Metrics for Migdal et al, Equation (64)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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 (17.2%)

Memory

-114.8MiB live, 1 777.1MiB allocated

Samples

937.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 714.0ms

ival-mult: 284.0ms (39.8% of total)

ival-cos: 232.0ms (32.5% of total)

ival-sqrt: 73.0ms (10.2% of total)

ival-add: 61.0ms (8.5% of total)

ival-div: 50.0ms (7% of total)

ival-true: 6.0ms (0.8% of total)

exact: 6.0ms (0.8% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

explain152.0ms (1.8%)

Memory

-0.8MiB live, 394.5MiB 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

69.0ms

512×

valid

Compiler

Compiled 138 to 40 computations (71% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-cos: 21.0ms (50.1% of total)

ival-mult: 12.0ms (28.6% of total)

ival-sqrt: 4.0ms (9.5% of total)

ival-div: 3.0ms (7.2% of total)

ival-add: 2.0ms (4.8% of total)

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

exact: 0.0ms (0% of total)

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

preprocess135.0ms (1.6%)

Memory

-7.9MiB live, 69.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Symmetry

(abs th)

(abs a2)

(abs a1)

(sort a1 a2)

Compiler

Compiled 22 to 12 computations (45.5% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(+.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)

simplify5.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB 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 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
(.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 (cos.f64 th)))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 a1 a1)
a1
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
(.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (cos.f64 th)))
(*.f64 a2 a2)
a2

localize43.0ms (0.5%)

Memory

-26.2MiB live, 92.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
accuracy	0.19140625	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
accuracy	0.193691259768442	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
accuracy	0.734375	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

34.0ms

256×

valid

Compiler

Compiled 58 to 14 computations (75.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-mult: 11.0ms (43.1% of total)

ival-cos: 6.0ms (23.5% of total)

ival-sqrt: 5.0ms (19.6% of total)

ival-div: 1.0ms (3.9% of total)

ival-add: 1.0ms (3.9% of total)

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

exact: 0.0ms (0% of total)

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

series21.0ms (0.2%)

Memory

14.9MiB live, 53.7MiB 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 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 0 a1) (#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 (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#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 (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#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 (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#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 (/ (* (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>) () ())) ())
#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)) (taylor inf a1) (#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 (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor inf a1) (#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 (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor inf a1) (#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 (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor inf a1) (#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 (/ (* (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>) () ())) ())
#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)) (taylor -inf a1) (#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 (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor -inf a1) (#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 (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor -inf a1) (#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 (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor -inf a1) (#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 (+ (/ (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>) () ())) ())
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#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor 0 a2) (#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 a2) (#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 a2) (#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 a2) (#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 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 (/.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)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#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)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#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)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#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 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 (/.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)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#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)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#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)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#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 -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

9 calls:

Time	Variable		Point	Expression
4.0ms	a2	@	0	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (cos th) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
2.0ms	a1	@	0	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (cos th) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
2.0ms	th	@	0	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (cos th) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
2.0ms	th	@	inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (cos th) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
2.0ms	th	@	-inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (cos th) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

simplify263.0ms (3%)

Memory

3.8MiB live, 410.1MiB 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	1206	1262
3	3900	1233
0	8428	1172

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

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 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 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 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 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 a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (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) (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)))
(/ 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)))
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)))
(/ (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 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 a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(cos th)
(cos th)
(cos th)
(cos th)
(/ (* (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 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 a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(cos th)
(cos th)
(cos th)
(cos th)
(/ (* (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 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 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 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 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 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 a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))

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

rewrite166.0ms (1.9%)

Memory

-2.6MiB live, 275.8MiB 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 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th)))
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(/.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a1 (cos.f64 th)) a1)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a1 (cos.f64 th)) a1)))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(neg.f64 (.f64 (neg.f64 a1) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (cos.f64 th)))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 (cos.f64 th)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 (cos.f64 th) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -1 binary64))
(/.f64 (/.f64 (neg.f64 (cos.f64 th)) #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))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 (neg.f64 (cos.f64 th)) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 (neg.f64 (cos.f64 th)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 th)))
(*.f64 #s(literal 1 binary64) (cos.f64 th))
(*.f64 (cos.f64 th) #s(literal 1 binary64))
(neg.f64 (neg.f64 (cos.f64 th)))
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 th)))
(cos.f64 th)
(.f64 (/.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (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 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (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) (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 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(.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 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.f64 (.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (*.f64 a2 (cos.f64 th)) (neg.f64 a2)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (*.f64 a2 (cos.f64 th)) a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) 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 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 a2 (cos.f64 th)) a2))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
(.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a2 a2) (neg.f64 (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 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2)) #s(literal -1 binary64))
(/.f64 (/.f64 (.f64 (.f64 a2 (cos.f64 th)) (neg.f64 a2)) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(/.f64 (neg.f64 (.f64 (.f64 a2 (cos.f64 th)) (neg.f64 a2))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (.f64 (*.f64 a2 (cos.f64 th)) a2) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 a2 a2) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.f64 (.f64 (.f64 (*.f64 a2 (cos.f64 th)) a2) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
(/.f64 (*.f64 (neg.f64 a2) a2) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.f64 (.f64 (.f64 a2 (cos.f64 th)) (neg.f64 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2))))
(/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2)))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(neg.f64 (.f64 (neg.f64 a2) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))))

eval58.0ms (0.7%)

Memory: -7.3MiB live, 149.3MiB allocated
Compiler: Compiled 14 708 to 1 019 computations (93.1% saved)

prune72.0ms (0.8%)

Memory

10.5MiB live, 176.8MiB allocated

Pruning

19 alts after pruning (19 fresh and 0 done)

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

Accuracy

100.0%

Counts

491 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	99.5%	(/.f64 (/.f64 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
	99.6%	(/.f64 (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
▶	14.5%	(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 a2 a2) a2) a2) (.f64 a2 a2) (.f64 (.f64 (.f64 (.f64 a1 a1) a1) a1) (.f64 a1 a1))) (cos.f64 th)) (.f64 (fma.f64 (.f64 (.f64 a1 a1) a1) a1 (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
	14.5%	(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 a2 a2) a2) a2) (.f64 a2 a2) (.f64 (.f64 (.f64 (.f64 a1 a1) a1) a1) (.f64 a1 a1))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 a1 a1) a1) a1 (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
	99.6%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	25.9%	(/.f64 (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (cos.f64 th)) (.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64))))
▶	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
	99.6%	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 2 binary64))))
	97.7%	(+.f64 #s(approx (* (/ (cos th) (sqrt 2)) (* a1 a1)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
▶	99.6%	(.f64 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64))
	99.5%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
▶	99.6%	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
▶	66.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
	48.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (/.f64 a2 (.f64 a1 a1)) a2 #s(literal 1 binary64)) (.f64 (.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	63.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64))))
	62.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
	99.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 898 to 504 computations (43.9% saved)

simplify127.0ms (1.5%)

Memory

-25.9MiB live, 171.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (.f64 (.f64 (.f64 a2 a2) a2) a2) (.f64 a2 a2) (.f64 (.f64 (.f64 (.f64 a1 a1) a1) a1) (*.f64 a1 a1)))
cost-diff	0	(.f64 (fma.f64 (.f64 (.f64 (.f64 a2 a2) a2) a2) (.f64 a2 a2) (.f64 (.f64 (.f64 (.f64 a1 a1) a1) a1) (.f64 a1 a1))) (cos.f64 th))
cost-diff	0	(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 a2 a2) a2) a2) (.f64 a2 a2) (.f64 (.f64 (.f64 (.f64 a1 a1) a1) a1) (.f64 a1 a1))) (cos.f64 th)) (.f64 (fma.f64 (.f64 (.f64 a1 a1) a1) a1 (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	128	(-.f64 (.f64 a2 a2) (.f64 a1 a1))
cost-diff	0	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))))
cost-diff	0	(*.f64 a1 a1)
cost-diff	0	(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff	0	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (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 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
cost-diff	1344	(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
cost-diff	0	(cos.f64 th)
cost-diff	0	(*.f64 a2 (cos.f64 th))
cost-diff	0	(.f64 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64))
cost-diff	7680	(fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))

Rules

9 230×	`lower-fma.f32`
9 220×	`lower-fma.f64`
5 138×	`lower-*.f32`
5 100×	`lower-*.f64`
2 144×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	426
0	83	420
1	164	355
2	316	334
3	686	334
4	1972	325
5	4399	325
6	7722	325
0	8275	322

Stop Event

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

Calls

Call 1

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

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

localize118.0ms (1.4%)

Memory

13.1MiB live, 248.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.09375	(.f64 (fma.f64 (.f64 (.f64 a1 a1) a1) a1 (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.11328125	(.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
accuracy	2.5937500000000004	(-.f64 (.f64 a2 a2) (.f64 a1 a1))
accuracy	49.66109055435331	(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 a2 a2) a2) a2) (.f64 a2 a2) (.f64 (.f64 (.f64 (.f64 a1 a1) a1) a1) (.f64 a1 a1))) (cos.f64 th)) (.f64 (fma.f64 (.f64 (.f64 a1 a1) a1) a1 (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0	(cos.f64 th)
accuracy	0.08041000976844202	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
accuracy	0.16015625	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))))
accuracy	0.9132533903959101	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.08203125	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
accuracy	0.2421875	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.16015625	(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
accuracy	0.40234375	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.484375	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.181229880298318	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
accuracy	0.1640625	(.f64 (.f64 a1 (cos.f64 th)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.1875	(fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.3984375	(*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.44921875	(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))

Samples

82.0ms

256×

valid

Compiler

Compiled 431 to 48 computations (88.9% saved)

Precisions

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

ival-mult: 31.0ms (55.3% of total)

ival-div: 9.0ms (16.1% of total)

ival-add: 6.0ms (10.7% of total)

ival-cos: 6.0ms (10.7% of total)

ival-sqrt: 3.0ms (5.4% of total)

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

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

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

exact: 0.0ms (0% of total)

series92.0ms (1.1%)

Memory

33.9MiB live, 190.8MiB allocated

Counts

26 → 624

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
14.0ms	a2	@	inf	((+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (* (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) 1/2) (* a2 (cos th)) (cos th) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (- (* a2 a2) (* a1 a1)) (/ (* (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (cos th)) (* (+ (* (* (* a1 a1) a1) a1) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2))) (* (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (cos th)) (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (* a1 (sqrt 2)) (* a2 (sqrt 2)) (* (* a1 (cos th)) (* a1 (sqrt 2))) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (* a2 a2) (- (* a2 a2) (* a1 a1))) (* (+ (* (* (* a1 a1) a1) a1) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2)))
12.0ms	a1	@	inf	((+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (* (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) 1/2) (* a2 (cos th)) (cos th) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (- (* a2 a2) (* a1 a1)) (/ (* (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (cos th)) (* (+ (* (* (* a1 a1) a1) a1) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2))) (* (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (cos th)) (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (* a1 (sqrt 2)) (* a2 (sqrt 2)) (* (* a1 (cos th)) (* a1 (sqrt 2))) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (* a2 a2) (- (* a2 a2) (* a1 a1))) (* (+ (* (* (* a1 a1) a1) a1) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2)))
7.0ms	th	@	-inf	((+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (* (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) 1/2) (* a2 (cos th)) (cos th) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (- (* a2 a2) (* a1 a1)) (/ (* (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (cos th)) (* (+ (* (* (* a1 a1) a1) a1) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2))) (* (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (cos th)) (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (* a1 (sqrt 2)) (* a2 (sqrt 2)) (* (* a1 (cos th)) (* a1 (sqrt 2))) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (* a2 a2) (- (* a2 a2) (* a1 a1))) (* (+ (* (* (* a1 a1) a1) a1) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2)))
7.0ms	a2	@	0	((+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (* (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) 1/2) (* a2 (cos th)) (cos th) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (- (* a2 a2) (* a1 a1)) (/ (* (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (cos th)) (* (+ (* (* (* a1 a1) a1) a1) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2))) (* (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (cos th)) (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (* a1 (sqrt 2)) (* a2 (sqrt 2)) (* (* a1 (cos th)) (* a1 (sqrt 2))) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (* a2 a2) (- (* a2 a2) (* a1 a1))) (* (+ (* (* (* a1 a1) a1) a1) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2)))
7.0ms	a1	@	0	((+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (* (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) 1/2) (* a2 (cos th)) (cos th) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (- (* a2 a2) (* a1 a1)) (/ (* (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (cos th)) (* (+ (* (* (* a1 a1) a1) a1) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2))) (* (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (cos th)) (+ (* (* (* (* a2 a2) a2) a2) (* a2 a2)) (* (* (* (* a1 a1) a1) a1) (* a1 a1))) (* a1 (sqrt 2)) (* a2 (sqrt 2)) (* (* a1 (cos th)) (* a1 (sqrt 2))) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (* a2 a2) (- (* a2 a2) (* a1 a1))) (* (+ (* (* (* a1 a1) a1) a1) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2)))

simplify197.0ms (2.3%)

Memory

-43.4MiB live, 330.5MiB allocated

Algorithm

1×	egg-herbie

Rules

11 948×	`lower-fma.f64`
11 948×	`lower-fma.f32`
6 516×	`lower-*.f64`
6 516×	`lower-*.f32`
3 466×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	509	9457
1	1804	8912
2	7123	8858
0	8521	8420

Stop Event

1×	iter limit
1×	node limit

Counts

624 → 623

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))))
(* 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)))))
(/ (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 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)))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (pow 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 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)
(pow a1 2)
(pow a1 2)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(* (pow a2 2) (cos th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(pow a2 2)
(+ (* -1 (pow a1 2)) (pow a2 2))
(+ (* -1 (pow a1 2)) (pow a2 2))
(+ (* -1 (pow a1 2)) (pow a2 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) (- (* -1 (* (pow a1 2) (+ (* -1 (/ (cos th) (* (pow a2 2) (sqrt 2)))) (/ (cos th) (* (pow a2 2) (sqrt 2)))))) (* -1 (/ (cos th) (sqrt 2))))) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* (pow a1 2) (- (/ (cos th) (* (pow a2 4) (sqrt 2))) (+ (* -1 (/ (cos th) (* (pow a2 4) (sqrt 2)))) (* 2 (/ (cos th) (* (pow a2 4) (sqrt 2))))))) (+ (* -1 (/ (cos th) (* (pow a2 2) (sqrt 2)))) (/ (cos th) (* (pow a2 2) (sqrt 2)))))) (* -1 (/ (cos th) (sqrt 2))))) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(* (pow a2 6) (cos th))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(pow a2 6)
(+ (pow a1 6) (pow a2 6))
(+ (pow a1 6) (pow a2 6))
(+ (pow a1 6) (pow a2 6))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (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 a2 4)
(+ (* -1 (* (pow a1 2) (pow a2 2))) (pow a2 4))
(+ (* -1 (* (pow a1 2) (pow a2 2))) (pow a2 4))
(+ (* -1 (* (pow a1 2) (pow a2 2))) (pow a2 4))
(* (pow a2 4) (sqrt 2))
(+ (* -1 (* (pow a1 2) (* (pow a2 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))
(+ (* (pow a1 2) (+ (* -1 (* (pow a2 2) (sqrt 2))) (* (pow a1 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))
(+ (* (pow a1 2) (+ (* -1 (* (pow a2 2) (sqrt 2))) (* (pow a1 2) (sqrt 2)))) (* (pow a2 4) (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))))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 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)))))
(/ (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) (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)))))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (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) (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)
(* (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 a1 2)
(pow a1 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)))))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a1 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (pow a1 2))
(/ (- (+ (* -1 (/ (* (pow a2 6) (sqrt 2)) (* (pow a1 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th))))) (pow a1 2))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* -1 (pow a1 2))
(* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))
(* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))
(* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))
(/ (* (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) (- (+ (* -1 (/ (+ (* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2))) (/ (* (pow a2 4) (cos th)) (sqrt 2))) (pow a1 4))) (/ (cos th) (sqrt 2))) (* -1 (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))))
(* (pow a1 2) (- (+ (* -1 (/ (* (pow a2 2) (+ (* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2))) (/ (* (pow a2 4) (cos th)) (sqrt 2)))) (pow a1 6))) (/ (cos th) (sqrt 2))) (+ (* -1 (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))) (+ (* -1 (/ (* (pow a2 4) (cos th)) (* (pow a1 4) (sqrt 2)))) (/ (* (pow a2 4) (cos th)) (* (pow a1 4) (sqrt 2)))))))
(* (pow a1 6) (cos th))
(* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))
(* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))
(* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))
(pow a1 6)
(* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))
(* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))
(* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (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 (* (pow a1 2) (pow a2 2)))
(* (pow a1 2) (+ (* -1 (pow a2 2)) (/ (pow a2 4) (pow a1 2))))
(* (pow a1 2) (+ (* -1 (pow a2 2)) (/ (pow a2 4) (pow a1 2))))
(* (pow a1 2) (+ (* -1 (pow a2 2)) (/ (pow a2 4) (pow a1 2))))
(* (pow a1 4) (sqrt 2))
(* (pow a1 4) (+ (sqrt 2) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))
(* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))
(* (pow a1 2) (* (cos th) (sqrt 2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 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)))))
(/ (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) (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)))))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (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) (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)
(* (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 a1 2)
(pow a1 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)))))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a1 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (pow a1 2))
(/ (- (+ (* -1 (/ (* (pow a2 6) (sqrt 2)) (* (pow a1 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th))))) (pow a1 2))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* -1 (pow a1 2))
(* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))
(* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))
(* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))
(/ (* (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) (- (+ (* -1 (/ (+ (* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2))) (/ (* (pow a2 4) (cos th)) (sqrt 2))) (pow a1 4))) (/ (cos th) (sqrt 2))) (* -1 (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))))
(* (pow a1 2) (- (+ (* -1 (/ (* (pow a2 2) (+ (* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2))) (/ (* (pow a2 4) (cos th)) (sqrt 2)))) (pow a1 6))) (/ (cos th) (sqrt 2))) (+ (* -1 (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))) (+ (* -1 (/ (* (pow a2 4) (cos th)) (* (pow a1 4) (sqrt 2)))) (/ (* (pow a2 4) (cos th)) (* (pow a1 4) (sqrt 2)))))))
(* (pow a1 6) (cos th))
(* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))
(* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))
(* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))
(pow a1 6)
(* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))
(* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))
(* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (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 (* (pow a1 2) (pow a2 2)))
(* (pow a1 2) (+ (* -1 (pow a2 2)) (/ (pow a2 4) (pow a1 2))))
(* (pow a1 2) (+ (* -1 (pow a2 2)) (/ (pow a2 4) (pow a1 2))))
(* (pow a1 2) (+ (* -1 (pow a2 2)) (/ (pow a2 4) (pow a1 2))))
(* (pow a1 4) (sqrt 2))
(* (pow a1 4) (+ (sqrt 2) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))
(* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))
(+ (* (pow a1 2) (sqrt 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)))))))))))))
(* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))
(+ (* 1/2 (* (pow th 2) (+ (* -1/2 (* (pow a1 2) (sqrt 2))) (* -1/2 (* (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) (+ (* 1/2 (* (pow th 2) (+ (* 1/24 (* (pow a1 2) (sqrt 2))) (* 1/24 (* (pow a2 2) (sqrt 2)))))) (* 1/2 (+ (* -1/2 (* (pow a1 2) (sqrt 2))) (* -1/2 (* (pow a2 2) (sqrt 2))))))))
(+ (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* (pow th 2) (+ (* 1/2 (+ (* -1/2 (* (pow a1 2) (sqrt 2))) (* -1/2 (* (pow a2 2) (sqrt 2))))) (* (pow th 2) (+ (* 1/2 (* (pow th 2) (+ (* -1/720 (* (pow a1 2) (sqrt 2))) (* -1/720 (* (pow a2 2) (sqrt 2)))))) (* 1/2 (+ (* 1/24 (* (pow a1 2) (sqrt 2))) (* 1/24 (* (pow a2 2) (sqrt 2))))))))))
a2
(+ a2 (* -1/2 (* a2 (pow th 2))))
(+ a2 (* (pow th 2) (+ (* -1/2 a2) (* 1/24 (* a2 (pow th 2))))))
(+ a2 (* (pow th 2) (+ (* -1/2 a2) (* (pow th 2) (+ (* -1/720 (* a2 (pow th 2))) (* 1/24 a2))))))
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)))
(+ (/ (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) (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))))
(/ (+ (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))))
(/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))
(+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (+ (pow a1 2) (pow a2 2)))) (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))
(+ (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))))) (* -1/2 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))))) (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))
(+ (* (pow th 2) (- (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/720 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (+ (* 1/48 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/2 (+ (* -1/4 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))))))))) (+ (* -1/4 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))))) (* -1/2 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))))) (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))
(+ (pow a1 2) (pow a2 2))
(+ (* -1/2 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (+ (pow a1 2) (pow a2 2)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (* 1/24 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))))) (+ (pow a1 2) (pow a2 2)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (* (pow th 2) (+ (* -1/720 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (+ (pow a1 2) (pow a2 2))))))) (+ (pow a1 2) (pow a2 2)))
(/ (+ (pow a1 6) (pow a2 6)) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))) (+ (/ (pow a1 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4)))) (/ (pow a2 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 6) (pow a2 6)) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))) (+ (/ (pow a1 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4)))) (/ (pow a2 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 6) (pow a2 6)) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))) (* 1/24 (/ (+ (pow a1 6) (pow a2 6)) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))))) (+ (/ (pow a1 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4)))) (/ (pow a2 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))
(+ (pow a1 6) (pow a2 6))
(+ (* -1/2 (* (pow th 2) (+ (pow a1 6) (pow a2 6)))) (+ (pow a1 6) (pow a2 6)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 6) (pow a2 6))) (* 1/24 (* (pow th 2) (+ (pow a1 6) (pow a2 6)))))) (+ (pow a1 6) (pow a2 6)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 6) (pow a2 6))) (* (pow th 2) (+ (* -1/720 (* (pow th 2) (+ (pow a1 6) (pow a2 6)))) (* 1/24 (+ (pow a1 6) (pow a2 6))))))) (+ (pow a1 6) (pow a2 6)))
(* (pow a1 2) (sqrt 2))
(+ (* -1/2 (* (pow a1 2) (* (pow th 2) (sqrt 2)))) (* (pow a1 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) (* (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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(* a2 (cos th))
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(cos th)
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(cos th)
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(* a2 (cos th))
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(pow a1 2)
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(/ (sqrt 2) (* (pow a1 2) (cos th)))
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(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(* -1 (pow a1 2))
(- (pow a2 2) (pow a1 2))
(- (pow a2 2) (pow a1 2))
(- (pow a2 2) (pow a1 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
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(* (pow a1 6) (cos th))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(pow a1 6)
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(+ (pow a1 6) (pow a2 6))
(+ (pow a1 6) (pow a2 6))
(* 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))
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(* (pow a2 2) (+ (* -1 (pow a1 2)) (pow a2 2)))
(* (pow a2 2) (+ (* -1 (pow a1 2)) (pow a2 2)))
(* (pow a1 4) (sqrt 2))
(+ (* -1 (* (pow a1 2) (* (pow a2 2) (sqrt 2)))) (* (pow a1 4) (sqrt 2)))
(+ (* (pow a1 4) (sqrt 2)) (* (pow a2 2) (+ (* -1 (* (pow a1 2) (sqrt 2))) (* (pow a2 2) (sqrt 2)))))
(+ (* (pow a1 4) (sqrt 2)) (* (pow a2 2) (+ (* -1 (* (pow a1 2) (sqrt 2))) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (* (cos th) (sqrt 2)))
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(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
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(* a2 (cos th))
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(/ (pow a2 2) (sqrt 2))
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(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
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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 a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (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)
(* (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) (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)))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 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) (- (+ (* -1 (/ (+ (* -1 (/ (* (pow a1 4) (cos th)) (sqrt 2))) (/ (* (pow a1 4) (cos th)) (sqrt 2))) (pow a2 4))) (/ (cos th) (sqrt 2))) (* -1 (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))))
(* (pow a2 2) (- (+ (* -1 (/ (* (pow a1 2) (+ (* -1 (/ (* (pow a1 4) (cos th)) (sqrt 2))) (/ (* (pow a1 4) (cos th)) (sqrt 2)))) (pow a2 6))) (/ (cos th) (sqrt 2))) (+ (* -1 (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))) (+ (* -1 (/ (* (pow a1 4) (cos th)) (* (pow a2 4) (sqrt 2)))) (/ (* (pow a1 4) (cos th)) (* (pow a2 4) (sqrt 2)))))))
(* (pow a2 6) (cos th))
(* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))
(* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))
(* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))
(pow a2 6)
(* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))
(* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))
(* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))
(* 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 4)
(* (pow a2 4) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 4) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 4) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 4) (sqrt 2))
(* (pow a2 4) (+ (sqrt 2) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(* (pow a2 2) (* (cos th) (sqrt 2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))
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(* 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)))))
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(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow 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 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)
(* (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) (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)))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 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) (- (+ (* -1 (/ (+ (* -1 (/ (* (pow a1 4) (cos th)) (sqrt 2))) (/ (* (pow a1 4) (cos th)) (sqrt 2))) (pow a2 4))) (/ (cos th) (sqrt 2))) (* -1 (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))))
(* (pow a2 2) (- (+ (* -1 (/ (* (pow a1 2) (+ (* -1 (/ (* (pow a1 4) (cos th)) (sqrt 2))) (/ (* (pow a1 4) (cos th)) (sqrt 2)))) (pow a2 6))) (/ (cos th) (sqrt 2))) (+ (* -1 (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))) (+ (* -1 (/ (* (pow a1 4) (cos th)) (* (pow a2 4) (sqrt 2)))) (/ (* (pow a1 4) (cos th)) (* (pow a2 4) (sqrt 2)))))))
(* (pow a2 6) (cos th))
(* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))
(* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))
(* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))
(pow a2 6)
(* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))
(* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))
(* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))
(* 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 4)
(* (pow a2 4) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 4) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 4) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 4) (sqrt 2))
(* (pow a2 4) (+ (sqrt 2) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))

Outputs
(* (pow a2 2) (* (cos th) (sqrt 2)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 #s(literal 1/2 binary64) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 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 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (fma.f64 a1 a1 (.f64 a2 a2)))
(/ (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)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (.f64 a2 (/.f64 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) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (.f64 a2 (/.f64 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) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(/ (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)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(pow a2 2)
(*.f64 a2 a2)
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (.f64 a2 (/.f64 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) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (.f64 (neg.f64 a1) a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (.f64 a2 a2) a2) a2) (cos.f64 th))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 th) a2) a2)))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (-.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 6 binary64)) (cos.f64 th))) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (.f64 a2 a2) a2) a2) (cos.f64 th)))) (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2)))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (neg.f64 a1) a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 8 binary64)) (cos.f64 th))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 6 binary64)) (cos.f64 th)))) (.f64 a1 a1) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (.f64 (.f64 a2 a2) a2) a2) (cos.f64 th)))) (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 th) a2) a2)))
(* (pow a2 2) (cos th))
(.f64 (.f64 (cos.f64 th) a2) a2)
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(pow a2 2)
(*.f64 a2 a2)
(+ (* -1 (pow a1 2)) (pow a2 2))
(*.f64 (+.f64 a2 a1) (-.f64 a2 a1))
(+ (* -1 (pow a1 2)) (pow a2 2))
(*.f64 (+.f64 a2 a1) (-.f64 a2 a1))
(+ (* -1 (pow a1 2)) (pow a2 2))
(*.f64 (+.f64 a2 a1) (-.f64 a2 a1))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (.f64 a2 (/.f64 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) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (- (* -1 (* (pow a1 2) (+ (* -1 (/ (cos th) (* (pow a2 2) (sqrt 2)))) (/ (cos th) (* (pow a2 2) (sqrt 2)))))) (* -1 (/ (cos th) (sqrt 2))))) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* (pow a1 2) (- (/ (cos th) (* (pow a2 4) (sqrt 2))) (+ (* -1 (/ (cos th) (* (pow a2 4) (sqrt 2)))) (* 2 (/ (cos th) (* (pow a2 4) (sqrt 2))))))) (+ (* -1 (/ (cos th) (* (pow a2 2) (sqrt 2)))) (/ (cos th) (* (pow a2 2) (sqrt 2)))))) (* -1 (/ (cos th) (sqrt 2))))) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a2 6) (cos th))
(*.f64 (pow.f64 a2 #s(literal 6 binary64)) (cos.f64 th))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(*.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (cos.f64 th))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(*.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (cos.f64 th))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(*.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (cos.f64 th))
(pow a2 6)
(pow.f64 a2 #s(literal 6 binary64))
(+ (pow a1 6) (pow a2 6))
(+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64)))
(+ (pow a1 6) (pow a2 6))
(+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64)))
(+ (pow a1 6) (pow a2 6))
(+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64)))
(* a1 (sqrt 2))
(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(* a1 (sqrt 2))
(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(* a1 (sqrt 2))
(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(* a1 (sqrt 2))
(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (* (cos th) (sqrt 2)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(* (pow a1 2) (* (cos th) (sqrt 2)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(* (pow a1 2) (* (cos th) (sqrt 2)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(* (pow a1 2) (* (cos th) (sqrt 2)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(pow a2 4)
(.f64 (.f64 (*.f64 a2 a2) a2) a2)
(+ (* -1 (* (pow a1 2) (pow a2 2))) (pow a2 4))
(.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (*.f64 a2 a2))
(+ (* -1 (* (pow a1 2) (pow a2 2))) (pow a2 4))
(.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (*.f64 a2 a2))
(+ (* -1 (* (pow a1 2) (pow a2 2))) (pow a2 4))
(.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (*.f64 a2 a2))
(* (pow a2 4) (sqrt 2))
(.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2) (.f64 a2 a2))
(+ (* -1 (* (pow a1 2) (* (pow a2 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (.f64 a2 a2))
(+ (* (pow a1 2) (+ (* -1 (* (pow a2 2) (sqrt 2))) (* (pow a1 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))
(.f64 (fma.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (.f64 a2 a2) (.f64 (.f64 a1 a1) (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* (pow a1 2) (+ (* -1 (* (pow a2 2) (sqrt 2))) (* (pow a1 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))
(.f64 (fma.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (.f64 a2 a2) (.f64 (.f64 a1 a1) (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (* (cos th) (sqrt 2)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (.f64 a1 a1))) (.f64 a1 a1))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (.f64 a1 a1))) (.f64 a1 a1))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (.f64 a1 a1))) (.f64 a1 a1))
(* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 #s(literal 1/2 binary64) (.f64 a1 a1)) (.f64 (sqrt.f64 #s(literal 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 (.f64 #s(literal 1/2 binary64) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.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 (.f64 #s(literal 1/2 binary64) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.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 (.f64 #s(literal 1/2 binary64) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.f64 a1 a1))))
(/ (pow a1 2) (sqrt 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (.f64 a1 (/.f64 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 (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) a1) a1)
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a2
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1
#s(literal 1 binary64)
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(.f64 (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (/.f64 a1 (.f64 a2 a2))))) (.f64 (.f64 (*.f64 a2 a2) a2) a2))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 a2 a2) a2) a2)) (.f64 (.f64 a1 a1) (.f64 a1 a1)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (/.f64 a1 (.f64 a2 a2)))))) (.f64 (.f64 (*.f64 a2 a2) a2) a2))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 a2 a2) a2) a2)) (.f64 (.f64 a1 a1) (.f64 a1 a1)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (/.f64 a1 (.f64 a2 a2)))))) (.f64 (.f64 (*.f64 a2 a2) a2) a2))

rewrite230.0ms (2.7%)

Memory

6.7MiB live, 440.8MiB allocated

Rules

4 946×	`lower-/.f32`
4 934×	`lower-/.f64`
4 616×	`lower-*.f32`
4 578×	`lower-*.f64`
3 442×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	319
0	83	285
1	287	247
2	2052	247
0	8144	245

Stop Event

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

Counts

26 → 1 272

Calls

Call 1

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

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

eval268.0ms (3.1%)

Memory: 15.1MiB live, 635.4MiB allocated
Compiler: Compiled 71 440 to 3 740 computations (94.8% saved)

prune213.0ms (2.5%)

Memory

1.2MiB live, 440.9MiB allocated

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	2 118	24	2 142
Fresh	11	3	14
Picked	5	0	5
Done	0	0	0
Total	2 134	27	2 161

Accuracy

100.0%

Counts

2 161 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	62.8%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))))
	66.7%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
▶	58.3%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))))
	97.9%	(.f64 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(approx ( (* a1 (cos th)) (* a1 (sqrt 2))) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))) #s(literal 1/2 binary64))
	62.4%	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)) (.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
	63.1%	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) (.f64 th th) #s(literal 1 binary64))))
	62.8%	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))
	99.3%	(.f64 (/.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
▶	99.6%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))) #s(literal 1/2 binary64))
	99.2%	(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th))
	66.8%	(.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))
	99.3%	(.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 a2))) #s(literal 1/2 binary64))
	66.7%	#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	66.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2)))
	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)))))
	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2)))
▶	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	66.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
	57.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	14.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (-.f64 a2 a1) (+.f64 a1 a2))) #s(literal 2 binary64)) (/.f64 (.f64 (-.f64 a2 a1) (+.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))))
	62.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
	99.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
▶	32.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))))
	66.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
▶	12.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))

Compiler

Compiled 1 030 to 614 computations (40.4% saved)

simplify195.0ms (2.2%)

Memory

-0.7MiB live, 128.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 th th) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))))
cost-diff	2048	(fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))
cost-diff	0	#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (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 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))))
cost-diff	960	(fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	1024	(.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))
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 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
cost-diff	320	(.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	1024	(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.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))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
cost-diff	0	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
cost-diff	0	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))) #s(literal 1/2 binary64))

Rules

7 906×	`lower-*.f32`
7 882×	`lower-*.f64`
2 584×	`lower-fma.f32`
2 574×	`lower-fma.f64`
1 780×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	481
0	83	435
1	143	423
2	265	423
3	579	423
4	1406	402
5	2765	400
6	3072	400
7	3715	400
8	3979	400
9	4255	400
10	4693	400
11	6070	400
12	6467	400
13	6936	400
14	7240	400
15	7460	400
16	7559	400
0	8090	396

Stop Event

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

Calls

Call 1

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

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

localize166.0ms (1.9%)

Memory

-7.5MiB live, 153.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.16015625	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))))
accuracy	0.9307876041051664	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
accuracy	11.851745321711705	(fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))
accuracy	26.254485634023325	#s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))))
accuracy	4.09327387952031	(fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
accuracy	7.372409228500944	(/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
accuracy	21.181229880298318	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))))
accuracy	27.005350746886037	(.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))
accuracy	0.209316259768442	(.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.40234375	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.181229880298318	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
accuracy	0.14453125	(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.40234375	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.181229880298318	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
accuracy	55.01743297979764	#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.08041000976844202	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
accuracy	0.228847509768442	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))

Samples

103.0ms

256×

valid

Compiler

Compiled 352 to 43 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-mult: 49.0ms (65.8% of total)

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

ival-add: 7.0ms (9.4% of total)

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

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

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

exact: 0.0ms (0% of total)

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

series243.0ms (2.8%)

Memory

25.4MiB live, 103.1MiB allocated

Counts

23 → 552

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
20.0ms	th	@	-inf	((* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* a1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2)) (+ (* (/ a1 (sqrt 2)) a1) (* (* a2 a2) (/ 1 (sqrt 2)))) (* (* a2 a2) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (+ (* a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (* a1 a1)) (+ (* a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (* (* th th) 1/2) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* th th) 1/2) (cos th) (/ 1 (sqrt 2)) (/ a2 (* (* a1 (sqrt 2)) a1)) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))))
5.0ms	a2	@	inf	((* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* a1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2)) (+ (* (/ a1 (sqrt 2)) a1) (* (* a2 a2) (/ 1 (sqrt 2)))) (* (* a2 a2) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (+ (* a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (* a1 a1)) (+ (* a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (* (* th th) 1/2) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* th th) 1/2) (cos th) (/ 1 (sqrt 2)) (/ a2 (* (* a1 (sqrt 2)) a1)) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))))
5.0ms	a1	@	inf	((* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* a1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2)) (+ (* (/ a1 (sqrt 2)) a1) (* (* a2 a2) (/ 1 (sqrt 2)))) (* (* a2 a2) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (+ (* a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (* a1 a1)) (+ (* a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (* (* th th) 1/2) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* th th) 1/2) (cos th) (/ 1 (sqrt 2)) (/ a2 (* (* a1 (sqrt 2)) a1)) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))))
5.0ms	a1	@	0	((* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* a1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2)) (+ (* (/ a1 (sqrt 2)) a1) (* (* a2 a2) (/ 1 (sqrt 2)))) (* (* a2 a2) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (+ (* a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (* a1 a1)) (+ (* a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (* (* th th) 1/2) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* th th) 1/2) (cos th) (/ 1 (sqrt 2)) (/ a2 (* (* a1 (sqrt 2)) a1)) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))))
4.0ms	a2	@	0	((* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* a1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2)) (+ (* (/ a1 (sqrt 2)) a1) (* (* a2 a2) (/ 1 (sqrt 2)))) (* (* a2 a2) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (+ (* a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (* a1 a1)) (+ (* a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (* (* th th) 1/2) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* th th) 1/2) (cos th) (/ 1 (sqrt 2)) (/ a2 (* (* a1 (sqrt 2)) a1)) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))))

simplify231.0ms (2.7%)

Memory

0.3MiB live, 155.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10 388×	`lower-fma.f64`
10 388×	`lower-fma.f32`
6 762×	`lower-*.f64`
6 762×	`lower-*.f32`
2 614×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	479	10290
1	1516	9610
2	5520	9569
0	8102	9044

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 552

Calls

Call 1

Inputs
(* 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)))))
(* (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))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (pow 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 a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (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 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) (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) (* (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 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) (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)))
(+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (pow a2 2))) (/ (sqrt 2) (pow a2 2)))
(+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (pow a2 2))) (+ (* (pow a1 2) (- (* -1/2 (/ (* (pow th 2) (sqrt 2)) (pow a2 4))) (/ (sqrt 2) (pow a2 4)))) (/ (sqrt 2) (pow a2 2))))
(+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (pow a2 2))) (+ (* (pow a1 2) (- (+ (* -1/2 (/ (* (pow th 2) (sqrt 2)) (pow a2 4))) (* (pow a1 2) (- (* 1/2 (/ (* (pow th 2) (sqrt 2)) (pow a2 6))) (* -1 (/ (sqrt 2) (pow a2 6)))))) (/ (sqrt 2) (pow a2 4)))) (/ (sqrt 2) (pow a2 2))))
(+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (pow a2 2))) (+ (* (pow a1 2) (- (+ (* -1/2 (/ (* (pow th 2) (sqrt 2)) (pow a2 4))) (* (pow a1 2) (- (+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (pow a2 6))) (* (pow a1 2) (- (* -1/2 (/ (* (pow th 2) (sqrt 2)) (pow a2 8))) (/ (sqrt 2) (pow a2 8))))) (* -1 (/ (sqrt 2) (pow a2 6)))))) (/ (sqrt 2) (pow a2 4)))) (/ (sqrt 2) (pow a2 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)))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ (sqrt 2) (pow a2 2))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 4))) (/ (sqrt 2) (pow a2 2)))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (pow a2 6)) (/ (sqrt 2) (pow a2 4)))) (/ (sqrt 2) (pow a2 2)))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 8))) (* -1 (/ (sqrt 2) (pow a2 6))))) (/ (sqrt 2) (pow a2 4)))) (/ (sqrt 2) (pow a2 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)))))
(* (pow a1 2) (* (cos th) (sqrt 2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 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) (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 a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (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) (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) (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)))))
(/ 1 (sqrt 2))
(+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2))))
(+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2))))
(+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (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) (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)))))
(/ (+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2)))) (pow a1 2))
(/ (- (+ (sqrt 2) (+ (* -1/2 (/ (* (pow a2 2) (* (pow th 2) (sqrt 2))) (pow a1 2))) (* 1/2 (* (pow th 2) (sqrt 2))))) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (pow a1 2))
(/ (- (+ (sqrt 2) (+ (* -1/2 (/ (* (pow a2 2) (* (pow th 2) (sqrt 2))) (pow a1 2))) (+ (* 1/2 (* (pow th 2) (sqrt 2))) (* 1/2 (/ (* (pow a2 4) (* (pow th 2) (sqrt 2))) (pow a1 4)))))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (pow a1 4))) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))) (pow a1 2))
(/ (- (+ (sqrt 2) (+ (* -1/2 (/ (* (pow a2 2) (* (pow th 2) (sqrt 2))) (pow a1 2))) (+ (* -1/2 (/ (* (pow a2 6) (* (pow th 2) (sqrt 2))) (pow a1 6))) (+ (* 1/2 (* (pow th 2) (sqrt 2))) (* 1/2 (/ (* (pow a2 4) (* (pow th 2) (sqrt 2))) (pow a1 4))))))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (pow a1 4))) (+ (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)) (/ (* (pow a2 6) (sqrt 2)) (pow a1 6))))) (pow a1 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)))))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a1 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (pow a1 2))
(/ (- (+ (* -1 (/ (* (pow a2 6) (sqrt 2)) (* (pow a1 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th))))) (pow a1 2))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ (sqrt 2) (pow a1 2))
(/ (+ (sqrt 2) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))) (pow a1 2))
(/ (- (+ (sqrt 2) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4))) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (pow a1 2))
(/ (- (+ (sqrt 2) (* -1 (/ (* (pow a2 6) (sqrt 2)) (pow a1 6)))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (pow a1 4))) (/ (* (pow a2 2) (sqrt 2)) (pow a1 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)))))
(* (pow a1 2) (* (cos th) (sqrt 2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 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) (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))
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1
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(+ (/ (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)))
(+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (pow a1 2))) (/ (sqrt 2) (pow a1 2)))
(+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (pow a1 2))) (+ (* (pow a2 2) (- (* -1/2 (/ (* (pow th 2) (sqrt 2)) (pow a1 4))) (/ (sqrt 2) (pow a1 4)))) (/ (sqrt 2) (pow a1 2))))
(+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (pow a1 2))) (+ (* (pow a2 2) (- (+ (* -1/2 (/ (* (pow th 2) (sqrt 2)) (pow a1 4))) (* (pow a2 2) (- (* 1/2 (/ (* (pow th 2) (sqrt 2)) (pow a1 6))) (* -1 (/ (sqrt 2) (pow a1 6)))))) (/ (sqrt 2) (pow a1 4)))) (/ (sqrt 2) (pow a1 2))))
(+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (pow a1 2))) (+ (* (pow a2 2) (- (+ (* -1/2 (/ (* (pow th 2) (sqrt 2)) (pow a1 4))) (* (pow a2 2) (- (+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (pow a1 6))) (* (pow a2 2) (- (* -1/2 (/ (* (pow th 2) (sqrt 2)) (pow a1 8))) (/ (sqrt 2) (pow a1 8))))) (* -1 (/ (sqrt 2) (pow a1 6)))))) (/ (sqrt 2) (pow a1 4)))) (/ (sqrt 2) (pow a1 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)))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(+ (* (pow a2 2) (- (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 6) (cos th))) (/ (sqrt 2) (* (pow a1 4) (cos th))))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(+ (* (pow a2 2) (- (* (pow a2 2) (- (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a1 6) (cos th)))))) (/ (sqrt 2) (* (pow a1 4) (cos th))))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ (sqrt 2) (pow a1 2))
(+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 4))) (/ (sqrt 2) (pow a1 2)))
(+ (* (pow a2 2) (- (/ (* (pow a2 2) (sqrt 2)) (pow a1 6)) (/ (sqrt 2) (pow a1 4)))) (/ (sqrt 2) (pow a1 2)))
(+ (* (pow a2 2) (- (* (pow a2 2) (- (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 8))) (* -1 (/ (sqrt 2) (pow a1 6))))) (/ (sqrt 2) (pow a1 4)))) (/ (sqrt 2) (pow a1 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)))))
(* (pow a2 2) (* (cos th) (sqrt 2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 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 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 a2 2) (sqrt 2))
(/ (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 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 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) (* (pow a1 2) (sqrt 2)))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (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 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) (* 1/2 (* (pow th 2) (sqrt 2)))) (pow a2 2))
(/ (- (+ (sqrt 2) (+ (* -1/2 (/ (* (pow a1 2) (* (pow th 2) (sqrt 2))) (pow a2 2))) (* 1/2 (* (pow th 2) (sqrt 2))))) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (pow a2 2))
(/ (- (+ (sqrt 2) (+ (* -1/2 (/ (* (pow a1 2) (* (pow th 2) (sqrt 2))) (pow a2 2))) (+ (* 1/2 (* (pow th 2) (sqrt 2))) (* 1/2 (/ (* (pow a1 4) (* (pow th 2) (sqrt 2))) (pow a2 4)))))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (pow a2 4))) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (pow a2 2))
(/ (- (+ (sqrt 2) (+ (* -1/2 (/ (* (pow a1 2) (* (pow th 2) (sqrt 2))) (pow a2 2))) (+ (* -1/2 (/ (* (pow a1 6) (* (pow th 2) (sqrt 2))) (pow a2 6))) (+ (* 1/2 (* (pow th 2) (sqrt 2))) (* 1/2 (/ (* (pow a1 4) (* (pow th 2) (sqrt 2))) (pow a2 4))))))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (pow a2 4))) (+ (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)) (/ (* (pow a1 6) (sqrt 2)) (pow a2 6))))) (pow a2 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)))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ (sqrt 2) (pow a2 2))
(/ (+ (sqrt 2) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (pow a2 2))
(/ (- (+ (sqrt 2) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4))) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (pow a2 2))
(/ (- (+ (sqrt 2) (* -1 (/ (* (pow a1 6) (sqrt 2)) (pow a2 6)))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (pow a2 4))) (/ (* (pow a1 2) (sqrt 2)) (pow a2 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)))))
(* (pow a2 2) (* (cos th) (sqrt 2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 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 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 a2 2) (sqrt 2))
(/ (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 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 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) (* (pow a1 2) (sqrt 2)))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (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 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) (* 1/2 (* (pow th 2) (sqrt 2)))) (pow a2 2))
(/ (- (+ (sqrt 2) (+ (* -1/2 (/ (* (pow a1 2) (* (pow th 2) (sqrt 2))) (pow a2 2))) (* 1/2 (* (pow th 2) (sqrt 2))))) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (pow a2 2))
(/ (- (+ (sqrt 2) (+ (* -1/2 (/ (* (pow a1 2) (* (pow th 2) (sqrt 2))) (pow a2 2))) (+ (* 1/2 (* (pow th 2) (sqrt 2))) (* 1/2 (/ (* (pow a1 4) (* (pow th 2) (sqrt 2))) (pow a2 4)))))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (pow a2 4))) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (pow a2 2))
(/ (- (+ (sqrt 2) (+ (* -1/2 (/ (* (pow a1 2) (* (pow th 2) (sqrt 2))) (pow a2 2))) (+ (* -1/2 (/ (* (pow a1 6) (* (pow th 2) (sqrt 2))) (pow a2 6))) (+ (* 1/2 (* (pow th 2) (sqrt 2))) (* 1/2 (/ (* (pow a1 4) (* (pow th 2) (sqrt 2))) (pow a2 4))))))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (pow a2 4))) (+ (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)) (/ (* (pow a1 6) (sqrt 2)) (pow a2 6))))) (pow a2 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)))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ a2 (* (pow a1 2) (sqrt 2)))
(/ (sqrt 2) (pow a2 2))
(/ (+ (sqrt 2) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (pow a2 2))
(/ (- (+ (sqrt 2) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4))) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (pow a2 2))
(/ (- (+ (sqrt 2) (* -1 (/ (* (pow a1 6) (sqrt 2)) (pow a2 6)))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (pow a2 4))) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (pow a2 2))

Outputs
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 (.f64 a2 a2) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 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 (cos.f64 th) #s(literal 1/2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (cos.f64 th) #s(literal 1/2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (cos.f64 th) #s(literal 1/2 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (* (cos th) (sqrt 2)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(* (pow a2 2) (cos th))
(.f64 (.f64 (cos.f64 th) a2) a2)
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) 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) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(/ (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)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (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))))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (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)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
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(/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 (/.f64 a1 (.f64 a2 a2))) (fma.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 a2) (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ (- (+ (sqrt 2) (* -1 (/ (* (pow a1 6) (sqrt 2)) (pow a2 6)))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (pow a2 4))) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))) (pow a2 2))
(/.f64 (fma.f64 (neg.f64 (pow.f64 a1 #s(literal 6 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 (/.f64 a1 (.f64 a2 a2))) (fma.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 a2) (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 a2 a2))

rewrite312.0ms (3.6%)

Memory

-9.3MiB live, 140.9MiB allocated

Rules

4 882×	`lower-*.f32`
4 858×	`lower-*.f64`
4 786×	`lower-/.f32`
4 776×	`lower-/.f64`
3 550×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	407
0	83	355
1	274	350
2	1998	344
0	8816	341

Stop Event

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

Counts

23 → 626

Calls

Call 1

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

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

eval241.0ms (2.8%)

Memory: 4.1MiB live, 166.1MiB allocated
Compiler: Compiled 35 910 to 2 671 computations (92.6% saved)

prune238.0ms (2.7%)

Memory

19.0MiB live, 187.0MiB allocated

Pruning

36 alts after pruning (32 fresh and 4 done)

	Pruned	Kept	Total
New	1 342	16	1 358
Fresh	6	16	22
Picked	1	4	5
Done	0	0	0
Total	1 349	36	1 385

Accuracy

100.0%

Counts

1 385 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
▶	62.8%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))))
	66.7%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
	60.1%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (+ (* (* (* th th) 1/2) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))))
	97.9%	(.f64 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(approx ( (* a1 (cos th)) (* a1 (sqrt 2))) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))) #s(literal 1/2 binary64))
	62.8%	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))
	99.3%	(.f64 (/.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
✓	99.6%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))) #s(literal 1/2 binary64))
	62.5%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)) (.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))) #s(literal 1/2 binary64))
	63.2%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) (.f64 th th) #s(literal 1 binary64))))) #s(literal 1/2 binary64))
	66.8%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) #s(literal 1/2 binary64))
	99.3%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (.f64 (.f64 (cos.f64 th) a2) a2))) #s(literal 1/2 binary64))
	99.3%	(.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 a2))) #s(literal 1/2 binary64))
	66.7%	#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	99.3%	#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
	66.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2)))
	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)))))
	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2)))
✓	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	66.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
	57.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	99.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
	12.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	12.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
✓	32.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))))
	34.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 a2 (.f64 (/.f64 a2 (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))))
	38.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 a2 a2) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 #s(literal 1 binary64))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))))
▶	29.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (*.f64 a1 a1))))
	12.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	29.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 #s(approx (+ ( a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (/.f64 (.f64 a2 a2) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))) (.f64 a1 a1))))
▶	66.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
✓	12.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	12.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))))
	12.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 a1 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1))))
▶	62.9%	#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.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))))

Compiler

Compiled 1 257 to 763 computations (39.3% saved)

simplify235.0ms (2.7%)

Memory

-9.4MiB live, 148.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	384	(/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (*.f64 a2 a2))))
cost-diff	960	(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	1280	(.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (*.f64 a1 a1))
cost-diff	1600	(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))
cost-diff	0	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))))
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))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.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))))
cost-diff	0	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.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))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
cost-diff	0	(*.f64 a1 a1)
cost-diff	0	(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff	0	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
cost-diff	0	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))

Rules

5 314×	`lower-*.f32`
5 290×	`lower-*.f64`
5 150×	`lower-fma.f32`
5 140×	`lower-fma.f64`
3 824×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	516
0	89	497
1	168	497
2	388	495
3	1470	458
4	3759	430
5	5431	430
6	6825	430
7	6949	430
8	6965	430
9	6967	430
10	7702	430
11	7894	430
0	8417	425

Stop Event

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

Calls

Call 1

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

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

localize203.0ms (2.3%)

Memory

-16.1MiB live, 107.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.44921875	(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	15.01174976370379	(/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (*.f64 a2 a2))
accuracy	21.181229880298318	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (*.f64 a1 a1))))
accuracy	27.005350746886037	(.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (*.f64 a1 a1))
accuracy	0.08041000976844202	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))
accuracy	0.16015625	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))))
accuracy	0.9132533903959101	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))))
accuracy	29.695155238555714	#s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))
accuracy	0.00390625	(fma.f64 #s(literal -1/4 binary64) (*.f64 th th) #s(literal 1/2 binary64))
accuracy	0.205410009768442	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	2.8724908383905365	(.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)))
accuracy	24.09224506570622	#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.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))))
accuracy	0.16015625	(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.20184978663461464	#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.484375	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.181229880298318	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.08041000976844202	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
accuracy	0.25	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))

Samples

115.0ms

256×

valid

Compiler

Compiled 382 to 47 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-mult: 27.0ms (40.1% of total)

ival-div: 25.0ms (37.2% of total)

ival-add: 7.0ms (10.4% of total)

ival-cos: 5.0ms (7.4% of total)

ival-sqrt: 2.0ms (3% of total)

exact: 1.0ms (1.5% of total)

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

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

series95.0ms (1.1%)

Memory

17.4MiB live, 55.4MiB allocated

Counts

26 → 624

Calls

Call 1

Inputs
#s(alt (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (patch (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) #<representation binary64>) () ())
#s(alt (fma.f64 a2 a2 (.f64 a1 a1)) (patch (fma.f64 a2 a2 (.f64 a1 a1)) #<representation binary64>) () ())
#s(alt (.f64 a1 a1) (patch (.f64 a1 a1) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (+ ( (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.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 a2 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.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)))) (patch #s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.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)))) #<representation binary64>) () ())
#s(alt (.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))) (patch (.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))) #<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 (fma.f64 a1 a1 (.f64 a2 a2)) (patch (fma.f64 a1 a1 (.f64 a2 a2)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))) (patch (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (.f64 a1 a1)) (patch (.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (.f64 a1 a1)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (patch (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) #<representation binary64>) () ())
#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))) (patch #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (.f64 a1 a1)))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (*.f64 a1 a1)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (patch (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) #<representation binary64>) () ())
#s(alt (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())

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

Calls

9 calls:

Time	Variable		Point	Expression
38.0ms	a2	@	inf	((/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* a2 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (* (* (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (+ (* -1/4 (* th th)) 1/2)) (* (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (+ (* a1 a1) (* a2 a2)) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (* (/ (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (* a1 a1)) (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (/ (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (cos th) (+ (* -1/4 (* th th)) 1/2) (cos th) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)) (* a1 (sqrt 2)))
5.0ms	a1	@	0	((/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* a2 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (* (* (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (+ (* -1/4 (* th th)) 1/2)) (* (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (+ (* a1 a1) (* a2 a2)) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (* (/ (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (* a1 a1)) (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (/ (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (cos th) (+ (* -1/4 (* th th)) 1/2) (cos th) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)) (* a1 (sqrt 2)))
5.0ms	a2	@	0	((/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* a2 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (* (* (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (+ (* -1/4 (* th th)) 1/2)) (* (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (+ (* a1 a1) (* a2 a2)) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (* (/ (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (* a1 a1)) (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (/ (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (cos th) (+ (* -1/4 (* th th)) 1/2) (cos th) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)) (* a1 (sqrt 2)))
4.0ms	a1	@	inf	((/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* a2 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (* (* (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (+ (* -1/4 (* th th)) 1/2)) (* (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (+ (* a1 a1) (* a2 a2)) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (* (/ (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (* a1 a1)) (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (/ (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (cos th) (+ (* -1/4 (* th th)) 1/2) (cos th) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)) (* a1 (sqrt 2)))
4.0ms	a1	@	-inf	((/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* a2 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (* (* (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (+ (* -1/4 (* th th)) 1/2)) (* (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (+ (* a1 a1) (* a2 a2)) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (* (/ (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (* a1 a1)) (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (/ (+ (* 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (cos th) (+ (* -1/4 (* th th)) 1/2) (cos th) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)) (* a1 (sqrt 2)))

simplify278.0ms (3.2%)

Memory

-22.6MiB live, 141.8MiB allocated

Algorithm

1×	egg-herbie

Rules

13 356×	`lower-fma.f64`
13 356×	`lower-fma.f32`
6 748×	`lower-*.f64`
6 748×	`lower-*.f32`
5 128×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	315	9588
1	1051	8867
2	4087	8503
0	8337	8002

Stop Event

1×	iter limit
1×	node limit

Counts

624 → 624

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 a2 2) (cos th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(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)
(pow a1 2)
(pow a1 2)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (pow 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)))
(* 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)))))
(* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))))
(+ (* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))))
(+ (* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))))
(+ (* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 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 a2 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 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)))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(* (pow a2 2) (cos th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 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)))
(sqrt 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)))
(/ (pow a2 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 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) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (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))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (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 a1 2)
(pow a1 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) (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)))))
(* 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)))))
(* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))))
(* (pow a1 2) (+ (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))) (/ (* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (pow a1 2))))
(* (pow a1 2) (+ (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))) (/ (* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (pow a1 2))))
(* (pow a1 2) (+ (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))) (/ (* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 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)
(* (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) (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)))))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a1 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (pow a1 2))
(/ (- (+ (* -1 (/ (* (pow a2 6) (sqrt 2)) (* (pow a1 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th))))) (pow a1 2))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 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) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(* (pow a1 2) (+ (/ (sqrt 2) (pow a1 2)) (/ (sqrt 2) (pow a2 2))))
(* (pow a1 2) (+ (/ (sqrt 2) (pow a1 2)) (/ (sqrt 2) (pow a2 2))))
(* (pow a1 2) (+ (/ (sqrt 2) (pow a1 2)) (/ (sqrt 2) (pow a2 2))))
(/ 1 (sqrt 2))
(+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2))))
(+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2))))
(+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (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) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (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))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (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 a1 2)
(pow a1 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) (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)))))
(* 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)))))
(* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))))
(* (pow a1 2) (+ (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))) (/ (* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (pow a1 2))))
(* (pow a1 2) (+ (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))) (/ (* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (pow a1 2))))
(* (pow a1 2) (+ (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))) (/ (* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 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)
(* (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) (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)))))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a1 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (pow a1 2))
(/ (- (+ (* -1 (/ (* (pow a2 6) (sqrt 2)) (* (pow a1 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th))))) (pow a1 2))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 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) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(* (pow a1 2) (+ (/ (sqrt 2) (pow a1 2)) (/ (sqrt 2) (pow a2 2))))
(* (pow a1 2) (+ (/ (sqrt 2) (pow a1 2)) (/ (sqrt 2) (pow a2 2))))
(* (pow a1 2) (+ (/ (sqrt 2) (pow a1 2)) (/ (sqrt 2) (pow a2 2))))
(/ 1 (sqrt 2))
(+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2))))
(+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2))))
(+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (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) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (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))))
(+ (pow a1 2) (pow a2 2))
(+ (* -1/2 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (+ (pow a1 2) (pow a2 2)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (* 1/24 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))))) (+ (pow a1 2) (pow a2 2)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (* (pow th 2) (+ (* -1/720 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (+ (pow a1 2) (pow a2 2))))))) (+ (pow a1 2) (pow a2 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(* 1/2 (* (sqrt 2) (+ (pow a1 2) (pow a2 2))))
(+ (* -1/4 (* (pow th 2) (* (sqrt 2) (+ (pow a1 2) (pow a2 2))))) (* 1/2 (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))))
(+ (* 1/2 (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* (pow th 2) (+ (* -1/4 (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/48 (* (pow th 2) (* (sqrt 2) (+ (pow a1 2) (pow a2 2))))))))
(+ (* 1/2 (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* (pow th 2) (+ (* -1/4 (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* (pow th 2) (+ (* -1/1440 (* (pow th 2) (* (sqrt 2) (+ (pow a1 2) (pow a2 2))))) (* 1/48 (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))))))))
(* 1/2 (* (sqrt 2) (+ (pow a1 2) (pow a2 2))))
(+ (* -1/4 (* (pow th 2) (* (sqrt 2) (+ (pow a1 2) (pow a2 2))))) (* 1/2 (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))))
(+ (* -1/4 (* (pow th 2) (* (sqrt 2) (+ (pow a1 2) (pow a2 2))))) (* 1/2 (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))))
(+ (* -1/4 (* (pow th 2) (* (sqrt 2) (+ (pow a1 2) (pow a2 2))))) (* 1/2 (* (sqrt 2) (+ (pow a1 2) (pow a2 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))))
(/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))
(+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (+ (pow a1 2) (pow a2 2)))) (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))
(+ (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))))) (* -1/2 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))))) (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))
(+ (* (pow th 2) (- (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/720 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (+ (* 1/48 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/2 (+ (* -1/4 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))))))))) (+ (* -1/4 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))))) (* -1/2 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))))) (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))
(+ (pow a1 2) (pow a2 2))
(+ (* -1/2 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (+ (pow a1 2) (pow a2 2)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (* 1/24 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))))) (+ (pow a1 2) (pow a2 2)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (* (pow th 2) (+ (* -1/720 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (+ (pow a1 2) (pow a2 2))))))) (+ (pow a1 2) (pow a2 2)))
1
(+ 1 (* -1/2 (pow th 2)))
(+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))
(+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))
1/2
(+ 1/2 (* -1/4 (pow th 2)))
(+ 1/2 (* -1/4 (pow th 2)))
(+ 1/2 (* -1/4 (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)))
(+ (/ (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))))
(/ (* (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)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 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)))
(* 1/2 (* (cos th) (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))))
(* 1/2 (* (cos th) (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))))
(* 1/2 (* (cos th) (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))))
(* 1/2 (* (cos th) (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))))
(* -1/4 (* (pow th 2) (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))))
(* (pow th 2) (+ (* -1/4 (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/2 (/ (* (sqrt 2) (+ (pow a1 2) (pow a2 2))) (pow th 2)))))
(* (pow th 2) (+ (* -1/4 (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/2 (/ (* (sqrt 2) (+ (pow a1 2) (pow a2 2))) (pow th 2)))))
(* (pow th 2) (+ (* -1/4 (* (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/2 (/ (* (sqrt 2) (+ (pow a1 2) (pow a2 2))) (pow th 2)))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (sqrt 2) (* (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))))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
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(pow a1 2)
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(pow a1 2)
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(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (pow a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
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(/ (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (pow a2 2))
(/ (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) (pow a2 2))
(/ 1 (sqrt 2))
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
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(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 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))
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(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(pow a2 2)
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(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 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 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) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (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)))))
(* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))))
(* (pow a2 2) (+ (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))) (/ (* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (pow a2 2))))
(* (pow a2 2) (+ (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))) (/ (* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (pow a2 2))))
(* (pow a2 2) (+ (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))) (/ (* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 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)
(* (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) (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)))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 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)
(+ (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)))
(/ (pow a2 2) (* (pow a1 2) (sqrt 2)))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (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)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 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))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (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) (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 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) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (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)))))
(* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))))
(* (pow a2 2) (+ (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))) (/ (* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (pow a2 2))))
(* (pow a2 2) (+ (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))) (/ (* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (pow a2 2))))
(* (pow a2 2) (+ (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))) (/ (* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 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)
(* (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) (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)))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 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)
(+ (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)))
(/ (pow a2 2) (* (pow a1 2) (sqrt 2)))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (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)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))

Outputs
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) 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) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a2 2) (cos th))
(.f64 (.f64 (cos.f64 th) a2) a2)
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(pow a2 2)
(*.f64 a2 a2)
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) 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) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(/ (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 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 #s(literal 1/2 binary64) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 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 (.f64 #s(literal 1/2 binary64) (cos.f64 th)) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 th)) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 th)) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))))
(.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
(+ (* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))))
(.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
(+ (* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))))
(.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
(+ (* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))) (* (pow a2 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2))))))
(.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
(* (pow a2 2) (sqrt 2))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(pow a2 2)
(*.f64 a2 a2)
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) 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) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (.f64 (neg.f64 a1) a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 4 binary64)) (cos.f64 th))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2)))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (-.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 6 binary64)) (cos.f64 th))) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 4 binary64)) (cos.f64 th)))) (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 th) a2) a2)))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (-.f64 (.f64 (.f64 (neg.f64 a1) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a1 (/.f64 a1 (pow.f64 a2 #s(literal 8 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 a2 #s(literal 6 binary64)))))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 4 binary64)) (cos.f64 th)))) (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 th) a2) a2)))
(* (pow a2 2) (cos th))
(.f64 (.f64 (cos.f64 th) a2) a2)
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(.f64 a1 (.f64 a1 (/.f64 #s(literal 2 binary64) (*.f64 a2 a2))))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(.f64 a1 (.f64 a1 (/.f64 #s(literal 2 binary64) (*.f64 a2 a2))))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(.f64 a1 (.f64 a1 (/.f64 #s(literal 2 binary64) (*.f64 a2 a2))))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(.f64 a1 (.f64 a1 (/.f64 #s(literal 2 binary64) (*.f64 a2 a2))))
(/ (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 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (* (pow a1 2) (sqrt 2)))
(/.f64 (.f64 a2 a2) (.f64 (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(/ (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (pow a1 2))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2))) (*.f64 a1 a1))
(/ (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (pow a1 2))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2))) (*.f64 a1 a1))
(/ (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (pow a1 2))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2))) (*.f64 a1 a1))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) 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) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (*.f64 a2 a2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (*.f64 a2 a2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (*.f64 a2 a2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (*.f64 a2 a2))
(* a1 (sqrt 2))
(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(* a1 (sqrt 2))
(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(* a1 (sqrt 2))
(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(* a1 (sqrt 2))
(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) 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 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (cos.f64 th) 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 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (cos.f64 th) 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 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (cos.f64 th) a1) a1) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (cos th))
(.f64 (.f64 (cos.f64 th) a1) a1)
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(.f64 (fma.f64 (/.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 a2 a2) (cos.f64 th)) (.f64 a1 a1))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(.f64 (fma.f64 (/.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 a2 a2) (cos.f64 th)) (.f64 a1 a1))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(.f64 (fma.f64 (/.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 a2 a2) (cos.f64 th)) (.f64 a1 a1))
(pow a1 2)
(*.f64 a1 a1)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (*.f64 a1 a1))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (*.f64 a1 a1))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (*.f64 a1 a1))
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) 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 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (cos.f64 th) 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 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (cos.f64 th) 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 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (cos.f64 th) 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) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 #s(literal 1/2 binary64) (.f64 a1 a1)) (.f64 (sqrt.f64 #s(literal 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 (.f64 #s(literal 1/2 binary64) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.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 (.f64 #s(literal 1/2 binary64) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.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 (.f64 #s(literal 1/2 binary64) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.f64 a1 a1))))
(* (pow a1 2) (* (sqrt 2) (+ 1/2 (* -1/4 (pow th 2)))))
(.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
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(pow a2 2)
(*.f64 a2 a2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (*.f64 a2 a2))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (*.f64 a2 a2))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (*.f64 a2 a2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/.f64 (.f64 (fma.f64 (neg.f64 a1) (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (*.f64 a2 a2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (-.f64 (+.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 a1 (/.f64 a1 (.f64 a2 a2))))) (.f64 a2 a2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (-.f64 (+.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 a1 (/.f64 a1 (.f64 a2 a2)))) (.f64 (neg.f64 (pow.f64 a1 #s(literal 6 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 6 binary64)) (cos.f64 th))))) (*.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 (.f64 (cos.f64 th) a2) a2)
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(.f64 (fma.f64 (/.f64 (cos.f64 th) (.f64 a2 a2)) (.f64 a1 a1) (cos.f64 th)) (.f64 a2 a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(.f64 (fma.f64 (/.f64 (cos.f64 th) (.f64 a2 a2)) (.f64 a1 a1) (cos.f64 th)) (.f64 a2 a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(.f64 (fma.f64 (/.f64 (cos.f64 th) (.f64 a2 a2)) (.f64 a1 a1) (cos.f64 th)) (.f64 a2 a2))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(.f64 a1 (.f64 a1 (/.f64 #s(literal 2 binary64) (*.f64 a2 a2))))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(.f64 a1 (.f64 a1 (/.f64 #s(literal 2 binary64) (*.f64 a2 a2))))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(.f64 a1 (.f64 a1 (/.f64 #s(literal 2 binary64) (*.f64 a2 a2))))
(/ (* (pow a1 2) (pow (sqrt 2) 2)) (pow a2 2))
(.f64 a1 (.f64 a1 (/.f64 #s(literal 2 binary64) (*.f64 a2 a2))))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 a2 (fma.f64 a2 (/.f64 (.f64 a1 a1) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 a2 (fma.f64 a2 (/.f64 (.f64 a1 a1) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 a2 (fma.f64 a2 (/.f64 (.f64 a1 a1) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (* (pow a1 2) (sqrt 2)))
(/.f64 (.f64 a2 a2) (.f64 (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2)))))
(fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2)))))
(fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ 1 (* (pow a1 2) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2)))))
(fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (*.f64 a2 a2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (*.f64 a2 a2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (*.f64 a2 a2))
(/ (* (pow a1 2) (sqrt 2)) (pow a2 2))
(/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (*.f64 a2 a2))

rewrite339.0ms (3.9%)

Memory

0.1MiB live, 272.2MiB allocated

Rules

4 850×	`lower-*.f32`
4 826×	`lower-*.f64`
4 706×	`lower-/.f32`
4 694×	`lower-/.f64`
2 920×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	404
0	89	386
1	309	378
2	2299	366
0	8498	362

Stop Event

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

Counts

26 → 870

Calls

Call 1

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

Outputs
(.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1))) (.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 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (+.f64 (pow.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (/.f64 (pow.f64 (.f64 (.f64 (cos.f64 th) a1) a1) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(.f64 (.f64 (neg.f64 (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (cos.f64 th) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (cos.f64 th) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (/.f64 (pow.f64 (.f64 (.f64 (cos.f64 th) a1) a1) #s(literal 2 binary64)) #s(literal 2 binary64))) (+.f64 (pow.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (fma.f64 a2 a2 (.f64 a1 a1)))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 a2 a2) a2) (.f64 (.f64 a2 a2) a2) (.f64 (.f64 (.f64 a1 a1) a1) (.f64 (.f64 a1 a1) a1))) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (fma.f64 (.f64 (.f64 a1 a1) a1) a1 (.f64 (.f64 a2 a2) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 a2 a2) a2) (.f64 (.f64 a2 a2) a2) (.f64 (.f64 (.f64 a1 a1) a1) (.f64 (.f64 a1 a1) a1))) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (fma.f64 (.f64 (.f64 a2 a2) a2) a2 (.f64 (.f64 a1 a1) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))
(/.f64 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))) (neg.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))))) (neg.f64 (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))))
(/.f64 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 (.f64 a2 a2) a2) (.f64 (.f64 a2 a2) a2) (.f64 (.f64 (.f64 a1 a1) a1) (.f64 (.f64 a1 a1) a1))))) (neg.f64 (fma.f64 (.f64 (.f64 a1 a1) a1) a1 (.f64 (.f64 a2 a2) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))))))
(/.f64 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 (.f64 a2 a2) a2) (.f64 (.f64 a2 a2) a2) (.f64 (.f64 (.f64 a1 a1) a1) (.f64 (.f64 a1 a1) a1))))) (neg.f64 (fma.f64 (.f64 (.f64 a2 a2) a2) a2 (.f64 (.f64 a1 a1) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))
(/.f64 (neg.f64 (.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(/.f64 (neg.f64 (/.f64 (-.f64 (pow.f64 (.f64 (.f64 (cos.f64 th) a2) a2) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 th) a1) a1) #s(literal 2 binary64))) #s(literal 2 binary64))) (neg.f64 (/.f64 (*.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))))
(/.f64 (.f64 (/.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2)) #s(literal 1 binary64))
(/.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 a1 (.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 a1 (.f64 a2 a2)))))
(neg.f64 (/.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))) #s(literal -1 binary64)))
(cos.f64 th)
(.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/64 binary64)) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 th th) #s(literal -1/8 binary64))))))
(pow.f64 (/.f64 (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64)) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) #s(literal -1/8 binary64)))) (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/64 binary64)) #s(literal 1/8 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 th th) #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/64 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) #s(literal -1/8 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64)) (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64)) (fma.f64 (*.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 th th) #s(literal -1/4 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/64 binary64)) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64)) (.f64 (*.f64 th th) #s(literal -1/8 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/64 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) #s(literal -1/8 binary64))))))
(/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) #s(literal -1/4 binary64)) (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/64 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64)) (.f64 (*.f64 th th) #s(literal -1/8 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/64 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) #s(literal -1/8 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64)) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) #s(literal -1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) #s(literal -1/8 binary64)))) (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/64 binary64)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64)) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 th th) #s(literal -1/8 binary64)))) (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/64 binary64)) #s(literal 1/8 binary64))))
(fma.f64 (*.f64 #s(literal -1/4 binary64) th) th #s(literal 1/2 binary64))
(fma.f64 (*.f64 th th) #s(literal -1/4 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 th th) #s(literal 1/2 binary64))
(fma.f64 th (*.f64 #s(literal -1/4 binary64) th) #s(literal 1/2 binary64))
(-.f64 (/.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/16 binary64)) (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 th th) #s(literal -1/4 binary64) #s(literal -1/2 binary64))))
(+.f64 (.f64 (.f64 th th) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 th th) #s(literal -1/4 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))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2)) (/.f64 a1 a2))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 a1 (.f64 a2 a2)))
(.f64 (/.f64 #s(literal 1 binary64) a2) (.f64 a1 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2)))
(.f64 (/.f64 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(.f64 (.f64 a1 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2)) (/.f64 #s(literal 1 binary64) a2))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 a2 a2)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 a2 a2)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))
(.f64 (/.f64 a1 a2) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2))
(.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2) (*.f64 (/.f64 a1 a2) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2) (/.f64 a1 a2))
(.f64 (.f64 (neg.f64 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 a2) a2)))
(.f64 (.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) #s(literal 1 binary64))
(.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 a2 a2)) #s(literal 1 binary64)))
(.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (/.f64 #s(literal 1 binary64) (.f64 a2 a2)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (/.f64 a1 (*.f64 a2 a2)))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (/.f64 a1 (*.f64 a2 a2))))
(.f64 a1 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (*.f64 a2 a2)))
(.f64 a1 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (/.f64 #s(literal 1 binary64) (.f64 a2 a2))))
(.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 a1 (*.f64 a2 a2))))
(pow.f64 (/.f64 a2 (.f64 a1 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 a2 (/.f64 a2 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (.f64 a2 (/.f64 a2 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2) a1)) (neg.f64 a2))
(/.f64 (neg.f64 (neg.f64 (.f64 a1 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2)))) (neg.f64 (neg.f64 a2)))
(/.f64 (neg.f64 (neg.f64 (.f64 (neg.f64 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))) (neg.f64 (neg.f64 (*.f64 (neg.f64 a2) a2))))
(/.f64 (neg.f64 (.f64 (.f64 a1 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2)) #s(literal 1 binary64))) (neg.f64 a2))
(/.f64 (neg.f64 (.f64 (.f64 (neg.f64 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) #s(literal 1 binary64))) (neg.f64 (.f64 (neg.f64 a2) a2)))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 a1 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2)))) (neg.f64 a2))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 (neg.f64 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))) (neg.f64 (.f64 (neg.f64 a2) a2)))
(/.f64 (.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2) a1) a2)
(/.f64 (neg.f64 (.f64 a1 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2))) (neg.f64 a2))
(/.f64 (neg.f64 (.f64 (neg.f64 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (neg.f64 (*.f64 (neg.f64 a2) a2)))
(/.f64 (.f64 (.f64 a1 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2)) #s(literal 1 binary64)) a2)
(/.f64 (.f64 (.f64 (neg.f64 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) #s(literal 1 binary64)) (.f64 (neg.f64 a2) a2))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 a1 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2))) a2)
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (neg.f64 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1))) (.f64 (neg.f64 a2) a2))
(/.f64 (.f64 a1 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2)) a2)
(/.f64 (.f64 (neg.f64 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (neg.f64 a2) a2))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 a2 (.f64 a1 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 a2 (/.f64 a2 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 a2 (/.f64 a2 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1)))))
(/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (*.f64 a2 a2))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (.f64 a2 (/.f64 a2 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))))))
(/.f64 #s(literal 1 binary64) (/.f64 a2 (.f64 a1 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 (/.f64 a2 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 a2 (/.f64 a2 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))))
(neg.f64 (/.f64 (.f64 (neg.f64 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 a2 a2)))
(neg.f64 (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (*.f64 (neg.f64 a2) a2)))
(exp.f64 (.f64 (log.f64 (.f64 a2 (/.f64 a2 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1)))) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) a1)
(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))

eval257.0ms (3%)

Memory: 18.1MiB live, 402.8MiB allocated
Compiler: Compiled 48 892 to 3 171 computations (93.5% saved)

prune204.0ms (2.3%)

Memory

29.8MiB live, 461.1MiB allocated

Pruning

36 alts after pruning (31 fresh and 5 done)

	Pruned	Kept	Total
New	1 714	16	1 730
Fresh	12	15	27
Picked	3	2	5
Done	1	3	4
Total	1 730	36	1 766

Accuracy

100.0%

Counts

1 766 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	62.8%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	99.3%	(/.f64 (.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	12.7%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))))
	60.1%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (+ (* (* (* th th) 1/2) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))))
	62.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))) (fma.f64 a2 a2 (.f64 a1 a1))))
✓	99.6%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))) #s(literal 1/2 binary64))
	62.5%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)) (.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))) #s(literal 1/2 binary64))
	63.2%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) (.f64 th th) #s(literal 1 binary64))))) #s(literal 1/2 binary64))
	66.8%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) #s(literal 1/2 binary64))
	99.3%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (.f64 (.f64 (cos.f64 th) a2) a2))) #s(literal 1/2 binary64))
	99.3%	(.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 a2))) #s(literal 1/2 binary64))
	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)))))
	66.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
	57.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	99.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
	12.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	66.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
	33.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a1 a1) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 a1 (.f64 a2 a2)))))))
✓	32.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))))
	34.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 a2 (.f64 (/.f64 a2 (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) a1)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))))
	38.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 a2 a2) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 #s(literal 1 binary64))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))))
	29.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 #s(approx (+ ( 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (*.f64 a1 a1))))
	66.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	12.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	29.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 #s(approx (/ (+ ( 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (/.f64 (.f64 a2 a2) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))) (.f64 a1 a1))))
✓	66.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
	66.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))))
	66.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 a2 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2))))
✓	12.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	12.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 a1 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1))))
	12.7%	#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 (.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64))))
	62.8%	#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 #s(approx ( (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)) (fma.f64 #s(literal -1/4 binary64) (*.f64 th th) #s(literal 1/2 binary64))))
	12.7%	#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 #s(approx ( (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (fma.f64 #s(literal -1/4 binary64) (*.f64 th th) #s(literal 1/2 binary64))))

Compiler

Compiled 1 966 to 629 computations (68% saved)

regimes177.0ms (2%)

Memory

-26.6MiB live, 346.5MiB allocated

Counts

76 → 1

Calls

Call 1

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

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

Calls

8 calls:

26.0ms	(*.f64 a2 a2)
22.0ms	a2
22.0ms	a1
22.0ms	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)))

Results

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

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes133.0ms (1.5%)

Memory

3.4MiB live, 279.5MiB allocated

Counts

58 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) 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))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.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 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 a1 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 a2 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) #s(literal 1/2 binary64))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 #s(approx ( (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (fma.f64 #s(literal -1/4 binary64) (*.f64 th th) #s(literal 1/2 binary64))))
#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 #s(approx ( (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)) (fma.f64 #s(literal -1/4 binary64) (*.f64 th th) #s(literal 1/2 binary64))))
#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 (.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a1 a1)) (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))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 #s(literal 1 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 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.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 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.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))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 #s(approx (+ ( a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (/.f64 (.f64 a2 a2) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))) (.f64 a1 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 #s(approx (/ (+ ( 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (/.f64 (.f64 a2 a2) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))) (.f64 a1 a1))))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (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 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))) (fma.f64 a2 a2 (.f64 a1 a1))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (+ (* (* (* th th) 1/2) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (.f64 a1 a1)) #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))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) (.f64 th th) #s(literal 1 binary64))))) #s(literal 1/2 binary64))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) (.f64 th th) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #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))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.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))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)) (.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))) #s(literal 1/2 binary64))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)) (.f64 th th) #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))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 a2 (.f64 (/.f64 a2 (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) a1)) (/.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))) (.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (-.f64 a2 a1) (+.f64 a1 a2))) #s(literal 2 binary64)) (/.f64 (.f64 (-.f64 a2 a1) (+.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 #s(approx (+ ( 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (*.f64 a1 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) (.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))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 a2 a2) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 #s(literal 1 binary64))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.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 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a1 a1) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 a1 (.f64 a2 a2)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (*.f64 a1 a1))))
(.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 a2))) #s(literal 1/2 binary64))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (.f64 (.f64 (cos.f64 th) a2) a2))) #s(literal 1/2 binary64))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th))
(.f64 (/.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(/.f64 (.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))

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

Calls

8 calls:

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

Results

Accuracy	Segments	Branch
99.3%	1	`a1`
99.3%	1	`a2`
99.3%	1	`th`
99.3%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
99.3%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.3%	1	`(cos.f64 th)`
99.3%	1	`(*.f64 a1 a1)`
99.3%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes127.0ms (1.5%)

Memory

13.1MiB live, 255.8MiB allocated

Counts

51 → 2

Calls

Call 1

Inputs
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) 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))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.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 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 a1 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 a2 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 a1 a1) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) #s(literal 1/2 binary64))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 #s(approx ( (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (fma.f64 #s(literal -1/4 binary64) (*.f64 th th) #s(literal 1/2 binary64))))
#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 #s(approx ( (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)) (fma.f64 #s(literal -1/4 binary64) (*.f64 th th) #s(literal 1/2 binary64))))
#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 (.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (.f64 a1 a1)) (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))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 #s(literal 1 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 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.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 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.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))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 #s(approx (+ ( a2 (/ a2 (* (* a1 (sqrt 2)) a1))) (/ 1 (sqrt 2))) (/.f64 (.f64 a2 a2) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))) (.f64 a1 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 #s(approx (/ (+ ( 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (* (* a1 (sqrt 2)) a1) (* a2 a2)))) (/.f64 (.f64 a2 a2) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))) (.f64 a1 a1))))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (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 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))) (fma.f64 a2 a2 (.f64 a1 a1))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (+ (* (* (* th th) 1/2) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (.f64 a1 a1)) #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))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) (.f64 th th) #s(literal 1 binary64))))) #s(literal 1/2 binary64))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) (.f64 th th) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #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))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (/.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))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)) (.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))) #s(literal 1/2 binary64))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)) (.f64 th th) #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))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 a2 (.f64 (/.f64 a2 (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) a1)) (/.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))) (.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (-.f64 a2 a1) (+.f64 a1 a2))) #s(literal 2 binary64)) (/.f64 (.f64 (-.f64 a2 a1) (+.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 #s(approx (+ ( 1 (/ (* (* a1 (sqrt 2)) a1) (* a2 a2))) (sqrt 2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (*.f64 a1 a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) (.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))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 a2 a2) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 #s(literal 1 binary64))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.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 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a1 a1) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 a1 (.f64 a2 a2)))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)))) (*.f64 a1 a1))))

Outputs

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

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

Calls

8 calls:

24.0ms	(*.f64 a2 a2)
15.0ms	a1
15.0ms	a2
15.0ms	th
14.0ms	(cos.f64 th)

Results

Accuracy	Segments	Branch
66.8%	1	`a1`
75.9%	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)))`
66.8%	1	`(*.f64 a1 a1)`
68.7%	2	`a2`
66.8%	1	`th`
75.8%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
75.8%	2	`(cos.f64 th)`
66.8%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes15.0ms (0.2%)

Memory

-6.7MiB live, 32.7MiB allocated

Counts

13 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

5.0ms

(+.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)))

4.0ms

(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

4.0ms

(cos.f64 th)

Results

Accuracy	Segments	Branch
70.3%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
70.3%	2	`(cos.f64 th)`
70.4%	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 35 to 23 computations (34.3% saved)

regimes22.0ms (0.3%)

Memory

9.2MiB live, 48.5MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

5 calls:

5.0ms	(cos.f64 th)
4.0ms	a2
4.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
4.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
4.0ms	(*.f64 a1 a1)

Results

Accuracy	Segments	Branch
66.8%	1	`(*.f64 a1 a1)`
66.8%	1	`a2`
66.8%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
66.8%	1	`(cos.f64 th)`
66.8%	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 45 to 30 computations (33.3% saved)

regimes27.0ms (0.3%)

Memory

-17.8MiB live, 62.9MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs

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

Calls

8 calls:

4.0ms	(*.f64 a2 a2)
4.0ms	(cos.f64 th)
3.0ms	th
3.0ms	(+.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)))
3.0ms	a2

Results

Accuracy	Segments	Branch
66.6%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
66.6%	1	`(cos.f64 th)`
66.6%	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)))`
66.6%	1	`a1`
66.6%	1	`th`
66.6%	1	`a2`
66.6%	1	`(*.f64 a2 a2)`
66.6%	1	`(*.f64 a1 a1)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes16.0ms (0.2%)

Memory

2.5MiB live, 41.9MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

Calls

8 calls:

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

Results

Accuracy	Segments	Branch
66.5%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
66.5%	1	`(cos.f64 th)`
66.5%	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)))`
66.5%	1	`a1`
66.5%	1	`th`
66.5%	1	`a2`
66.5%	1	`(*.f64 a1 a1)`
66.5%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes11.0ms (0.1%)

Memory

-11.0MiB live, 28.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs

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

Calls

8 calls:

2.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
1.0ms	(+.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	a1
1.0ms	th

Results

Accuracy	Segments	Branch
12.1%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
12.1%	1	`(cos.f64 th)`
12.1%	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)))`
12.1%	1	`th`
12.1%	1	`a1`
12.1%	1	`a2`
12.1%	1	`(*.f64 a2 a2)`
12.1%	1	`(*.f64 a1 a1)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0010782425355868e-191	-3.208277761233871e-222

Compiler

Compiled 25 to 18 computations (28% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.208277761233871e-222	-1.660598733877796e-268

Compiler

Compiled 25 to 18 computations (28% saved)

simplify7.0ms (0.1%)

Memory

17.5MiB live, 17.6MiB allocated

Algorithm

1×	egg-herbie

Rules

36×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	382
1	100	382

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))) #s(literal 1/2 binary64))
(.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 a2))) #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 -802633041618099/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816 binary64)) #s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 #s(approx ( (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64)))) (.f64 #s(approx (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) #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 -6511732844609233/3255866422304616344765552632188114158762089024568314531443485259650408807528140659922574316831813618526821245406949824436469141432675471230646169947427163108444901161872077421124549944292877941762189949285100879873872435565174053364826112 binary64)) #s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 #s(approx ( (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64)))) (.f64 #s(approx (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.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 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))

Outputs
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 a2))) #s(literal 1/2 binary64))
(.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) #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 -802633041618099/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816 binary64)) #s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 #s(approx ( (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64)))) (.f64 #s(approx (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(if (<=.f64 (+.f64 (.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))) #s(literal -802633041618099/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816 binary64)) #s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64)) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (.f64 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))) (.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) #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 -6511732844609233/3255866422304616344765552632188114158762089024568314531443485259650408807528140659922574316831813618526821245406949824436469141432675471230646169947427163108444901161872077421124549944292877941762189949285100879873872435565174053364826112 binary64)) #s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 #s(approx ( (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64)))) (.f64 #s(approx (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(if (<=.f64 (+.f64 (.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))) #s(literal -6511732844609233/3255866422304616344765552632188114158762089024568314531443485259650408807528140659922574316831813618526821245406949824436469141432675471230646169947427163108444901161872077421124549944292877941762189949285100879873872435565174053364826112 binary64)) #s(approx (* (* (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) 1/2) (.f64 #s(approx ( (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (fma.f64 #s(literal -1/4 binary64) (.f64 th th) #s(literal 1/2 binary64)))) (.f64 #s(approx (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(.f64 #s(approx (+ ( (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.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 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) 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))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))

soundness1.2s (13.6%)

Memory

18.2MiB live, 1 091.8MiB allocated

Rules

34 694×	`lower-fma.f64`
34 694×	`lower-fma.f32`
13 356×	`lower-fma.f64`
13 356×	`lower-fma.f32`
11 948×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	404
0	89	386
1	309	378
2	2299	366
0	8498	362
0	48	319
0	83	285
1	287	247
2	2052	247
0	8144	245
0	479	10290
1	1516	9610
2	5520	9569
0	8102	9044
0	315	9588
1	1051	8867
2	4087	8503
0	8337	8002
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	1206	1262
3	3900	1233
0	8428	1172
0	509	9457
1	1804	8912
2	7123	8858
0	8521	8420

Stop Event

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

Compiler

Compiled 551 to 285 computations (48.3% saved)

preprocess76.0ms (0.9%)

Memory

-9.3MiB live, 228.5MiB allocated

Remove

(sort a1 a2)

(abs a1)

(abs a2)

(abs th)

Compiler

Compiled 1 050 to 590 computations (43.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.5s (17.2%)

explain152.0ms (1.8%)

preprocess135.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize43.0ms (0.5%)

series21.0ms (0.2%)

simplify263.0ms (3%)

rewrite166.0ms (1.9%)

eval58.0ms (0.7%)

prune72.0ms (0.8%)

simplify127.0ms (1.5%)

localize118.0ms (1.4%)

series92.0ms (1.1%)

simplify197.0ms (2.3%)

rewrite230.0ms (2.7%)

eval268.0ms (3.1%)

prune213.0ms (2.5%)

simplify195.0ms (2.2%)

localize166.0ms (1.9%)

series243.0ms (2.8%)

simplify231.0ms (2.7%)

rewrite312.0ms (3.6%)

eval241.0ms (2.8%)

prune238.0ms (2.7%)

simplify235.0ms (2.7%)

localize203.0ms (2.3%)

series95.0ms (1.1%)

simplify278.0ms (3.2%)

rewrite339.0ms (3.9%)

eval257.0ms (3%)

prune204.0ms (2.3%)

regimes177.0ms (2%)

regimes133.0ms (1.5%)

regimes127.0ms (1.5%)

regimes15.0ms (0.2%)

regimes22.0ms (0.3%)

regimes27.0ms (0.3%)

regimes16.0ms (0.2%)

regimes11.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

soundness1.2s (13.6%)

preprocess76.0ms (0.9%)

end0.0ms (0%)

Profiling