Metrics for Migdal et al, Equation (64)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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)

sample1.5s (13.8%)

Memory

22.9MiB live, 1 404.6MiB allocated

Samples

1.1s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 804.0ms

ival-cos: 327.0ms (40.7% of total)

ival-mult: 264.0ms (32.8% of total)

ival-sqrt: 77.0ms (9.6% of total)

ival-div: 75.0ms (9.3% of total)

ival-add: 45.0ms (5.6% of total)

ival-true: 6.0ms (0.7% of total)

exact: 6.0ms (0.7% of total)

ival-assert: 4.0ms (0.5% of total)

Bogosity

explain192.0ms (1.8%)

Memory

-55.7MiB live, 208.1MiB 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

61.0ms

512×

valid

Compiler

Compiled 138 to 40 computations (71% saved)

Precisions

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

ival-mult: 15.0ms (42.5% of total)

ival-cos: 10.0ms (28.3% of total)

ival-sqrt: 4.0ms (11.3% of total)

ival-div: 3.0ms (8.5% of total)

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

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

exact: 0.0ms (0% of total)

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

preprocess138.0ms (1.3%)

Memory

14.0MiB live, 52.7MiB 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)

Compiler

Compiled 22 to 12 computations (45.5% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB 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)

simplify6.0ms (0.1%)

Memory

8.6MiB live, 8.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

localize41.0ms (0.4%)

Memory

-6.4MiB live, 70.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 th)
accuracy	0.142910009768442	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
accuracy	0.19207001953688402	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
accuracy	0.70703125	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

29.0ms

256×

valid

Compiler

Compiled 58 to 14 computations (75.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-cos: 7.0ms (34.3% of total)

ival-mult: 6.0ms (29.4% of total)

ival-add: 4.0ms (19.6% of total)

ival-div: 2.0ms (9.8% of total)

ival-sqrt: 2.0ms (9.8% 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

1.1MiB live, 43.6MiB allocated

Counts

5 → 108

Calls

Call 1

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

Outputs
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 th) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 th) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 th) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 th) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor inf th) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor inf th) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor inf th) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor inf th) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor -inf th) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor -inf th) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor -inf th) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor -inf th) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor inf a1) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(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))) (patch (+.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))) #<representation binary64>) () ())) ())
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#s(alt 1 (taylor 0 th) (#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow th 2))) (taylor 0 th) (#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2))) (taylor 0 th) (#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (taylor 0 th) (#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor inf th) (#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor inf th) (#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor inf th) (#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor inf th) (#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor -inf th) (#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor -inf th) (#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor -inf th) (#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor -inf th) (#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor 0 th) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (/ (pow a2 2) (sqrt 2))) (taylor 0 th) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(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))) (taylor 0 th) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(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))) (taylor 0 th) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf th) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf th) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf th) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf th) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf th) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf th) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf th) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf th) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a2) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a2) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a2) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a2) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf a2) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf a2) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf a2) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf a2) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (patch (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) #<representation binary64>) () ())) ())

Calls

27 calls:

Time	Variable		Point	Expression
6.0ms	th	@	inf	(/ (cos th) (sqrt 2))
3.0ms	th	@	0	(/ (cos th) (sqrt 2))
2.0ms	th	@	inf	(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
2.0ms	th	@	-inf	(/ (cos th) (sqrt 2))
2.0ms	th	@	-inf	(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

simplify497.0ms (4.6%)

Memory

5.0MiB live, 478.2MiB 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 a1) (/.f64 (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 a1) (/.f64 (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 a1) (/.f64 (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 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (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)))

rewrite265.0ms (2.5%)

Memory

6.3MiB live, 278.9MiB allocated

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

eval93.0ms (0.9%)

Memory: 13.0MiB live, 135.2MiB allocated
Compiler: Compiled 14 708 to 1 014 computations (93.1% saved)

prune290.0ms (2.7%)

Memory

-22.9MiB live, 224.6MiB allocated

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	473	17	490
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	474	17	491

Accuracy

100.0%

Counts

491 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(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))))))
▶	99.7%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	15.8%	(/.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))))
	24.3%	(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
	24.3%	(/.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))))
	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))))
▶	44.7%	(+.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))))))
	99.7%	(.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))))
▶	99.7%	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	99.6%	(.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
▶	99.6%	(.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))))
▶	70.5%	#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)))))
	99.5%	#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))))
	54.8%	#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))))
	72.0%	#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))))))
	67.4%	#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 802 to 456 computations (43.1% saved)

simplify483.0ms (4.5%)

Memory

-15.5MiB live, 341.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
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	128	(+.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))))))
cost-diff	1664	(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))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	320	(.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))))
cost-diff	1088	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
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))
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 (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	384	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))

Rules

13 216×	`lower-fma.f32`
13 206×	`lower-fma.f64`
4 848×	`lower-*.f32`
4 830×	`lower-*.f64`
2 184×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	402
0	74	394
1	134	392
2	328	380
3	1208	371
4	3077	371
5	6551	371
6	6921	371
7	7101	371
8	7101	371
9	7649	371
0	8097	367

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

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

localize325.0ms (3%)

Memory

22.7MiB live, 384.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.8875312426197615	(.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)))
accuracy	3.0780919712667223	(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))))
accuracy	17.88236403911815	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (*.f64 th th))
accuracy	19.126096706587873	#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)))))
accuracy	0.0859375	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
accuracy	0.109375	(/.f64 #s(literal 1 binary64) (cos.f64 th))
accuracy	0.20378876953688402	(.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))))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.04296875	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
accuracy	0.18359375	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.1875	(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.3984375	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	18.73062718858967	#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	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.17578125	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
accuracy	0.197597509768442	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))

Samples

225.0ms

256×

valid

Compiler

Compiled 351 to 42 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 119.0ms

ival-add: 40.0ms (33.6% of total)

ival-cos: 25.0ms (21% of total)

ival-mult: 23.0ms (19.3% of total)

ival-div: 22.0ms (18.5% of total)

const: 6.0ms (5% of total)

ival-sqrt: 2.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series115.0ms (1.1%)

Memory

-9.2MiB live, 109.6MiB allocated

Counts

23 → 492

Calls

Call 1

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

Outputs
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor inf a1) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor -inf a1) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor -inf a1) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor -inf a1) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor -inf a1) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor 0 a2) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a2) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a2) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a2) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf a2) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<representation binary64>) () ())) ())
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#s(alt (/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2)) (taylor -inf a2) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2)) (taylor -inf a2) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2)) (taylor -inf a2) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (taylor 0 th) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))))) (taylor 0 th) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(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))))))) (taylor 0 th) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(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))))))) (taylor 0 th) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt (* -1/720 (/ (* (pow a2 2) (pow th 6)) (sqrt 2))) (taylor inf th) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt (* (pow th 6) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2)))))) (taylor inf th) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt (* (pow th 6) (+ (* -1/2 (/ (pow a2 2) (* (pow th 4) (sqrt 2)))) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2))))))) (taylor inf th) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt (* (pow th 6) (+ (* -1/2 (/ (pow a2 2) (* (pow th 4) (sqrt 2)))) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2))))))) (taylor inf th) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt (* -1/720 (/ (* (pow a2 2) (pow th 6)) (sqrt 2))) (taylor -inf th) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt (* (pow th 6) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2)))))) (taylor -inf th) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt (* (pow th 6) (+ (* -1/2 (/ (pow a2 2) (* (pow th 4) (sqrt 2)))) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2))))))) (taylor -inf th) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt (* (pow th 6) (+ (* -1/2 (/ (pow a2 2) (* (pow th 4) (sqrt 2)))) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2))))))) (taylor -inf th) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())

Calls

123 calls:

Time	Variable		Point	Expression
34.0ms	th	@	-inf	(/ (sqrt 2) (cos th))
20.0ms	th	@	0	(* (* (/ (* a2 a2) (sqrt 2)) (* th th)) (+ (* th (* th (+ (* (* th th) -1/720) 1/24))) -1/2))
3.0ms	a1	@	-inf	(/ (+ (* a1 a1) (* a2 a2)) (/ 1 (cos th)))
2.0ms	a2	@	0	(+ (* a2 (/ a2 (sqrt 2))) (* (* (/ (* a2 a2) (sqrt 2)) (* th th)) (+ (* th (* th (+ (* (* th th) -1/720) 1/24))) -1/2)))
1.0ms	th	@	inf	(+ (* a2 (/ a2 (sqrt 2))) (* (* (/ (* a2 a2) (sqrt 2)) (* th th)) (+ (* th (* th (+ (* (* th th) -1/720) 1/24))) -1/2)))

simplify349.0ms (3.2%)

Memory

26.9MiB live, 734.8MiB allocated

Algorithm

1×	egg-herbie

Rules

18 450×	`lower-fma.f64`
18 450×	`lower-fma.f32`
5 484×	`lower-*.f64`
5 484×	`lower-*.f32`
4 622×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	235	7352
1	755	6539
2	2650	6089
3	6653	6006
0	8075	5611

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 492

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 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 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)))
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(/ (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))
(/ (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))
1
(+ 1 (* 1/2 (pow th 2)))
(+ 1 (* (pow th 2) (+ 1/2 (* 5/24 (pow th 2)))))
(+ 1 (* (pow th 2) (+ 1/2 (* (pow th 2) (+ 5/24 (* 61/720 (pow th 2)))))))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (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))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (pow th 2)) (sqrt 2))
(/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2))
(/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2))
(/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2))
(/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2))
(/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2))
(/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2))
(/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2))
(/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2))
(/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2))
(/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2))
(/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2))
(/ (* (pow a2 2) (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (sqrt 2))
(* -1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2)))
(* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (* (pow a2 2) (pow th 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 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)))))))
(* -1/720 (/ (* (pow a2 2) (pow th 6)) (sqrt 2)))
(* (pow th 6) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2))))))
(* (pow th 6) (+ (* -1/2 (/ (pow a2 2) (* (pow th 4) (sqrt 2)))) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2)))))))
(* (pow th 6) (+ (* -1/2 (/ (pow a2 2) (* (pow th 4) (sqrt 2)))) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2)))))))
(* -1/720 (/ (* (pow a2 2) (pow th 6)) (sqrt 2)))
(* (pow th 6) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2))))))
(* (pow th 6) (+ (* -1/2 (/ (pow a2 2) (* (pow th 4) (sqrt 2)))) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2)))))))
(* (pow th 6) (+ (* -1/2 (/ (pow a2 2) (* (pow th 4) (sqrt 2)))) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 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))))
(fma.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th th)) (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 (.f64 th (.f64 th (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 (.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 -1/720 binary64) #s(literal 1/24 binary64))) (/.f64 (.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))))
(/ (* (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))
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 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 (*.f64 th th) #s(literal 5/24 binary64) #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 th (.f64 th (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 61/720 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 th th) #s(literal 5/24 binary64) #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))
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(* -1/720 (/ (* (pow a2 2) (pow th 6)) (sqrt 2)))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -1/720 binary64) (pow.f64 th #s(literal 6 binary64))))
(* (pow th 6) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2))))))
(.f64 (pow.f64 th #s(literal 6 binary64)) (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 th th)))))
(* (pow th 6) (+ (* -1/2 (/ (pow a2 2) (* (pow th 4) (sqrt 2)))) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2)))))))
(.f64 (pow.f64 th #s(literal 6 binary64)) (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 th th)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 th th) (*.f64 th th)))))))
(* (pow th 6) (+ (* -1/2 (/ (pow a2 2) (* (pow th 4) (sqrt 2)))) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2)))))))
(.f64 (pow.f64 th #s(literal 6 binary64)) (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 th th)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 th th) (*.f64 th th)))))))
(* -1/720 (/ (* (pow a2 2) (pow th 6)) (sqrt 2)))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -1/720 binary64) (pow.f64 th #s(literal 6 binary64))))
(* (pow th 6) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2))))))
(.f64 (pow.f64 th #s(literal 6 binary64)) (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 th th)))))
(* (pow th 6) (+ (* -1/2 (/ (pow a2 2) (* (pow th 4) (sqrt 2)))) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2)))))))
(.f64 (pow.f64 th #s(literal 6 binary64)) (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 th th)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 th th) (*.f64 th th)))))))
(* (pow th 6) (+ (* -1/2 (/ (pow a2 2) (* (pow th 4) (sqrt 2)))) (+ (* -1/720 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (* (pow th 2) (sqrt 2)))))))
(.f64 (pow.f64 th #s(literal 6 binary64)) (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 th th)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 th th) (*.f64 th th)))))))

rewrite437.0ms (4.1%)

Memory

-12.4MiB live, 947.6MiB allocated

Rules

5 626×	`lower-*.f32`
5 608×	`lower-*.f64`
4 494×	`lower-/.f32`
4 474×	`lower-/.f64`
4 438×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	300
0	74	292
1	285	270
2	2257	270
0	8896	269

Stop Event

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

Counts

23 → 2 195

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

Outputs
(+.f64 (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (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 (cos.f64 th) a2) a2) #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)))))
(fma.f64 a1 (.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (*.f64 (cos.f64 th) 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 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 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (*.f64 (cos.f64 th) a2) 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 (.f64 (.f64 (cos.f64 th) 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 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (/.f64 (.f64 (*.f64 (cos.f64 th) 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 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) a1 (/.f64 (.f64 (*.f64 (cos.f64 th) 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 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (.f64 (cos.f64 th) 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 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (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 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
(/.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 (fma.f64 (/.f64 (.f64 (.f64 (cos.f64 th) 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 (*.f64 (cos.f64 th) 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 (fma.f64 a1 a1 (.f64 a2 a2)) (/.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))))))
(/.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 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 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 (.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 #s(literal 1 binary64) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)))))
(/.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 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.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) (neg.f64 (/.f64 (fma.f64 (/.f64 (.f64 (.f64 (cos.f64 th) 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 (*.f64 (cos.f64 th) 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 (fma.f64 a1 a1 (.f64 a2 a2)) (/.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)))))))
(/.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 (neg.f64 (cos.f64 th)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(/.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 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 (cos.f64 th) 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 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (.f64 (.f64 (cos.f64 th) a2) a2) #s(literal 2 binary64)) #s(literal 1/2 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 (*.f64 (cos.f64 th) a2) a2))) #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))))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a1 (.f64 a1 (.f64 a1 a1))))))
(/.f64 (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.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)))) (.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)) (.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 (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 (.f64 (cos.f64 th) 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 (fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 th) a2) a2))) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 1 binary64) (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 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a1 (.f64 a1 (*.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 (fma.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a1 (.f64 a1 (*.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 (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)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a1 (.f64 a1 (*.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))))
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(exp.f64 (fma.f64 (log.f64 (cos.f64 th)) #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))))
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(neg.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.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))))
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(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (cos.f64 th)))
(/.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 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (neg.f64 (cos.f64 th))))
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(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1 binary64))
(pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
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(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
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(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 th)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
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(+.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.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 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)))
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(neg.f64 (/.f64 (neg.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) #s(literal 1 binary64)))
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(neg.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))))
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(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
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(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
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(/.f64 (neg.f64 (.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal -1/8 binary64)) (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (fma.f64 (.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) (.f64 (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/4 binary64)) (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(.f64 (.f64 a2 a2) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 th (*.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(.f64 (.f64 th th) (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(.f64 (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 (.f64 a2 a2) th) (sqrt.f64 #s(literal 2 binary64))) (.f64 th (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(.f64 (.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (.f64 (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 th th))
(.f64 (.f64 (fma.f64 (.f64 th th) (fma.f64 th (.f64 th #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (/.f64 (.f64 (.f64 a2 a2) th) (sqrt.f64 #s(literal 2 binary64)))) th)

eval432.0ms (4%)

Memory: 58.9MiB live, 983.3MiB allocated
Compiler: Compiled 117 116 to 5 410 computations (95.4% saved)

prune389.0ms (3.6%)

Memory

-48.2MiB live, 970.8MiB allocated

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	3 137	26	3 163
Fresh	10	2	12
Picked	5	0	5
Done	0	0	0
Total	3 152	28	3 180

Accuracy

100.0%

Counts

3 180 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	72.0%	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
▶	67.0%	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	70.5%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
	99.6%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
	99.5%	(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	99.6%	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
	99.6%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
	99.7%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
▶	99.7%	(.f64 (/.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)) (cos.f64 th))
	70.9%	(.f64 (/.f64 (fma.f64 a1 a1 (.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))))
▶	67.4%	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
	72.0%	(.f64 (/.f64 (fma.f64 a1 a1 (.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))))
	99.5%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) (cos.f64 th))
	70.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (fma.f64 a2 a2 (*.f64 a1 a1))))
	72.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))))
	99.5%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
	70.5%	#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 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	70.5%	#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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	70.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 (neg.f64 a1) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
	70.6%	#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)))
	70.5%	#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)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	66.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	17.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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)))))
▶	99.5%	#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))))
	70.5%	#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)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
	70.4%	#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)))))
▶	16.0%	#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)))))

Compiler

Compiled 1 024 to 620 computations (39.5% saved)

simplify71.0ms (0.7%)

Memory

4.0MiB live, 82.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 a2 a2)
cost-diff	0	(.f64 (.f64 a2 a2) (cos.f64 th))
cost-diff	0	(/.f64 (.f64 (.f64 a2 a2) (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 a2 a2) (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)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
cost-diff	0	#s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (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)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(*.f64 a1 a1)
cost-diff	0	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
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	0	(*.f64 a2 a2)
cost-diff	0	(.f64 (/.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)) (cos.f64 th))
cost-diff	384	(/.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))
cost-diff	960	(fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))

Rules

1 308×	`lower-*.f32`
1 290×	`lower-*.f64`
684×	`lower-fma.f32`
674×	`lower-fma.f64`
426×	`associate-r`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	47	355
0	75	345
1	130	336
2	215	336
3	328	336
4	590	336
5	776	336
6	1128	324
7	1341	324
8	1490	324
9	1532	324
10	1538	324
11	1558	324
12	1563	324
13	1563	324
14	1563	324
15	1585	324
16	1585	324
0	1585	324

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize136.0ms (1.3%)

Memory

-3.4MiB live, 351.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 th)
accuracy	0.05859375	(.f64 (.f64 a2 a2) (cos.f64 th))
accuracy	0.11917160968349072	#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))))
accuracy	0.1953125	(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.05859375	(.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
accuracy	0.18359375	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.32469188510136804	(fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
accuracy	27.79581021881543	#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)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.11947250976844202	(.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.17578125	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	27.76678657401846	#s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.281913769536884	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
accuracy	18.73062718858967	#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	51.76091590097476	#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0	(cos.f64 th)
accuracy	0.04296875	(.f64 (/.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)) (cos.f64 th))
accuracy	0.205410009768442	(fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))
accuracy	0.21226503907376804	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))

Samples

79.0ms

256×

valid

Compiler

Compiled 289 to 44 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-mult: 23.0ms (40.7% of total)

ival-div: 14.0ms (24.8% of total)

ival-add: 7.0ms (12.4% of total)

ival-cos: 5.0ms (8.9% of total)

const: 4.0ms (7.1% of total)

ival-sqrt: 2.0ms (3.5% of total)

exact: 1.0ms (1.8% of total)

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

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

series33.0ms (0.3%)

Memory

-2.4MiB live, 80.0MiB allocated

Counts

23 → 468

Calls

Call 1

Inputs
#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())
#s(alt (/.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)) (patch (/.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)) #<representation binary64>) () ())
#s(alt (.f64 (/.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)) (cos.f64 th)) (patch (.f64 (/.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)) (cos.f64 th)) #<representation binary64>) () ())
#s(alt (.f64 a2 a2) (patch (.f64 a2 a2) #<representation binary64>) () ())
#s(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))))) (patch #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))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (+ ( a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 a1 a1) (patch (.f64 a1 a1) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (fma.f64 a1 a1 (.f64 a2 a2)) (patch (fma.f64 a1 a1 (.f64 a2 a2)) #<representation binary64>) () ())
#s(alt #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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)))) (patch (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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)))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #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)))) (patch #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)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 a2 a2) (cos.f64 th)) (patch (.f64 (.f64 a2 a2) (cos.f64 th)) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) #<representation binary64>) () ())
#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #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))) (patch #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))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (* (pow a1 2) (sqrt 2)) (taylor 0 a2) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (taylor 0 a2) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (taylor 0 a2) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (taylor 0 a2) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (sqrt 2)) (taylor inf a2) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (taylor inf a2) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (taylor inf a2) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (taylor inf a2) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (sqrt 2)) (taylor -inf a2) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (taylor -inf a2) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (taylor -inf a2) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (taylor -inf a2) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (sqrt 2)) (taylor 0 a1) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (sqrt 2)) (taylor inf a1) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))) (taylor inf a1) (#s(alt (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (patch (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #<representation binary64>) () ())) ())
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#s(alt (+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2)))) (taylor 0 a1) (#s(alt (/.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)) (patch (/.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)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2)))) (taylor 0 a1) (#s(alt (/.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)) (patch (/.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)) #<representation binary64>) () ())) ())
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#s(alt (* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))) (taylor -inf a1) (#s(alt (/.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)) (patch (/.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)) #<representation binary64>) () ())) ())
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#s(alt (* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))) (taylor inf a2) (#s(alt (.f64 (/.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)) (cos.f64 th)) (patch (.f64 (/.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)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))) (taylor inf a2) (#s(alt (.f64 (/.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)) (cos.f64 th)) (patch (.f64 (/.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)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))) (taylor inf a2) (#s(alt (.f64 (/.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)) (cos.f64 th)) (patch (.f64 (/.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)) (cos.f64 th)) #<representation binary64>) () ())) ())
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#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor 0 a2) (#s(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))))) (patch #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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a2) (#s(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))))) (patch #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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a2) (#s(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))))) (patch #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))))) #<representation binary64>) () ())) ())
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#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(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))))) (patch #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))))) #<representation binary64>) () ())) ())
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#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(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))))) (patch #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))))) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2))) (taylor 0 th) (#s(alt #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))) (patch #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))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2))) (taylor 0 th) (#s(alt #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))) (patch #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))) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor inf th) (#s(alt #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))) (patch #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))) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor inf th) (#s(alt #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))) (patch #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))) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor inf th) (#s(alt #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))) (patch #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))) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor inf th) (#s(alt #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))) (patch #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))) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor -inf th) (#s(alt #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))) (patch #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))) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor -inf th) (#s(alt #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))) (patch #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))) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor -inf th) (#s(alt #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))) (patch #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))) #<representation binary64>) () ())) ())
#s(alt (cos th) (taylor -inf th) (#s(alt #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))) (patch #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))) #<representation binary64>) () ())) ())
#s(alt -1/2 (taylor 0 th) (#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/24 (pow th 2)) 1/2) (taylor 0 th) (#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/24 (pow th 2)) 1/2) (taylor 0 th) (#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/24 (pow th 2)) 1/2) (taylor 0 th) (#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow th 2)) (taylor inf th) (#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2))))) (taylor inf th) (#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2))))) (taylor inf th) (#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2))))) (taylor inf th) (#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow th 2)) (taylor -inf th) (#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2))))) (taylor -inf th) (#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2))))) (taylor -inf th) (#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2))))) (taylor -inf th) (#s(alt (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 th) (taylor 0 th) (#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* th (- (* 1/24 (pow th 2)) 1/2)) (taylor 0 th) (#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* th (- (* 1/24 (pow th 2)) 1/2)) (taylor 0 th) (#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* th (- (* 1/24 (pow th 2)) 1/2)) (taylor 0 th) (#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow th 3)) (taylor inf th) (#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow th 3) (- 1/24 (* 1/2 (/ 1 (pow th 2))))) (taylor inf th) (#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow th 3) (- 1/24 (* 1/2 (/ 1 (pow th 2))))) (taylor inf th) (#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow th 3) (- 1/24 (* 1/2 (/ 1 (pow th 2))))) (taylor inf th) (#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow th 3)) (taylor -inf th) (#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow th 3) (- (* 1/2 (/ 1 (pow th 2))) 1/24))) (taylor -inf th) (#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow th 3) (- (* 1/2 (/ 1 (pow th 2))) 1/24))) (taylor -inf th) (#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow th 3) (- (* 1/2 (/ 1 (pow th 2))) 1/24))) (taylor -inf th) (#s(alt (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch (.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())

Calls

117 calls:

Time	Variable		Point	Expression
1.0ms	th	@	inf	(* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th))
1.0ms	th	@	0	(* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th))
1.0ms	th	@	-inf	(* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th))
0.0ms	a2	@	0	(* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th))
0.0ms	a2	@	inf	(* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th))

simplify278.0ms (2.6%)

Memory

50.2MiB live, 557.9MiB allocated

Algorithm

1×	egg-herbie

Rules

14 544×	`lower-fma.f64`
14 544×	`lower-fma.f32`
5 958×	`lower-*.f64`
5 958×	`lower-*.f32`
4 442×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	223	6651
1	761	5987
2	2899	5769
3	7666	5768
0	8068	5441

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 468

Calls

Call 1

Inputs
(* (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) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 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) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(* 1/2 (* (pow a2 2) (sqrt 2)))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* 1/2 (* (pow a2 2) (sqrt 2)))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* 1/2 (* (pow a2 2) (sqrt 2)))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))
(+ (* -1/4 (* (pow th 2) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(+ (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* (pow th 2) (+ (* -1/4 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* 1/48 (* (pow th 2) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))))))
(+ (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* (pow th 2) (+ (* -1/4 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* (pow th 2) (+ (* -1/1440 (* (pow th 2) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (* 1/48 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(pow a2 2)
(pow a2 2)
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(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
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(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
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(/ (* (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))))
(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))
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(+ (/ (* (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))
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
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(* (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))
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(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
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(/ (* (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)))))
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(/ (pow a1 2) (sqrt 2))
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(/ (pow a2 2) (sqrt 2))
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
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(/ (* (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))
(* (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))
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)
(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))))
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)
-1/2
(- (* 1/24 (pow th 2)) 1/2)
(- (* 1/24 (pow th 2)) 1/2)
(- (* 1/24 (pow th 2)) 1/2)
(* 1/24 (pow th 2))
(* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(* 1/24 (pow th 2))
(* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(* -1/2 th)
(* th (- (* 1/24 (pow th 2)) 1/2))
(* th (- (* 1/24 (pow th 2)) 1/2))
(* th (- (* 1/24 (pow th 2)) 1/2))
(* 1/24 (pow th 3))
(* (pow th 3) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(* (pow th 3) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(* (pow th 3) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(* 1/24 (pow th 3))
(* -1 (* (pow th 3) (- (* 1/2 (/ 1 (pow th 2))) 1/24)))
(* -1 (* (pow th 3) (- (* 1/2 (/ 1 (pow th 2))) 1/24)))
(* -1 (* (pow th 3) (- (* 1/2 (/ 1 (pow th 2))) 1/24)))

Outputs
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a2 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(* 1/2 (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 a2 a2) #s(literal 1/2 binary64)))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* 1/2 (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 a2 a2) #s(literal 1/2 binary64)))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* 1/2 (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 a2 a2) #s(literal 1/2 binary64)))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(.f64 (.f64 (.f64 a1 a1) #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(.f64 (.f64 (.f64 a1 a1) #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(.f64 (.f64 (.f64 a1 a1) #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(.f64 (.f64 (.f64 a1 a1) #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(.f64 (.f64 (.f64 a1 a1) #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(.f64 (.f64 (.f64 a1 a1) #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 a1 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 th))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 a2) #s(literal 1/2 binary64))) (cos.f64 th))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (fma.f64 (.f64 a1 a1) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (fma.f64 (.f64 a1 a1) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (fma.f64 (.f64 a1 a1) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 a2) #s(literal 1/2 binary64))) (cos.f64 th))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (fma.f64 (.f64 a1 a1) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (fma.f64 (.f64 a1 a1) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (fma.f64 (.f64 a1 a1) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 a2) #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))
(* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 a1 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 th))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (.f64 a2 (cos.f64 th)))) (.f64 a1 a1))) (*.f64 a1 a1)))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (.f64 a2 (cos.f64 th)))) (.f64 a1 a1))) (*.f64 a1 a1)))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
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(fma.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 th th))) (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 (.f64 a2 (.f64 a2 (.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 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 a2 a2) (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))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (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))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (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))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (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))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(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 th) (.f64 (.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 a2 (.f64 a2 #s(literal -1/2 binary64)) (.f64 (.f64 a2 (.f64 a2 (.f64 th th))) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (sqrt 2))
(.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow th 2)))
(fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))
(fma.f64 th (.f64 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)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 1/2 (* (pow th 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 th th)))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(.f64 (.f64 th th) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 th th))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(.f64 (.f64 th th) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 th th))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(.f64 (.f64 th th) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 th th))))
(* 1/2 (* (pow th 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 th th)))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(.f64 (.f64 th th) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 th th))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(.f64 (.f64 th th) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 th th))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(.f64 (.f64 th th) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 th th))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow th 2)))
(fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))
(fma.f64 th (.f64 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)
-1/2
#s(literal -1/2 binary64)
(- (* 1/24 (pow th 2)) 1/2)
(fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(- (* 1/24 (pow th 2)) 1/2)
(fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(- (* 1/24 (pow th 2)) 1/2)
(fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(* 1/24 (pow th 2))
(.f64 (.f64 th th) #s(literal 1/24 binary64))
(* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 th th))) th) th)
(* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 th th))) th) th)
(* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 th th))) th) th)
(* 1/24 (pow th 2))
(.f64 (.f64 th th) #s(literal 1/24 binary64))
(* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 th th))) th) th)
(* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 th th))) th) th)
(* (pow th 2) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 th th))) th) th)
(* -1/2 th)
(*.f64 th #s(literal -1/2 binary64))
(* th (- (* 1/24 (pow th 2)) 1/2))
(.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
(* th (- (* 1/24 (pow th 2)) 1/2))
(.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
(* th (- (* 1/24 (pow th 2)) 1/2))
(.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
(* 1/24 (pow th 3))
(.f64 th (.f64 (*.f64 th th) #s(literal 1/24 binary64)))
(* (pow th 3) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(.f64 th (.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 th th))) th) th))
(* (pow th 3) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(.f64 th (.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 th th))) th) th))
(* (pow th 3) (- 1/24 (* 1/2 (/ 1 (pow th 2)))))
(.f64 th (.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 th th))) th) th))
(* 1/24 (pow th 3))
(.f64 th (.f64 (*.f64 th th) #s(literal 1/24 binary64)))
(* -1 (* (pow th 3) (- (* 1/2 (/ 1 (pow th 2))) 1/24)))
(.f64 th (.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 th th))) th) th))
(* -1 (* (pow th 3) (- (* 1/2 (/ 1 (pow th 2))) 1/24)))
(.f64 th (.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 th th))) th) th))
(* -1 (* (pow th 3) (- (* 1/2 (/ 1 (pow th 2))) 1/24)))
(.f64 th (.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 th th))) th) th))

rewrite294.0ms (2.7%)

Memory

-3.5MiB live, 675.1MiB allocated

Rules

6 242×	`lower-fma.f32`
6 232×	`lower-fma.f64`
4 394×	`lower-*.f32`
4 376×	`lower-*.f64`
4 256×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	282
0	75	273
1	268	253
2	2094	247
0	8243	247

Stop Event

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

Counts

23 → 800

Calls

Call 1

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

Outputs
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)))
(-.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (.f64 #s(literal 2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(-.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (-.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))) (/.f64 (.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2)))) (-.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))))
(fma.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))
(fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1) (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal 2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 a2 (.f64 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))))) (fma.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2)))) (.f64 (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (-.f64 (.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2)))) (.f64 #s(literal 2 binary64) (.f64 a1 (.f64 a1 (*.f64 a1 a1)))))))
(/.f64 (fma.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2)))) (.f64 (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (-.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal 2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 a2 (.f64 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))))))
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(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fma.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2)))) (.f64 (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))) (/.f64 (cos.f64 th) (-.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal 2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 a2 (.f64 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)))))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2)))) (.f64 #s(literal 2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))))) (/.f64 (cos.f64 th) (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 a2)))
(pow.f64 a2 #s(literal 2 binary64))
(pow.f64 (*.f64 a2 a2) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 a2)) #s(literal 2 binary64))
(*.f64 a2 a2)
(*.f64 (exp.f64 (log.f64 a2)) (exp.f64 (log.f64 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 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (log.f64 (.f64 a1 a1)) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 (*.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 (neg.f64 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(/.f64 (neg.f64 a1) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(/.f64 (neg.f64 (*.f64 a1 a1)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) #s(literal 1 binary64))))
(/.f64 (.f64 (.f64 a1 a1) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (neg.f64 (*.f64 a1 a1))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 a1 #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(/.f64 (*.f64 #s(literal 1 binary64) a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(/.f64 (neg.f64 (.f64 (.f64 a1 a1) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (*.f64 a1 a1)))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (*.f64 a1 #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) a1)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a1)))
(.f64 #s(literal 1 binary64) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (neg.f64 (.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 a1 a1)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a1 (/.f64 #s(literal 1 binary64) a1)))
(*.f64 (/.f64 a1 #s(literal -1 binary64)) (/.f64 (neg.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 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 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 (neg.f64 a1) #s(literal -1 binary64)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (log.f64 (*.f64 a1 a1)))
(pow.f64 a1 #s(literal 2 binary64))
(pow.f64 (*.f64 a1 a1) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 a1)) #s(literal 2 binary64))
(*.f64 a1 a1)
(*.f64 (exp.f64 (log.f64 a1)) (exp.f64 (log.f64 a1)))
(exp.f64 (.f64 (log.f64 (/.f64 #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 a2 a2 (.f64 a1 a1)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (+.f64 a1 a2) (-.f64 a1 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))))) (/.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (+.f64 a1 a2) (-.f64 a1 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))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #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 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 #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 (/.f64 (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 #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 (+.f64 a1 a2) (-.f64 a1 a2)))) (/.f64 (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #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 (+.f64 a1 a2) (-.f64 a1 a2)))))
(neg.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 #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)))))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))) #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 (fma.f64 a2 a2 (.f64 a1 a1)) #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 #s(literal 1 binary64) (/.f64 #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 a2 a2 (*.f64 a1 a1))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #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 a2 a2 (*.f64 a1 a1))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #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 a2 a2 (*.f64 a1 a1))))))
(/.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (neg.f64 #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 (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(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 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a1 (.f64 a1 (.f64 a1 a1))))))
(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 #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 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #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 a2 a2 (*.f64 a1 a1)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #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 a2 a2 (*.f64 a1 a1))) #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) #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 (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 1 binary64)) (.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 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))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1)))) (neg.f64 (neg.f64 #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 (neg.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 (.f64 #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 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a1 (.f64 a1 (.f64 a1 a1)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (neg.f64 (.f64 #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 (+.f64 a1 a2) (-.f64 a1 a2)))))
(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #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 (.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 #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)))))) (fma.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a1 (.f64 a1 (.f64 a1 a1)))))
(/.f64 (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 #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 (+.f64 a1 a2) (-.f64 a1 a2)))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a1 (.f64 a1 (.f64 a1 a1)))) #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 (neg.f64 (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 1 binary64))) (neg.f64 (.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 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)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))))) (neg.f64 (neg.f64 (neg.f64 #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 (neg.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal 1 binary64))) (neg.f64 #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 (neg.f64 (.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 #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))))))) (neg.f64 (fma.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a1 (.f64 a1 (.f64 a1 a1))))))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 #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))))))) (neg.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(pow.f64 (/.f64 #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 a2 a2 (*.f64 a1 a1))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #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 a2 a2 (*.f64 a1 a1))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #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 #s(literal 1 binary64) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #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 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #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 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
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(.f64 (/.f64 #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))))) (fma.f64 a2 a2 (.f64 a1 a1)))
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(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 th th) #s(literal 1/24 binary64)))
(+.f64 (.f64 (.f64 th th) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(-.f64 (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th))) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 th th) #s(literal 1/24 binary64)))) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th))) (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 th th) #s(literal 1/24 binary64)))))
(fma.f64 th (*.f64 th #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64))
(fma.f64 (*.f64 th #s(literal 1/24 binary64)) th #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/4 binary64)) (.f64 (.f64 th th) #s(literal -1/48 binary64))) (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/4 binary64))))
(/.f64 (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) (-.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/4 binary64)) (.f64 (.f64 th th) #s(literal -1/48 binary64))))
(/.f64 (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 (*.f64 th th) #s(literal -1/48 binary64)))))
(/.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/4 binary64)) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/4 binary64)) (.f64 (.f64 th th) #s(literal -1/48 binary64))) (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64))) (neg.f64 (-.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/4 binary64)) (.f64 (.f64 th th) #s(literal -1/48 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 (*.f64 th th) #s(literal -1/48 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)))) (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 th th) #s(literal 1/24 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/4 binary64)) (.f64 (.f64 th th) #s(literal -1/48 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th))))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 th th) #s(literal 1/24 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th))) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th))) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th))) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (.f64 (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th))) (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 th (*.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))))))
(pow.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/4 binary64)) (.f64 (.f64 th th) #s(literal -1/48 binary64))) (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 th (.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/4 binary64)) (.f64 (*.f64 th th) #s(literal -1/48 binary64)))))
(.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 th (*.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(+.f64 (.f64 th #s(literal -1/2 binary64)) (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))))
(+.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (.f64 th #s(literal -1/2 binary64)))
(-.f64 (/.f64 (.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64)))) (-.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (.f64 th #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 th #s(literal -1/2 binary64)) (.f64 th #s(literal -1/2 binary64))) (-.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (.f64 th #s(literal -1/2 binary64)))))
(fma.f64 th #s(literal -1/2 binary64) (.f64 th (.f64 (*.f64 th th) #s(literal 1/24 binary64))))
(fma.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64)) (*.f64 th #s(literal -1/2 binary64)))
(fma.f64 (.f64 th th) (.f64 th #s(literal 1/24 binary64)) (*.f64 th #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 th (.f64 th th)) (*.f64 th #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) th (.f64 th (.f64 (*.f64 th th) #s(literal 1/24 binary64))))
(fma.f64 (.f64 (.f64 th th) #s(literal 1/24 binary64)) th (*.f64 th #s(literal -1/2 binary64)))
(fma.f64 (.f64 th #s(literal 1/24 binary64)) (.f64 th th) (*.f64 th #s(literal -1/2 binary64)))
(fma.f64 (.f64 th (.f64 th th)) #s(literal 1/24 binary64) (*.f64 th #s(literal -1/2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 th (.f64 th th)) (.f64 th (.f64 th th))) #s(literal 1/13824 binary64)) (.f64 th (.f64 th th)) (.f64 #s(literal -1/8 binary64) (.f64 th (.f64 th th)))) (fma.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (-.f64 (.f64 (.f64 th #s(literal -1/2 binary64)) (.f64 th #s(literal -1/2 binary64))) (.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (*.f64 th #s(literal -1/2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64)))) (.f64 (.f64 th #s(literal -1/2 binary64)) (.f64 th #s(literal -1/2 binary64)))) (-.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (.f64 th #s(literal -1/2 binary64))))
(/.f64 (.f64 th (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64))) (-.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/4 binary64)) (.f64 (*.f64 th th) #s(literal -1/48 binary64))))
(/.f64 (.f64 th (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/4 binary64))) (fma.f64 th (*.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) th) (-.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/4 binary64)) (.f64 (*.f64 th th) #s(literal -1/48 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/4 binary64)) th) (fma.f64 th (*.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 th (.f64 th th)) (.f64 th (.f64 th th))) #s(literal 1/13824 binary64)) (.f64 th (.f64 th th)) (.f64 #s(literal -1/8 binary64) (.f64 th (.f64 th th))))) (neg.f64 (fma.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (-.f64 (.f64 (.f64 th #s(literal -1/2 binary64)) (.f64 th #s(literal -1/2 binary64))) (.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (*.f64 th #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64)))) (.f64 (.f64 th #s(literal -1/2 binary64)) (.f64 th #s(literal -1/2 binary64))))) (neg.f64 (-.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (.f64 th #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (.f64 th (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (-.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/4 binary64)) (.f64 (*.f64 th th) #s(literal -1/48 binary64)))))
(/.f64 (neg.f64 (.f64 th (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 th (*.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 th (.f64 th th)) (.f64 (.f64 th (.f64 th th)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) th)) (neg.f64 (-.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/4 binary64)) (.f64 (*.f64 th th) #s(literal -1/48 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/4 binary64)) th)) (neg.f64 (fma.f64 th (*.f64 th #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 th (.f64 th th)) (.f64 (.f64 (.f64 (.f64 th (.f64 th th)) (.f64 th (.f64 th th))) #s(literal 1/13824 binary64)) (.f64 th (.f64 th th)))) (fma.f64 (.f64 th #s(literal -1/2 binary64)) (.f64 th #s(literal -1/2 binary64)) (-.f64 (.f64 (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64))) (.f64 th (.f64 (.f64 th th) #s(literal 1/24 binary64)))) (.f64 (.f64 th #s(literal -1/2 binary64)) (.f64 th (.f64 (*.f64 th th) #s(literal 1/24 binary64)))))))
(.f64 th (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
(.f64 (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) th)

eval191.0ms (1.8%)

Memory: 0.7MiB live, 481.6MiB allocated
Compiler: Compiled 36 944 to 2 337 computations (93.7% saved)

prune213.0ms (2%)

Memory

-10.9MiB live, 553.9MiB allocated

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	1 425	15	1 440
Fresh	12	11	23
Picked	4	1	5
Done	0	0	0
Total	1 441	27	1 468

Accuracy

100.0%

Counts

1 468 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	72.0%	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
	70.5%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
	66.9%	(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
▶	99.7%	(.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th))
	67.2%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
	70.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (fma.f64 a2 a2 (*.f64 a1 a1))))
	72.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))))
	99.5%	(.f64 #s(approx (/ (+ ( (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 a2 a2) #s(literal 1/2 binary64)))) (cos.f64 th))
	99.5%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
▶	70.5%	#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 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	70.5%	#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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	70.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 (neg.f64 a1) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
	70.5%	#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)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
▶	17.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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)))))
	70.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) #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)))) (sqrt.f64 #s(literal 2 binary64))))
	70.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (* (* a2 a2) (cos th)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	70.5%	#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)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
	99.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
	71.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (* (* a2 a2) (cos th)) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
✓	16.0%	#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)))))
	16.0%	#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 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
▶	16.0%	#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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
▶	16.0%	#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)))
	16.0%	#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 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))
	42.7%	#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 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
	72.1%	#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
	70.6%	#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))

Compiler

Compiled 931 to 567 computations (39.1% saved)

simplify200.0ms (1.9%)

Memory

-13.4MiB live, 338.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 a1 a1 (*.f64 a2 a2))
cost-diff	0	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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)))))
cost-diff	2048	(/.f64 (.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))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 a2 (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 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
cost-diff	1344	(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))
cost-diff	0	#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))))
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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))
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 (sqrt.f64 #s(literal 2 binary64)) a1)
cost-diff	0	(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64))
cost-diff	0	(.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th))
cost-diff	960	(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))

Rules

10 040×	`lower-fma.f32`
10 034×	`lower-fma.f64`
5 330×	`lower-+.f32`
5 328×	`lower-+.f64`
3 152×	`lower-*.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	409
0	74	345
1	125	345
2	291	336
3	1159	336
4	5019	312
0	8413	312

Stop Event

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

Calls

Call 1

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

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

localize121.0ms (1.1%)

Memory

-3.4MiB live, 232.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.12890625	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
accuracy	0.205410009768442	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
accuracy	18.73062718858967	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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)))))
accuracy	42.005587497259945	(/.f64 (.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))))
accuracy	0.16796875	(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.3984375	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.46875	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	18.73062718858967	#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 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
accuracy	0.3587001839684516	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))
accuracy	0.7154236121798901	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))
accuracy	18.73062718858967	#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)))))
accuracy	51.76091590097476	#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))))
accuracy	0.16796875	(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
accuracy	0.3984375	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	18.73062718858967	#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	51.76091590097476	#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
accuracy	0.04296875	(.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th))
accuracy	0.12109375	(.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.44140625	(*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.46484375	(*.f64 (sqrt.f64 #s(literal 2 binary64)) a1)

Samples

69.0ms

256×

valid

Compiler

Compiled 319 to 39 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-mult: 20.0ms (40.6% of total)

ival-div: 11.0ms (22.3% of total)

ival-add: 8.0ms (16.2% of total)

ival-cos: 5.0ms (10.1% of total)

ival-sqrt: 2.0ms (4.1% of total)

ival-sub: 1.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series37.0ms (0.3%)

Memory

35.2MiB live, 74.3MiB allocated

Counts

24 → 504

Calls

Call 1

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

Outputs
#s(alt (* (pow a2 2) (sqrt 2)) (taylor 0 a1) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (sqrt 2)) (taylor inf a1) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))) (taylor inf a1) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))) (taylor inf a1) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))) (taylor inf a1) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (sqrt 2)) (taylor -inf a1) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))) (taylor -inf a1) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))) (taylor -inf a1) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))) (taylor -inf a1) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (sqrt 2)) (taylor 0 a2) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (taylor 0 a2) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (taylor 0 a2) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (taylor 0 a2) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (sqrt 2)) (taylor inf a2) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (taylor inf a2) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (taylor inf a2) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (taylor inf a2) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (sqrt 2)) (taylor -inf a2) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (taylor -inf a2) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (taylor -inf a2) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (taylor -inf a2) (#s(alt (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))) (taylor 0 a1) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))) (taylor 0 a1) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))) (taylor 0 a1) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))) (taylor 0 a1) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (taylor inf a1) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))) (taylor inf a1) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))) (taylor inf a1) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))) (taylor inf a1) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (taylor -inf a1) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))) (taylor -inf a1) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
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#s(alt (+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))) (taylor 0 a2) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))) (taylor 0 a2) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))) (taylor 0 a2) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
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#s(alt (* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))) (taylor inf a2) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))) (taylor inf a2) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))) (taylor inf a2) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))) (taylor -inf a2) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))) (taylor -inf a2) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))) (taylor -inf a2) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))) (taylor -inf a2) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (taylor 0 th) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (* (pow th 2) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (taylor 0 th) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* (pow th 2) (+ (* -1/4 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* 1/48 (* (pow th 2) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))))) (taylor 0 th) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* (pow th 2) (+ (* -1/4 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* (pow th 2) (+ (* -1/1440 (* (pow th 2) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (* 1/48 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))))))) (taylor 0 th) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (taylor inf th) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (taylor inf th) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (taylor inf th) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (taylor inf th) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (taylor -inf th) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (taylor -inf th) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (taylor -inf th) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (taylor -inf th) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) (patch (.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2)))) (taylor 0 a1) (#s(alt (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2)))) (taylor 0 a1) (#s(alt (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2)))) (taylor 0 a1) (#s(alt (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (pow a1 2) (sqrt 2))) (taylor inf a1) (#s(alt (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))) (taylor inf a1) (#s(alt (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))) (taylor inf a1) (#s(alt (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))) (taylor inf a1) (#s(alt (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))) (taylor -inf a1) (#s(alt (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (/ (pow a1 2) (sqrt 2)) (taylor inf a1) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (/ (pow a1 2) (sqrt 2)) (taylor -inf a1) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2))))) (taylor -inf a1) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2))))) (taylor -inf a1) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2))))) (taylor -inf a1) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (/ (pow a1 2) (sqrt 2)) (taylor 0 a2) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a2) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a2) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a2) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor inf a2) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor -inf a2) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (/.f64 (.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)))) (patch (/.f64 (.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)))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 th) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 th) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 th) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 th) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor inf th) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor inf th) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor inf th) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor inf th) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor -inf th) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor -inf th) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor -inf th) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor -inf th) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor inf a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor -inf a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor -inf a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor -inf a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor -inf a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
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#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow a2 4)) (taylor 0 a1) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow a2 4)) (* a1 (+ (* -1 (pow a2 3)) (pow a2 3)))) (taylor 0 a1) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow a2 4)) (* a1 (+ (* -1 (pow a2 3)) (+ (* a1 (+ (* -1 (pow a2 2)) (pow a2 2))) (pow a2 3))))) (taylor 0 a1) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow a2 4)) (* a1 (+ (* -1 (pow a2 3)) (+ (* a1 (+ (* -1 (pow a2 2)) (+ (* a1 (+ a2 (* -1 a2))) (pow a2 2)))) (pow a2 3))))) (taylor 0 a1) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (pow a1 4) (taylor inf a1) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 4) (+ 1 (+ (* -1 (/ a2 a1)) (/ a2 a1)))) (taylor inf a1) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 4) (+ 1 (+ (* -1 (/ a2 a1)) (+ (* -1 (/ (pow a2 2) (pow a1 2))) (+ (/ a2 a1) (/ (pow a2 2) (pow a1 2))))))) (taylor inf a1) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 4) (+ 1 (+ (* -1 (/ a2 a1)) (+ (* -1 (/ (pow a2 2) (pow a1 2))) (+ (* -1 (/ (pow a2 3) (pow a1 3))) (+ (/ a2 a1) (+ (/ (pow a2 2) (pow a1 2)) (/ (pow a2 3) (pow a1 3))))))))) (taylor inf a1) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (pow a1 4) (taylor -inf a1) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 4) (+ 1 (+ (* -1 (/ a2 a1)) (/ a2 a1)))) (taylor -inf a1) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 4) (+ 1 (* -1 (/ (+ (* -1 (+ a2 (* -1 a2))) (+ (* -1 (/ (pow a2 2) a1)) (/ (pow a2 2) a1))) a1)))) (taylor -inf a1) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 4) (+ 1 (* -1 (/ (+ (* -1 (+ a2 (* -1 a2))) (* -1 (/ (+ (* -1 (+ (* -1 (pow a2 2)) (pow a2 2))) (+ (* -1 (/ (pow a2 3) a1)) (/ (pow a2 3) a1))) a1))) a1)))) (taylor -inf a1) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (pow a1 4) (taylor 0 a2) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (* a2 (+ (* -1 (pow a1 3)) (pow a1 3))) (pow a1 4)) (taylor 0 a2) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (* a2 (+ (* -1 (pow a1 3)) (+ (* a2 (+ (* -1 (pow a1 2)) (pow a1 2))) (pow a1 3)))) (pow a1 4)) (taylor 0 a2) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (* a2 (+ (* -1 (pow a1 3)) (+ (* a2 (+ (* -1 (pow a1 2)) (+ (* a2 (+ a1 (* -1 a1))) (pow a1 2)))) (pow a1 3)))) (pow a1 4)) (taylor 0 a2) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow a2 4)) (taylor inf a2) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 4) (- (+ (* -1 (/ a1 a2)) (/ a1 a2)) 1)) (taylor inf a2) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 4) (- (+ (* -1 (/ a1 a2)) (+ (* -1 (/ (pow a1 2) (pow a2 2))) (+ (/ a1 a2) (/ (pow a1 2) (pow a2 2))))) 1)) (taylor inf a2) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 4) (- (+ (* -1 (/ a1 a2)) (+ (* -1 (/ (pow a1 2) (pow a2 2))) (+ (* -1 (/ (pow a1 3) (pow a2 3))) (+ (/ a1 a2) (+ (/ (pow a1 2) (pow a2 2)) (/ (pow a1 3) (pow a2 3))))))) 1)) (taylor inf a2) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow a2 4)) (taylor -inf a2) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 4) (- (* -1 (/ (+ a1 (* -1 a1)) a2)) 1)) (taylor -inf a2) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 4) (- (* -1 (/ (+ a1 (+ (* -1 a1) (* -1 (/ (+ (* -1 (pow a1 2)) (pow a1 2)) a2)))) a2)) 1)) (taylor -inf a2) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 4) (- (* -1 (/ (+ a1 (+ (* -1 a1) (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow a1 3)) (pow a1 3)) a2)) (+ (* -1 (pow a1 2)) (pow a1 2))) a2)))) a2)) 1)) (taylor -inf a2) (#s(alt (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
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#s(alt (* (pow a2 2) (+ (* -1 (sqrt 2)) (* -1 (/ (* (sqrt 2) (+ a1 (* -1 a1))) a2)))) (taylor -inf a2) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* -1 (sqrt 2)) (* -1 (/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) a2)) (* (sqrt 2) (+ a1 (* -1 a1)))) a2)))) (taylor -inf a2) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* -1 (sqrt 2)) (* -1 (/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) a2)) (* (sqrt 2) (+ a1 (* -1 a1)))) a2)))) (taylor -inf a2) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #<representation binary64>) () ())) ())

Calls

126 calls:

Time	Variable		Point	Expression
6.0ms	a1	@	inf	(* (sqrt 2) (* (+ a1 a2) (- a1 a2)))
1.0ms	a1	@	0	(* (sqrt 2) (* (+ a1 a2) (- a1 a2)))
0.0ms	a2	@	inf	(/ a2 (sqrt 2))
0.0ms	a1	@	inf	(* (+ (* a1 a1) (* a2 a2)) (* (+ a1 a2) (- a1 a2)))
0.0ms	a1	@	0	(* (+ (* a1 a1) (* a2 a2)) (* (+ a1 a2) (- a1 a2)))

simplify480.0ms (4.5%)

Memory

-163.0MiB live, 366.6MiB allocated

Algorithm

1×	egg-herbie

Rules

9 848×	`lower-fma.f64`
9 848×	`lower-fma.f32`
5 318×	`lower-*.f64`
5 318×	`lower-*.f32`
3 824×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	306	7272
1	1073	6526
2	4008	6202
0	8474	5868

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 504

Calls

Call 1

Inputs
(* (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) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 2) (/ (* (pow a2 2) (sqrt 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) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))
(+ (* -1/4 (* (pow th 2) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(+ (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* (pow th 2) (+ (* -1/4 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* 1/48 (* (pow th 2) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))))))
(+ (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* (pow th 2) (+ (* -1/4 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* (pow th 2) (+ (* -1/1440 (* (pow th 2) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))) (* 1/48 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (cos th) (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(* 1/2 (* (pow a2 2) (sqrt 2)))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* (pow a1 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (sqrt 2))) (* 1/2 (* (pow a2 2) (sqrt 2))))
(* 1/2 (* (pow a2 2) (sqrt 2)))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* 1/2 (* (pow a2 2) (sqrt 2)))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 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 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 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)))))
(/ (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))
(/ (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)))))
(/ 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 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 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)))))
(* -1 (pow a2 4))
(+ (* -1 (pow a2 4)) (* a1 (+ (* -1 (pow a2 3)) (pow a2 3))))
(+ (* -1 (pow a2 4)) (* a1 (+ (* -1 (pow a2 3)) (+ (* a1 (+ (* -1 (pow a2 2)) (pow a2 2))) (pow a2 3)))))
(+ (* -1 (pow a2 4)) (* a1 (+ (* -1 (pow a2 3)) (+ (* a1 (+ (* -1 (pow a2 2)) (+ (* a1 (+ a2 (* -1 a2))) (pow a2 2)))) (pow a2 3)))))
(pow a1 4)
(* (pow a1 4) (+ 1 (+ (* -1 (/ a2 a1)) (/ a2 a1))))
(* (pow a1 4) (+ 1 (+ (* -1 (/ a2 a1)) (+ (* -1 (/ (pow a2 2) (pow a1 2))) (+ (/ a2 a1) (/ (pow a2 2) (pow a1 2)))))))
(* (pow a1 4) (+ 1 (+ (* -1 (/ a2 a1)) (+ (* -1 (/ (pow a2 2) (pow a1 2))) (+ (* -1 (/ (pow a2 3) (pow a1 3))) (+ (/ a2 a1) (+ (/ (pow a2 2) (pow a1 2)) (/ (pow a2 3) (pow a1 3)))))))))
(pow a1 4)
(* (pow a1 4) (+ 1 (+ (* -1 (/ a2 a1)) (/ a2 a1))))
(* (pow a1 4) (+ 1 (* -1 (/ (+ (* -1 (+ a2 (* -1 a2))) (+ (* -1 (/ (pow a2 2) a1)) (/ (pow a2 2) a1))) a1))))
(* (pow a1 4) (+ 1 (* -1 (/ (+ (* -1 (+ a2 (* -1 a2))) (* -1 (/ (+ (* -1 (+ (* -1 (pow a2 2)) (pow a2 2))) (+ (* -1 (/ (pow a2 3) a1)) (/ (pow a2 3) a1))) a1))) a1))))
(pow a1 4)
(+ (* a2 (+ (* -1 (pow a1 3)) (pow a1 3))) (pow a1 4))
(+ (* a2 (+ (* -1 (pow a1 3)) (+ (* a2 (+ (* -1 (pow a1 2)) (pow a1 2))) (pow a1 3)))) (pow a1 4))
(+ (* a2 (+ (* -1 (pow a1 3)) (+ (* a2 (+ (* -1 (pow a1 2)) (+ (* a2 (+ a1 (* -1 a1))) (pow a1 2)))) (pow a1 3)))) (pow a1 4))
(* -1 (pow a2 4))
(* (pow a2 4) (- (+ (* -1 (/ a1 a2)) (/ a1 a2)) 1))
(* (pow a2 4) (- (+ (* -1 (/ a1 a2)) (+ (* -1 (/ (pow a1 2) (pow a2 2))) (+ (/ a1 a2) (/ (pow a1 2) (pow a2 2))))) 1))
(* (pow a2 4) (- (+ (* -1 (/ a1 a2)) (+ (* -1 (/ (pow a1 2) (pow a2 2))) (+ (* -1 (/ (pow a1 3) (pow a2 3))) (+ (/ a1 a2) (+ (/ (pow a1 2) (pow a2 2)) (/ (pow a1 3) (pow a2 3))))))) 1))
(* -1 (pow a2 4))
(* (pow a2 4) (- (* -1 (/ (+ a1 (* -1 a1)) a2)) 1))
(* (pow a2 4) (- (* -1 (/ (+ a1 (+ (* -1 a1) (* -1 (/ (+ (* -1 (pow a1 2)) (pow a1 2)) a2)))) a2)) 1))
(* (pow a2 4) (- (* -1 (/ (+ a1 (+ (* -1 a1) (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow a1 3)) (pow a1 3)) a2)) (+ (* -1 (pow a1 2)) (pow a1 2))) a2)))) a2)) 1))
(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))))
(* 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 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))
(/ (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))
(* -1 (* (pow a2 2) (sqrt 2)))
(+ (* -1 (* (pow a2 2) (sqrt 2))) (* a1 (* (sqrt 2) (+ a2 (* -1 a2)))))
(+ (* -1 (* (pow a2 2) (sqrt 2))) (* a1 (+ (* a1 (sqrt 2)) (* (sqrt 2) (+ a2 (* -1 a2))))))
(+ (* -1 (* (pow a2 2) (sqrt 2))) (* a1 (+ (* a1 (sqrt 2)) (* (sqrt 2) (+ a2 (* -1 a2))))))
(* (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (sqrt 2) (/ (* (sqrt 2) (+ a2 (* -1 a2))) a1)))
(* (pow a1 2) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (sqrt 2) (+ a2 (* -1 a2))) a1))))
(* (pow a1 2) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (sqrt 2) (+ a2 (* -1 a2))) a1))))
(* (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (sqrt 2) (/ (* (sqrt 2) (+ a2 (* -1 a2))) a1)))
(* (pow a1 2) (+ (sqrt 2) (* -1 (/ (+ (* -1 (* (sqrt 2) (+ a2 (* -1 a2)))) (/ (* (pow a2 2) (sqrt 2)) a1)) a1))))
(* (pow a1 2) (+ (sqrt 2) (* -1 (/ (+ (* -1 (* (sqrt 2) (+ a2 (* -1 a2)))) (/ (* (pow a2 2) (sqrt 2)) a1)) a1))))
(* (pow a1 2) (sqrt 2))
(+ (* a2 (* (sqrt 2) (+ a1 (* -1 a1)))) (* (pow a1 2) (sqrt 2)))
(+ (* a2 (+ (* -1 (* a2 (sqrt 2))) (* (sqrt 2) (+ a1 (* -1 a1))))) (* (pow a1 2) (sqrt 2)))
(+ (* a2 (+ (* -1 (* a2 (sqrt 2))) (* (sqrt 2) (+ a1 (* -1 a1))))) (* (pow a1 2) (sqrt 2)))
(* -1 (* (pow a2 2) (sqrt 2)))
(* (pow a2 2) (+ (* -1 (sqrt 2)) (/ (* (sqrt 2) (+ a1 (* -1 a1))) a2)))
(* (pow a2 2) (+ (* -1 (sqrt 2)) (+ (/ (* (sqrt 2) (+ a1 (* -1 a1))) a2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* -1 (sqrt 2)) (+ (/ (* (sqrt 2) (+ a1 (* -1 a1))) a2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* -1 (* (pow a2 2) (sqrt 2)))
(* (pow a2 2) (+ (* -1 (sqrt 2)) (* -1 (/ (* (sqrt 2) (+ a1 (* -1 a1))) a2))))
(* (pow a2 2) (+ (* -1 (sqrt 2)) (* -1 (/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) a2)) (* (sqrt 2) (+ a1 (* -1 a1)))) a2))))
(* (pow a2 2) (+ (* -1 (sqrt 2)) (* -1 (/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) a2)) (* (sqrt 2) (+ a1 (* -1 a1)))) a2))))

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

rewrite275.0ms (2.5%)

Memory

28.1MiB live, 298.6MiB allocated

Rules

4 958×	`lower-/.f32`
4 946×	`lower-/.f64`
4 408×	`lower-*.f32`
4 386×	`lower-*.f64`
3 478×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	361
0	74	325
1	254	286
2	1980	280
0	8410	280

Stop Event

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

Counts

24 → 900

Calls

Call 1

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

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

eval204.0ms (1.9%)

Memory: 9.4MiB live, 320.6MiB allocated
Compiler: Compiled 34 502 to 2 191 computations (93.6% saved)

prune239.0ms (2.2%)

Memory

-11.5MiB live, 464.6MiB allocated

Pruning

36 alts after pruning (32 fresh and 4 done)

	Pruned	Kept	Total
New	1 465	14	1 479
Fresh	3	18	21
Picked	2	3	5
Done	0	1	1
Total	1 470	36	1 506

Accuracy

100.0%

Counts

1 506 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	72.0%	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
	70.5%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
	66.9%	(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	67.2%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
	70.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (fma.f64 a2 a2 (*.f64 a1 a1))))
	72.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))))
	99.5%	(.f64 #s(approx (/ (+ ( (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (.f64 a2 (.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (cos.f64 th))
	99.5%	(.f64 #s(approx (/ (+ ( (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 a2 a2) #s(literal 1/2 binary64)))) (cos.f64 th))
	99.5%	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
✓	70.5%	#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 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	70.5%	#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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	70.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 (neg.f64 a1) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
	70.5%	#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)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	16.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2)) (.f64 (fma.f64 a1 a1 (.f64 a2 (+.f64 a1 a2))) (-.f64 a1 a2))) (fma.f64 a1 a1 (.f64 a2 (+.f64 a1 a2))))))
	11.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(approx ( (sqrt 2) (* (+ a1 a2) (- a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)))))
	17.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
	70.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) #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)))) (sqrt.f64 #s(literal 2 binary64))))
	17.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
	70.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (* (* a2 a2) (cos th)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	70.5%	#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)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
	70.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) (+.f64 a1 a2)))
	65.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 a1 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) #s(literal 1 binary64)))
	17.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
	99.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
	42.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (* (+ (* a1 a1) (* a2 a2)) (* (+ a1 a2) (- a1 a2))) (* (sqrt 2) (* (+ a1 a2) (- a1 a2)))) (.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
	71.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (* (* a2 a2) (cos th)) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
✓	16.0%	#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)))))
	16.0%	#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 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
✓	16.0%	#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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
✓	16.0%	#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)))
	16.0%	#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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) a1)))
	16.0%	#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 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))
	16.0%	#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 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1) a1)))
	72.1%	#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
	99.5%	#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))))
	70.6%	#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (fma.f64 a2 a2 (*.f64 a1 a1)))))

Compiler

Compiled 1 943 to 617 computations (68.2% saved)

regimes170.0ms (1.6%)

Memory

-6.1MiB live, 246.9MiB allocated

Counts

73 → 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))) (/.f64 #s(approx (* (* a2 a2) (cos th)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (fma.f64 a2 a2 (*.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 (.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))))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (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 #s(literal 1 binary64) (/.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (fma.f64 a2 a2 (*.f64 a1 a1))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (* (* a2 a2) (cos th)) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) (+.f64 a1 a2)))
(.f64 (/.f64 (fma.f64 a1 a1 (.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 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (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 (.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 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 a1 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) #s(literal 1 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)))))
#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 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(approx ( (sqrt 2) (* (+ a1 a2) (- a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) #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)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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)))))
#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 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 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))) #s(approx (/ (* (+ (* a1 a1) (* a2 a2)) (* (+ a1 a2) (- a1 a2))) (* (sqrt 2) (* (+ a1 a2) (- a1 a2)))) (.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 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))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.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 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
#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 (fma.f64 (.f64 (neg.f64 a1) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) (.f64 (neg.f64 (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 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2)) (.f64 (fma.f64 a1 a1 (.f64 a2 (+.f64 a1 a2))) (-.f64 a1 a2))) (fma.f64 a1 a1 (.f64 a2 (+.f64 a1 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))))
(.f64 #s(approx (/ (+ ( (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 a2 a2) #s(literal 1/2 binary64)))) (cos.f64 th))
(.f64 #s(approx (/ (+ ( (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (.f64 a2 (.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (cos.f64 th))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
#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 a2 (.f64 a2 (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 (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)) (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 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) (cos.f64 th))
(/.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 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.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)) (cos.f64 th))
(.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 2 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 #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 (.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 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (*.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 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 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.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))
(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))))))
(+.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) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))

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

Calls

8 calls:

25.0ms	(cos.f64 th)
21.0ms	(+.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)))
21.0ms	a1
21.0ms	(*.f64 a1 a1)
21.0ms	th

Results

Accuracy	Segments	Branch
99.7%	1	`a1`
99.7%	1	`a2`
99.7%	1	`th`
99.7%	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)))`
99.7%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.7%	1	`(cos.f64 th)`
99.7%	1	`(*.f64 a1 a1)`
99.7%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes154.0ms (1.4%)

Memory

17.0MiB live, 173.3MiB allocated

Counts

56 → 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))) (/.f64 #s(approx (* (* a2 a2) (cos th)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (fma.f64 a2 a2 (*.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 (.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))))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (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 #s(literal 1 binary64) (/.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (fma.f64 a2 a2 (*.f64 a1 a1))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (* (* a2 a2) (cos th)) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) (+.f64 a1 a2)))
(.f64 (/.f64 (fma.f64 a1 a1 (.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 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (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 (.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 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 a1 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) #s(literal 1 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)))))
#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 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(approx ( (sqrt 2) (* (+ a1 a2) (- a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) #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)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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)))))
#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 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 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))) #s(approx (/ (* (+ (* a1 a1) (* a2 a2)) (* (+ a1 a2) (- a1 a2))) (* (sqrt 2) (* (+ a1 a2) (- a1 a2)))) (.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 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))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.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 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
#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 (fma.f64 (.f64 (neg.f64 a1) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) (.f64 (neg.f64 (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 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2)) (.f64 (fma.f64 a1 a1 (.f64 a2 (+.f64 a1 a2))) (-.f64 a1 a2))) (fma.f64 a1 a1 (.f64 a2 (+.f64 a1 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))))
(.f64 #s(approx (/ (+ ( (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 a2 a2) #s(literal 1/2 binary64)))) (cos.f64 th))
(.f64 #s(approx (/ (+ ( (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (.f64 a2 (.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (cos.f64 th))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
#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 a2 (.f64 a2 (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 (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)) (fma.f64 a1 a1 (*.f64 a2 a2))))

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

Calls

8 calls:

46.0ms	th
18.0ms	a1
15.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
15.0ms	a2
14.0ms	(*.f64 a1 a1)

Results

Accuracy	Segments	Branch
99.7%	1	`a1`
99.7%	1	`a2`
99.7%	1	`th`
99.7%	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)))`
99.7%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.7%	1	`(cos.f64 th)`
99.7%	1	`(*.f64 a1 a1)`
99.7%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes141.0ms (1.3%)

Memory

1.1MiB live, 154.5MiB allocated

Counts

52 → 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))) (/.f64 #s(approx (* (* a2 a2) (cos th)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (fma.f64 a2 a2 (*.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 (.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))))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (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 #s(literal 1 binary64) (/.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (fma.f64 a2 a2 (*.f64 a1 a1))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (* (* a2 a2) (cos th)) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) (+.f64 a1 a2)))
(.f64 (/.f64 (fma.f64 a1 a1 (.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 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (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 (.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 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 a1 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) #s(literal 1 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)))))
#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 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(approx ( (sqrt 2) (* (+ a1 a2) (- a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) #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)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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)))))
#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 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 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))) #s(approx (/ (* (+ (* a1 a1) (* a2 a2)) (* (+ a1 a2) (- a1 a2))) (* (sqrt 2) (* (+ a1 a2) (- a1 a2)))) (.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 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))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.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 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
#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 (fma.f64 (.f64 (neg.f64 a1) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) (.f64 (neg.f64 (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 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2)) (.f64 (fma.f64 a1 a1 (.f64 a2 (+.f64 a1 a2))) (-.f64 a1 a2))) (fma.f64 a1 a1 (.f64 a2 (+.f64 a1 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))))
(.f64 #s(approx (/ (+ ( (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 a2 a2) #s(literal 1/2 binary64)))) (cos.f64 th))
(.f64 #s(approx (/ (+ ( (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (.f64 a2 (.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (cos.f64 th))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
#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 a2 (.f64 a2 (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))

Outputs
#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))))

Calls

8 calls:

39.0ms	a1
16.0ms	(cos.f64 th)
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)))
14.0ms	(*.f64 a2 a2)
14.0ms	a2

Results

Accuracy	Segments	Branch
99.5%	1	`a1`
99.5%	1	`a2`
99.5%	1	`th`
99.5%	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)))`
99.5%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.5%	1	`(cos.f64 th)`
99.5%	1	`(*.f64 a1 a1)`
99.5%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes118.0ms (1.1%)

Memory

8.6MiB live, 163.4MiB allocated

Counts

49 → 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))) (/.f64 #s(approx (* (* a2 a2) (cos th)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (fma.f64 a2 a2 (*.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 (.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))))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (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 #s(literal 1 binary64) (/.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (fma.f64 a2 a2 (*.f64 a1 a1))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (* (* a2 a2) (cos th)) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) (+.f64 a1 a2)))
(.f64 (/.f64 (fma.f64 a1 a1 (.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 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (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 (.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 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 a1 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) #s(literal 1 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)))))
#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 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(approx ( (sqrt 2) (* (+ a1 a2) (- a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) #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)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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)))))
#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 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 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))) #s(approx (/ (* (+ (* a1 a1) (* a2 a2)) (* (+ a1 a2) (- a1 a2))) (* (sqrt 2) (* (+ a1 a2) (- a1 a2)))) (.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 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))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.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 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
#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 (fma.f64 (.f64 (neg.f64 a1) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) (.f64 (neg.f64 (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 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2)) (.f64 (fma.f64 a1 a1 (.f64 a2 (+.f64 a1 a2))) (-.f64 a1 a2))) (fma.f64 a1 a1 (.f64 a2 (+.f64 a1 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))))
(.f64 #s(approx (/ (+ ( (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 a2 a2) #s(literal 1/2 binary64)))) (cos.f64 th))
(.f64 #s(approx (/ (+ ( (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (.f64 a2 (.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (cos.f64 th))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

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

Calls

8 calls:

22.0ms	a1
15.0ms	th
14.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
14.0ms	(*.f64 a1 a1)
13.0ms	a2

Results

Accuracy	Segments	Branch
99.5%	1	`a1`
99.5%	1	`a2`
99.5%	1	`th`
99.5%	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)))`
99.5%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.5%	1	`(cos.f64 th)`
99.5%	1	`(*.f64 a1 a1)`
99.5%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes103.0ms (1%)

Memory

16.8MiB live, 130.4MiB allocated

Counts

45 → 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))) (/.f64 #s(approx (* (* a2 a2) (cos th)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (fma.f64 a2 a2 (*.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 (.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))))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (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 #s(literal 1 binary64) (/.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (fma.f64 a2 a2 (*.f64 a1 a1))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (* (* a2 a2) (cos th)) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) (+.f64 a1 a2)))
(.f64 (/.f64 (fma.f64 a1 a1 (.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 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (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 (.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 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 a1 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) #s(literal 1 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)))))
#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 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1)))))
(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(approx ( (sqrt 2) (* (+ a1 a2) (- a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #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))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) #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)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.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)))))
#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 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 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))) #s(approx (/ (* (+ (* a1 a1) (* a2 a2)) (* (+ a1 a2) (- a1 a2))) (* (sqrt 2) (* (+ a1 a2) (- a1 a2)))) (.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 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))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.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 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
#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 (fma.f64 (.f64 (neg.f64 a1) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) (.f64 (neg.f64 (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 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2)) (.f64 (fma.f64 a1 a1 (.f64 a2 (+.f64 a1 a2))) (-.f64 a1 a2))) (fma.f64 a1 a1 (.f64 a2 (+.f64 a1 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))

Outputs

#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (*.f64 th th) #s(literal 1/2 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)))

Calls

8 calls:

15.0ms	a2
13.0ms	(*.f64 a1 a1)
13.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
12.0ms	a1
12.0ms	th

Results

Accuracy	Segments	Branch
75.2%	2	`a1`
74.3%	2	`a2`
72.1%	1	`th`
84.1%	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)))`
83.3%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
83.3%	2	`(cos.f64 th)`
75.2%	2	`(*.f64 a1 a1)`
74.3%	2	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes7.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

21 → 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))) (/.f64 #s(approx (* (* a2 a2) (cos th)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (fma.f64 a2 a2 (*.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 (.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))))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (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 #s(literal 1 binary64) (/.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (fma.f64 a2 a2 (*.f64 a1 a1))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (* (* a2 a2) (cos th)) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a1 a2))) (+.f64 a1 a2)))
(.f64 (/.f64 (fma.f64 a1 a1 (.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 (fma.f64 a1 a1 (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))

Outputs

#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (*.f64 th th) #s(literal 1/2 binary64))))

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

Calls

1 calls:

6.0ms

(+.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
84.1%	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)

regimes40.0ms (0.4%)

Memory

-21.3MiB live, 61.2MiB 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))) (/.f64 #s(approx (* (* a2 a2) (cos th)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (fma.f64 a2 a2 (*.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 (.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))))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (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 #s(literal 1 binary64) (/.f64 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (fma.f64 a2 a2 (*.f64 a1 a1))))

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

Calls

8 calls:

9.0ms	(+.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)))
5.0ms	(*.f64 a2 a2)
4.0ms	a1
4.0ms	th
4.0ms	a2

Results

Accuracy	Segments	Branch
70.6%	1	`th`
70.6%	1	`a2`
70.6%	1	`(*.f64 a2 a2)`
70.6%	1	`a1`
70.6%	1	`(*.f64 a1 a1)`
70.6%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
70.6%	1	`(cos.f64 th)`
70.6%	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)))`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes19.0ms (0.2%)

Memory

-2.6MiB live, 35.6MiB allocated

Counts

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

Calls

8 calls:

4.0ms	th
2.0ms	a2
2.0ms	a1
2.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
2.0ms	(*.f64 a2 a2)

Results

Accuracy	Segments	Branch
70.4%	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)))`
70.4%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
70.4%	1	`(cos.f64 th)`
70.4%	1	`th`
70.4%	1	`a1`
70.4%	1	`(*.f64 a1 a1)`
70.4%	1	`a2`
70.4%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes17.0ms (0.2%)

Memory

-6.8MiB live, 29.4MiB 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:

5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
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)))
1.0ms	a2
1.0ms	th
1.0ms	a1

Results

Accuracy	Segments	Branch
16.0%	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)))`
16.0%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
16.0%	1	`(cos.f64 th)`
16.0%	1	`th`
16.0%	1	`a1`
16.0%	1	`(*.f64 a1 a1)`
16.0%	1	`a2`
16.0%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.1403050371880055e-94	-3.424443242370674e-179

Compiler

Compiled 25 to 18 computations (28% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.1403050371880055e-94	-3.424443242370674e-179

Compiler

Compiled 25 to 18 computations (28% saved)

simplify8.0ms (0.1%)

Memory

16.1MiB live, 16.1MiB allocated

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	371
1	87	371

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
#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 (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))))
(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 -3757668132438133/37576681324381331646231689548629392438010920782533117931316655544515344401833735095419183974156299248510959616 binary64)) #s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 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))))
(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 -3757668132438133/37576681324381331646231689548629392438010920782533117931316655544515344401833735095419183974156299248510959616 binary64)) #s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64)))) #s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.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 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 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (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 (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 th)))))
#s(approx (* (/ (+ (* (* (sqrt 2) a1) a1) (* a2 (* a2 (sqrt 2)))) 2) (cos th)) (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(literal 1/2 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 -3757668132438133/37576681324381331646231689548629392438010920782533117931316655544515344401833735095419183974156299248510959616 binary64)) #s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 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))))
(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 -3757668132438133/37576681324381331646231689548629392438010920782533117931316655544515344401833735095419183974156299248510959616 binary64)) #s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 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))))
(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 -3757668132438133/37576681324381331646231689548629392438010920782533117931316655544515344401833735095419183974156299248510959616 binary64)) #s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64)))) #s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(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 -3757668132438133/37576681324381331646231689548629392438010920782533117931316655544515344401833735095419183974156299248510959616 binary64)) #s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64)))) #s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
#s(approx (* (/ (+ (* (* a2 a2) (sqrt 2)) (* (sqrt 2) (* a1 a1))) 2) (cos th)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (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))) #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))))))

soundness1.5s (14.3%)

Memory

-36.7MiB live, 1 040.6MiB allocated

Rules

34 694×	`lower-fma.f64`
34 694×	`lower-fma.f32`
18 450×	`lower-fma.f64`
18 450×	`lower-fma.f32`
14 544×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	223	6651
1	761	5987
2	2899	5769
3	7666	5768
0	8068	5441
0	306	7272
1	1073	6526
2	4008	6202
0	8474	5868
0	47	282
0	75	273
1	268	253
2	2094	247
0	8243	247
0	45	300
0	74	292
1	285	270
2	2257	270
0	8896	269
0	12	44
0	20	38
1	58	38
2	411	38
3	7331	38
0	8434	37
0	111	1498
1	343	1366
2	1205	1262
3	3898	1233
0	8422	1172
0	235	7352
1	755	6539
2	2650	6089
3	6653	6006
0	8075	5611

Stop Event

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

Compiler

Compiled 787 to 353 computations (55.1% saved)

preprocess127.0ms (1.2%)

Memory

20.9MiB live, 175.3MiB allocated

Remove

(sort a1 a2)

(abs a1)

(abs a2)

(abs th)

Compiler

Compiled 1 008 to 504 computations (50% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.5s (13.8%)

explain192.0ms (1.8%)

preprocess138.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize41.0ms (0.4%)

series24.0ms (0.2%)

simplify497.0ms (4.6%)

rewrite265.0ms (2.5%)

eval93.0ms (0.9%)

prune290.0ms (2.7%)

simplify483.0ms (4.5%)

localize325.0ms (3%)

series115.0ms (1.1%)

simplify349.0ms (3.2%)

rewrite437.0ms (4.1%)

eval432.0ms (4%)

prune389.0ms (3.6%)

simplify71.0ms (0.7%)

localize136.0ms (1.3%)

series33.0ms (0.3%)

simplify278.0ms (2.6%)

rewrite294.0ms (2.7%)

eval191.0ms (1.8%)

prune213.0ms (2%)

simplify200.0ms (1.9%)

localize121.0ms (1.1%)

series37.0ms (0.3%)

simplify480.0ms (4.5%)

rewrite275.0ms (2.5%)

eval204.0ms (1.9%)

prune239.0ms (2.2%)

regimes170.0ms (1.6%)

regimes154.0ms (1.4%)

regimes141.0ms (1.3%)

regimes118.0ms (1.1%)

regimes103.0ms (1%)

regimes7.0ms (0.1%)

regimes40.0ms (0.4%)

regimes19.0ms (0.2%)

regimes17.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

soundness1.5s (14.3%)

preprocess127.0ms (1.2%)

end0.0ms (0%)

Profiling