 2)))
(.f64 th (.f64 th (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)))
(* 1/2 (* (pow th 2) (sqrt 2)))
(.f64 th (.f64 th (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)))
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)
(/ (* (pow a2 2) (sqrt 2)) a1)
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)

rewrite315.0ms (3%)

Memory

31.6MiB live, 429.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 728×	`lower-/.f32`
4 710×	`lower-/.f64`
4 498×	`lower-*.f32`
4 480×	`lower-*.f64`
3 446×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	315
0	81	297
1	267	285
2	1859	285
0	8127	280

Stop Event

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

Counts

22 → 690

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 a1 a1 (*.f64 a2 a2))
(*.f64 a2 a2)
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
#s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 a2 (cos.f64 th))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/.f64 #s(literal -1 binary64) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (cos.f64 th)))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th)))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (neg.f64 (cos.f64 th))))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th))) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (neg.f64 (cos.f64 th))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (neg.f64 (neg.f64 (cos.f64 th)))))
(pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th))) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (/.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) #s(literal 2 binary64))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (cos.f64 th) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 a1 (/.f64 (.f64 (cos.f64 th) a1) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (.f64 (cos.f64 th) a2) (neg.f64 a2)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (.f64 a2 a2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) (.f64 a2 a2))) #s(literal -1 binary64)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a1) (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (+.f64 (pow.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))))))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 (/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (+.f64 (pow.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.f64 (fma.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (.f64 (.f64 a2 a2) (.f64 a2 a2)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (.f64 (pow.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 #s(literal 1/2 binary64) (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) #s(literal 2 binary64)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (cos.f64 th) (*.f64 a2 a2)))) #s(literal 2 binary64))))
(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
(/.f64 (fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (*.f64 a2 a2)))) #s(literal 2 binary64))
(/.f64 (fma.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (*.f64 a1 a1)))) #s(literal 2 binary64))
(/.f64 (.f64 (fma.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (.f64 (.f64 a2 a2) (.f64 a2 a2)))) #s(literal 1 binary64)) (.f64 (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(/.f64 (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 1 binary64)) (.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (.f64 (.f64 a2 a2) (.f64 a2 a2))))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (.f64 (.f64 a2 a2) (.f64 a2 a2))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(/.f64 (.f64 (cos.f64 th) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (.f64 (neg.f64 (cos.f64 th)) (fma.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (.f64 (.f64 a2 a2) (.f64 a2 a2))))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(/.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (.f64 (fma.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (.f64 (.f64 a2 a2) (.f64 a2 a2)))) (cos.f64 th)) (.f64 (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (.f64 (.f64 a2 a2) (.f64 a2 a2)))) (neg.f64 (cos.f64 th))) (.f64 (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (cos.f64 th)) (.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (neg.f64 (cos.f64 th))) (.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (neg.f64 (cos.f64 th))) (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
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(/.f64 (fma.f64 (.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/8 binary64))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 th (.f64 th #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 th (.f64 th #s(literal 1/2 binary64)))) (-.f64 #s(literal 2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 th (.f64 th #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 th (.f64 th #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 th (.f64 th #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (-.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 th (.f64 th #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal 1/2 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64))) (fma.f64 th (*.f64 th #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal 1/2 binary64))))))
(/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 th (*.f64 th #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/8 binary64))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 th (.f64 th #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 th (.f64 th #s(literal 1/2 binary64)))) (-.f64 #s(literal 2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 th (.f64 th #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 th (.f64 th #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 th (.f64 th #s(literal 1/2 binary64))))) #s(literal 2 binary64))) (neg.f64 (-.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 th (.f64 th #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/8 binary64)) #s(literal 1 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)))) (neg.f64 (fma.f64 th (*.f64 th #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (fma.f64 th (*.f64 th #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 th (.f64 th #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (fma.f64 th (.f64 th #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (neg.f64 a1)))
(neg.f64 (/.f64 (.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) a1))
(/.f64 #s(literal 1 binary64) (/.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))))))
(/.f64 (*.f64 a2 a2) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) a1)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))) #s(literal 1 binary64))))
(/.f64 (.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a1))
(/.f64 (neg.f64 (*.f64 a2 a2)) (neg.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)) #s(literal 1 binary64)) a1)
(/.f64 (.f64 #s(literal 1 binary64) (.f64 a2 a2)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (neg.f64 a1)))
(/.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (neg.f64 a1))
(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)) #s(literal 1 binary64))) (neg.f64 a1))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 a2 a2))) (neg.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64))) (neg.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))) (neg.f64 (neg.f64 (neg.f64 a1))))
(/.f64 (neg.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) (neg.f64 (neg.f64 a1)))
(pow.f64 (/.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 a2 (*.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) a1) (*.f64 a2 a2)))
(.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 a2 a2))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 a2 (/.f64 #s(literal 1 binary64) a1)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 a2 a1))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) a1))
(.f64 (.f64 (*.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 a1)))
(.f64 (/.f64 #s(literal 1 binary64) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))
(.f64 (/.f64 #s(literal 1 binary64) a1) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2))) #s(literal -1 binary64)))
(.f64 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) a2)

eval179.0ms (1.7%)

Memory: 13.4MiB live, 237.5MiB allocated
Compiler: Compiled 26 424 to 1 954 computations (92.6% saved)

prune210.0ms (2%)

Memory

-21.9MiB live, 300.0MiB allocated

Pruning

47 alts after pruning (41 fresh and 6 done)

	Pruned	Kept	Total
New	1 237	12	1 249
Fresh	8	29	37
Picked	2	3	5
Done	0	3	3
Total	1 247	47	1 294

Accuracy

100.0%

Counts

1 294 → 47

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.7%	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (cos th) (sqrt 2)) (fma.f64 (.f64 th th) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
	99.6%	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
	28.2%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (-.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	99.6%	(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	98.2%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))))
	98.9%	(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	98.9%	(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
	56.3%	(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
	98.1%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
	60.2%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	65.8%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	98.9%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	59.6%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	59.7%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	98.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (cos.f64 th) (/.f64 #s(literal 1 binary64) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
	99.6%	(.f64 (neg.f64 (cos.f64 th)) (/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) #s(literal 2 binary64)))
	98.8%	(.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
	65.9%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
✓	98.9%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
	59.7%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 #s(approx ( a2 (cos th)) (fma.f64 th (.f64 th (.f64 #s(literal -1/2 binary64) a2)) a2))) (sqrt.f64 #s(literal 2 binary64))))
	61.1%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (.f64 (.f64 a2 a2) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
	65.2%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	98.9%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) a2))
✓	65.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	65.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	65.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	65.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2 (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	61.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a1))))
	65.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))) #s(literal 2 binary64)))
	51.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	35.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) #s(approx (cos th) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
	60.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a1))))
	60.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (/.f64 #s(literal 2 binary64) a1)))
✓	60.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	61.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 (/.f64 a2 a1) a1))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	60.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) a1) (/.f64 (/.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
	65.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))))))
	65.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2))))))
	65.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
	60.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(approx (+ ( (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) a1))
	60.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(literal 1/2 binary64) a1) #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))))
✓	15.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	15.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	15.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
✓	15.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
	15.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))
	15.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1) a1)))

Compiler

Compiled 2 337 to 781 computations (66.6% saved)

regimes245.0ms (2.4%)

Memory

8.5MiB live, 363.4MiB allocated

Counts

89 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(literal 1/2 binary64) a1) #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (.f64 (.f64 a2 a2) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 #s(approx ( a2 (cos th)) (fma.f64 th (.f64 th (.f64 #s(literal -1/2 binary64) a2)) a2))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (* (* a1 a1) (* (+ (* a2 (/ a2 (* a1 a1))) 1) (cos th))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))) #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (/.f64 #s(literal 2 binary64) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) #s(approx (cos th) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2 (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2))))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 th (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(approx (+ ( (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) a1))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 (/.f64 a2 a1) a1))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (fma.f64 th (/.f64 (.f64 th (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1)))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (cos th) (sqrt 2)) (fma.f64 (.f64 th th) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) a1))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) a1) (/.f64 (/.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) a2))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(.f64 (.f64 (cos.f64 th) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (cos.f64 th) (/.f64 #s(literal 1 binary64) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 #s(approx (+ ( a2 (/ a2 (* a1 a1))) 1) (/.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (cos.f64 th) (/.f64 #s(literal 1 binary64) (fma.f64 a1 a1 (.f64 a2 a2)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.f64 (neg.f64 (cos.f64 th)) (/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (-.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 a1 (.f64 a1 (.f64 a1 a1)))))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 (.f64 (fma.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))))) (cos.f64 th)) (.f64 (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) #s(approx (* (/ (cos th) (sqrt 2)) (* a2 a2)) (fma.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 th th)) (fma.f64 th (.f64 th (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(.f64 (fma.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (.f64 a1 a1)))) #s(literal 1/2 binary64))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(/.f64 (/.f64 (fma.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))

Outputs
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))

Calls

8 calls:

57.0ms	a1
29.0ms	a2
28.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
26.0ms	th
26.0ms	(cos.f64 th)

Results

Accuracy	Segments	Branch
99.6%	1	`a1`
99.6%	1	`a2`
99.6%	1	`th`
99.6%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
99.6%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.6%	1	`(cos.f64 th)`
99.6%	1	`(*.f64 a1 a1)`
99.6%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes160.0ms (1.5%)

Memory

-2.0MiB live, 205.8MiB allocated

Counts

59 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(literal 1/2 binary64) a1) #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (.f64 (.f64 a2 a2) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 #s(approx ( a2 (cos th)) (fma.f64 th (.f64 th (.f64 #s(literal -1/2 binary64) a2)) a2))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (* (* a1 a1) (* (+ (* a2 (/ a2 (* a1 a1))) 1) (cos th))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))) #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (/.f64 #s(literal 2 binary64) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) #s(approx (cos th) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2 (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2))))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 th (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(approx (+ ( (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) a1))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 (/.f64 a2 a1) a1))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (fma.f64 th (/.f64 (.f64 th (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1)))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (cos th) (sqrt 2)) (fma.f64 (.f64 th th) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) a1))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) a1) (/.f64 (/.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) a2))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(.f64 (.f64 (cos.f64 th) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))

Outputs
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) a2))

Calls

8 calls:

35.0ms	th
23.0ms	(*.f64 a1 a1)
18.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
17.0ms	a1
16.0ms	a2

Results

Accuracy	Segments	Branch
98.9%	1	`a1`
98.9%	1	`a2`
98.9%	1	`th`
98.9%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
98.9%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
98.9%	1	`(cos.f64 th)`
98.9%	1	`(*.f64 a1 a1)`
98.9%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes123.0ms (1.2%)

Memory

25.4MiB live, 253.8MiB allocated

Counts

54 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(literal 1/2 binary64) a1) #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (.f64 (.f64 a2 a2) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 #s(approx ( a2 (cos th)) (fma.f64 th (.f64 th (.f64 #s(literal -1/2 binary64) a2)) a2))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (* (* a1 a1) (* (+ (* a2 (/ a2 (* a1 a1))) 1) (cos th))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))) #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (/.f64 #s(literal 2 binary64) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) #s(approx (cos th) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2 (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2))))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 th (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(approx (+ ( (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) a1))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 (/.f64 a2 a1) a1))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (fma.f64 th (/.f64 (.f64 th (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1)))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (cos th) (sqrt 2)) (fma.f64 (.f64 th th) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) a1))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) a1) (/.f64 (/.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))

Outputs
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))

Calls

8 calls:

17.0ms	a1
16.0ms	a2
16.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
15.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
15.0ms	(*.f64 a2 a2)

Results

Accuracy	Segments	Branch
98.9%	1	`a1`
98.9%	1	`a2`
98.9%	1	`th`
98.9%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
98.9%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
98.9%	1	`(cos.f64 th)`
98.9%	1	`(*.f64 a1 a1)`
98.9%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes155.0ms (1.5%)

Memory

-4.3MiB live, 200.0MiB allocated

Counts

52 → 2

Calls

Call 1

Inputs
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(literal 1/2 binary64) a1) #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (.f64 (.f64 a2 a2) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 #s(approx ( a2 (cos th)) (fma.f64 th (.f64 th (.f64 #s(literal -1/2 binary64) a2)) a2))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (* (* a1 a1) (* (+ (* a2 (/ a2 (* a1 a1))) 1) (cos th))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))) #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (/.f64 #s(literal 2 binary64) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) #s(approx (cos th) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2 (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2))))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 th (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(approx (+ ( (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) a1))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 (/.f64 a2 a1) a1))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (/.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (fma.f64 th (/.f64 (.f64 th (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1)))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (cos th) (sqrt 2)) (fma.f64 (.f64 th th) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) a1))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) a1) (/.f64 (/.f64 (fma.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))

Outputs

#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (*.f64 a2 #s(approx (* a2 (cos th)) (fma.f64 th (*.f64 th (*.f64 #s(literal -1/2 binary64) a2)) a2))) (sqrt.f64 #s(literal 2 binary64))))

#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))

Calls

8 calls:

33.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
22.0ms	(cos.f64 th)
21.0ms	(*.f64 a2 a2)
19.0ms	a2
16.0ms	(*.f64 a1 a1)

Results

Accuracy	Segments	Branch
69.0%	2	`a2`
77.6%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
67.9%	2	`(*.f64 a1 a1)`
65.9%	1	`(*.f64 a2 a2)`
67.9%	2	`a1`
65.9%	1	`th`
76.7%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
76.7%	2	`(cos.f64 th)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes5.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

14 → 2

Calls

Call 1

Inputs
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(literal 1/2 binary64) a1) #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (.f64 (.f64 a2 a2) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))

Outputs

#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (*.f64 (*.f64 a2 a2) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64))))

#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))

Calls

1 calls:

4.0ms

(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))

Results

Accuracy	Segments	Branch
77.6%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 22 to 12 computations (45.5% saved)

regimes77.0ms (0.7%)

Memory

-22.8MiB live, 50.9MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(literal 1/2 binary64) a1) #s(approx (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (.f64 a2 (.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))))

Outputs
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))

Calls

6 calls:

36.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
22.0ms	a1
4.0ms	a2
4.0ms	(cos.f64 th)
4.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
65.9%	1	`a1`
65.9%	1	`(*.f64 a1 a1)`
65.9%	1	`a2`
65.9%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
65.9%	1	`(cos.f64 th)`
65.9%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 49 to 33 computations (32.7% saved)

regimes48.0ms (0.5%)

Memory

20.1MiB live, 58.8MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a2 a2) (/ (sqrt 2) a1)) (* (sqrt 2) a1)) (* (sqrt 2) (/ (sqrt 2) a1))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))

Outputs

#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))

Calls

8 calls:

26.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
3.0ms	a1
3.0ms	a2
3.0ms	th
3.0ms	(cos.f64 th)

Results

Accuracy	Segments	Branch
65.2%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
65.2%	1	`th`
65.2%	1	`a2`
65.2%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
65.2%	1	`(cos.f64 th)`
65.2%	1	`(*.f64 a2 a2)`
65.2%	1	`a1`
65.2%	1	`(*.f64 a1 a1)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes37.0ms (0.4%)

Memory

-67.3MiB live, 23.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))

#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))

Outputs

#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))

Calls

8 calls:

26.0ms	(*.f64 a2 a2)
2.0ms	a2
2.0ms	th
2.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
2.0ms	a1

Results

Accuracy	Segments	Branch
15.3%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
15.3%	1	`th`
15.3%	1	`a2`
15.3%	1	`(*.f64 a2 a2)`
15.3%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
15.3%	1	`(cos.f64 th)`
15.3%	1	`a1`
15.3%	1	`(*.f64 a1 a1)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

bsearch1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-4.467396411976095e-162	-2.776957894300675e-203

Compiler

Compiled 25 to 18 computations (28% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-4.467396411976095e-162	-2.776957894300675e-203

Compiler

Compiled 25 to 18 computations (28% saved)

simplify8.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	341
1	84	341

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) a2))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) #s(literal -8104522595470689/2026130648867672343023636652192949780767796011837127392576004555513014068072709055859231957493703024554784124321924213467966382361040905912054138102594708831572842677442143322112 binary64)) #s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 #s(approx ( a2 (cos th)) (fma.f64 th (.f64 th (.f64 #s(literal -1/2 binary64) a2)) a2))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) #s(literal -8104522595470689/2026130648867672343023636652192949780767796011837127392576004555513014068072709055859231957493703024554784124321924213467966382361040905912054138102594708831572842677442143322112 binary64)) #s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (.f64 (.f64 a2 a2) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))

Outputs
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 2 binary64))) a2))
#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) #s(literal -8104522595470689/2026130648867672343023636652192949780767796011837127392576004555513014068072709055859231957493703024554784124321924213467966382361040905912054138102594708831572842677442143322112 binary64)) #s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 #s(approx ( a2 (cos th)) (fma.f64 th (.f64 th (.f64 #s(literal -1/2 binary64) a2)) a2))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) #s(literal -8104522595470689/2026130648867672343023636652192949780767796011837127392576004555513014068072709055859231957493703024554784124321924213467966382361040905912054138102594708831572842677442143322112 binary64)) #s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 #s(approx ( a2 (cos th)) (fma.f64 th (.f64 th (.f64 a2 #s(literal -1/2 binary64))) a2))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) #s(literal -8104522595470689/2026130648867672343023636652192949780767796011837127392576004555513014068072709055859231957493703024554784124321924213467966382361040905912054138102594708831572842677442143322112 binary64)) #s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (.f64 (.f64 a2 a2) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) #s(literal -8104522595470689/2026130648867672343023636652192949780767796011837127392576004555513014068072709055859231957493703024554784124321924213467966382361040905912054138102594708831572842677442143322112 binary64)) #s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* a2 (* a2 (cos th))) (.f64 (.f64 a2 a2) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))

soundness1.4s (13.9%)

Memory

21.9MiB live, 1 048.1MiB allocated

Rules

34 694×	`lower-fma.f64`
34 694×	`lower-fma.f32`
16 784×	`lower-fma.f64`
16 784×	`lower-fma.f32`
15 540×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	189	6278
1	613	5324
2	2232	5104
3	5867	4894
0	8600	4520
0	53	315
0	81	297
1	267	285
2	1859	285
0	8127	280
0	12	44
0	20	38
1	58	38
2	411	38
3	7331	38
0	8434	37
0	39	265
0	60	242
1	219	222
2	1762	222
0	8491	222
0	111	1498
1	343	1366
2	1205	1262
3	3898	1233
0	8422	1172
0	204	6059
1	666	5216
2	2335	4910
3	5567	4902
0	8120	4586
0	148	5641
1	482	4816
2	1754	4497
3	4978	4490
4	7903	4490
0	8069	4158

Stop Event

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

Compiler

Compiled 474 to 227 computations (52.1% saved)

preprocess136.0ms (1.3%)

Memory

-4.0MiB live, 152.3MiB allocated

Remove

(sort a1 a2)

(abs a1)

(abs a2)

(abs th)

Compiler

Compiled 714 to 344 computations (51.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample1.1s (11.1%)

preprocess139.0ms (1.3%)

explain150.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize41.0ms (0.4%)

series14.0ms (0.1%)

simplify800.0ms (7.7%)

rewrite420.0ms (4.1%)

eval82.0ms (0.8%)

prune128.0ms (1.2%)

simplify329.0ms (3.2%)

localize330.0ms (3.2%)

series53.0ms (0.5%)

simplify661.0ms (6.4%)

rewrite384.0ms (3.7%)

eval286.0ms (2.8%)

prune228.0ms (2.2%)

simplify185.0ms (1.8%)

localize124.0ms (1.2%)

series18.0ms (0.2%)

simplify353.0ms (3.4%)

rewrite345.0ms (3.3%)

eval169.0ms (1.6%)

prune181.0ms (1.7%)

simplify61.0ms (0.6%)

localize147.0ms (1.4%)

series24.0ms (0.2%)

simplify414.0ms (4%)

rewrite315.0ms (3%)

eval179.0ms (1.7%)

prune210.0ms (2%)

regimes245.0ms (2.4%)

regimes160.0ms (1.5%)

regimes123.0ms (1.2%)

regimes155.0ms (1.5%)

regimes5.0ms (0.1%)

regimes77.0ms (0.7%)

regimes48.0ms (0.5%)

regimes37.0ms (0.4%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

soundness1.4s (13.9%)

preprocess136.0ms (1.3%)

end0.0ms (0%)

Profiling