Metrics for Migdal et al, Equation (64)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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)

sample1.3s (14.7%)

Memory

29.2MiB live, 1 494.9MiB allocated

Samples

1.0s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 642.0ms

ival-cos: 258.0ms (40.2% of total)

ival-mult: 216.0ms (33.6% of total)

ival-sqrt: 58.0ms (9% of total)

ival-div: 49.0ms (7.6% of total)

ival-add: 48.0ms (7.5% of total)

ival-true: 5.0ms (0.8% of total)

exact: 5.0ms (0.8% of total)

ival-assert: 4.0ms (0.6% of total)

Bogosity

explain263.0ms (2.9%)

Memory

4.1MiB live, 205.6MiB 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

76.0ms

512×

valid

Compiler

Compiled 138 to 40 computations (71% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 38.0ms (65.1% of total)

ival-cos: 11.0ms (18.9% of total)

ival-div: 3.0ms (5.1% of total)

ival-sqrt: 3.0ms (5.1% of total)

ival-add: 2.0ms (3.4% of total)

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

exact: 0.0ms (0% of total)

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

preprocess172.0ms (1.9%)

Memory

-42.0MiB live, 55.8MiB 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

1.0MiB live, 1.0MiB 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

5.3MiB live, 5.3MiB 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

localize44.0ms (0.5%)

Memory

4.8MiB live, 44.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 th)
accuracy	0.2265625	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
accuracy	0.2584762695368841	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
accuracy	0.721035009768442	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

36.0ms

256×

valid

Compiler

Compiled 58 to 14 computations (75.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 16.0ms (58.8% of total)

ival-cos: 6.0ms (22.1% of total)

ival-sqrt: 2.0ms (7.4% of total)

ival-div: 1.0ms (3.7% of total)

ival-add: 1.0ms (3.7% of total)

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

exact: 0.0ms (0% of total)

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

series36.0ms (0.4%)

Memory

-9.7MiB live, 29.4MiB 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
19.0ms	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)))

simplify366.0ms (4%)

Memory

24.5MiB live, 214.6MiB 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))))

rewrite322.0ms (3.5%)

Memory

-34.3MiB live, 174.7MiB 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))))

eval97.0ms (1.1%)

Memory: 28.3MiB live, 105.3MiB allocated
Compiler: Compiled 14 708 to 1 019 computations (93.1% saved)

prune269.0ms (2.9%)

Memory

-18.8MiB live, 182.1MiB allocated

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	474	16	490
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	475	16	491

Accuracy

100.0%

Counts

491 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	16.3%	(/.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))) (/.f64 (cos.f64 th) (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)))))
	16.3%	(/.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)))
▶	28.1%	(/.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)))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1))))
	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))))
▶	99.7%	(.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))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
▶	61.7%	#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)))
	49.5%	#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))))))
	55.6%	#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))))
	62.6%	#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 738 to 420 computations (43.1% saved)

simplify180.0ms (2%)

Memory

0.7MiB live, 156.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 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 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
cost-diff	2432	(/.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)))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
cost-diff	0	(*.f64 a1 a1)
cost-diff	0	(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff	384	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (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	(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
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	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

5 070×	`lower-*.f32`
5 046×	`lower-*.f64`
4 626×	`lower-fma.f32`
4 620×	`lower-fma.f64`
1 980×	`lower-+.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	304
0	67	281
1	124	277
2	311	269
3	1504	269
4	6401	269
0	8075	269

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

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

localize232.0ms (2.5%)

Memory

16.0MiB live, 217.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.08984375	(.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))))
accuracy	0.1328125	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
accuracy	0.721035009768442	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
accuracy	42.48234123607839	(/.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)))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.21712875976844204	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
accuracy	0.2701950195368841	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.09603500976844201	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
accuracy	0.24056625976844204	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.1328125	(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
accuracy	0.46484375	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.47265625	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	24.401830135439017	#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	0.140625	(*.f64 a2 (cos.f64 th))
accuracy	0.15625	(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	0.41796875	(*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.44921875	(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))

Samples

113.0ms

256×

valid

Compiler

Compiled 305 to 39 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-add: 47.0ms (53.7% of total)

ival-mult: 22.0ms (25.1% of total)

ival-div: 9.0ms (10.3% of total)

ival-cos: 6.0ms (6.9% of total)

ival-sqrt: 2.0ms (2.3% of total)

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

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

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

exact: 0.0ms (0% of total)

series170.0ms (1.9%)

Memory

1.6MiB live, 160.7MiB allocated

Counts

22 → 480

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

Calls

9 calls:

Time	Variable		Point	Expression
74.0ms	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) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) 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) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (sqrt 2) (cos th)) (/ (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (* (+ a1 a2) (- a1 a2))) (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/ (cos th) (sqrt 2)) (* a1 (sqrt 2)) (* a2 (sqrt 2)) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))))
39.0ms	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) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) 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) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (sqrt 2) (cos th)) (/ (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (* (+ a1 a2) (- a1 a2))) (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/ (cos th) (sqrt 2)) (* a1 (sqrt 2)) (* a2 (sqrt 2)) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))))
7.0ms	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) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) 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) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (sqrt 2) (cos th)) (/ (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (* (+ a1 a2) (- a1 a2))) (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/ (cos th) (sqrt 2)) (* a1 (sqrt 2)) (* a2 (sqrt 2)) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))))
6.0ms	th	@	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) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) 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) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (sqrt 2) (cos th)) (/ (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (* (+ a1 a2) (- a1 a2))) (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/ (cos th) (sqrt 2)) (* a1 (sqrt 2)) (* a2 (sqrt 2)) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))))
5.0ms	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) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) 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) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (sqrt 2) (cos th)) (/ (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (* (+ a1 a2) (- a1 a2))) (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/ (cos th) (sqrt 2)) (* a1 (sqrt 2)) (* a2 (sqrt 2)) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))))

simplify132.0ms (1.4%)

Memory

-3.9MiB live, 229.1MiB allocated

Algorithm

1×	egg-herbie

Rules

7 564×	`lower-fma.f64`
7 564×	`lower-fma.f32`
4 744×	`lower-*.f64`
4 744×	`lower-*.f32`
2 168×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	494	6819
1	1757	6376
2	6824	6313
0	8078	5942

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 479

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) (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)))
(/ 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)))
(/ (* (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 (/ (* (pow a2 4) (cos th)) (sqrt 2)))
(+ (* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2))) (/ (* a1 (* (cos th) (+ (* -1 (pow a2 3)) (pow a2 3)))) (sqrt 2)))
(+ (* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2))) (* a1 (+ (/ (* a1 (* (cos th) (+ (* -1 (pow a2 2)) (pow a2 2)))) (sqrt 2)) (/ (* (cos th) (+ (* -1 (pow a2 3)) (pow a2 3))) (sqrt 2)))))
(+ (* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2))) (* a1 (+ (* a1 (+ (/ (* a1 (* (cos th) (+ a2 (* -1 a2)))) (sqrt 2)) (/ (* (cos th) (+ (* -1 (pow a2 2)) (pow a2 2))) (sqrt 2)))) (/ (* (cos th) (+ (* -1 (pow a2 3)) (pow a2 3))) (sqrt 2)))))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* -1 (pow a2 4))
(+ (* -1 (pow a2 4)) (* a1 (+ (* -1 (pow a2 3)) (pow a2 3))))
(+ (* -1 (pow a2 4)) (* a1 (+ (* -1 (pow a2 3)) (+ (* a1 (+ (* -1 (pow a2 2)) (pow a2 2))) (pow a2 3)))))
(+ (* -1 (pow a2 4)) (* a1 (+ (* -1 (pow a2 3)) (+ (* a1 (+ (* -1 (pow a2 2)) (+ (* a1 (+ a2 (* -1 a2))) (pow a2 2)))) (pow a2 3)))))
(* (pow a1 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) (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)))))
(/ 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)))))
(/ (* (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 4) (cos th)) (sqrt 2))
(* (pow a1 4) (+ (/ (cos th) (sqrt 2)) (/ (* (cos th) (+ a2 (* -1 a2))) (* a1 (sqrt 2)))))
(* (pow a1 4) (+ (/ (cos th) (sqrt 2)) (+ (/ (* (cos th) (+ a2 (* -1 a2))) (* a1 (sqrt 2))) (/ (* (cos th) (+ (* -1 (pow a2 2)) (pow a2 2))) (* (pow a1 2) (sqrt 2))))))
(* (pow a1 4) (+ (/ (cos th) (sqrt 2)) (+ (/ (* (cos th) (+ a2 (* -1 a2))) (* a1 (sqrt 2))) (+ (/ (* (cos th) (+ (* -1 (pow a2 2)) (pow a2 2))) (* (pow a1 2) (sqrt 2))) (/ (* (cos th) (+ (* -1 (pow a2 3)) (pow a2 3))) (* (pow a1 3) (sqrt 2)))))))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(pow a1 4)
(* (pow a1 4) (+ 1 (+ (* -1 (/ a2 a1)) (/ a2 a1))))
(* (pow a1 4) (+ 1 (+ (* -1 (/ a2 a1)) (+ (* -1 (/ (pow a2 2) (pow a1 2))) (+ (/ a2 a1) (/ (pow a2 2) (pow a1 2)))))))
(* (pow a1 4) (+ 1 (+ (* -1 (/ a2 a1)) (+ (* -1 (/ (pow a2 2) (pow a1 2))) (+ (* -1 (/ (pow a2 3) (pow a1 3))) (+ (/ a2 a1) (+ (/ (pow a2 2) (pow a1 2)) (/ (pow a2 3) (pow a1 3)))))))))
(* (pow a1 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) (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)))))
(/ 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)))))
(/ (* (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 4) (cos th)) (sqrt 2))
(* (pow a1 4) (+ (/ (cos th) (sqrt 2)) (/ (* (cos th) (+ a2 (* -1 a2))) (* a1 (sqrt 2)))))
(* (pow a1 4) (+ (* -1 (/ (+ (* -1 (/ (* (cos th) (+ a2 (* -1 a2))) (sqrt 2))) (/ (* (cos th) (+ (* -1 (pow a2 2)) (pow a2 2))) (* a1 (sqrt 2)))) a1)) (/ (cos th) (sqrt 2))))
(* (pow a1 4) (+ (* -1 (/ (+ (* -1 (/ (* (cos th) (+ a2 (* -1 a2))) (sqrt 2))) (* -1 (/ (+ (* -1 (/ (* (cos th) (+ (* -1 (pow a2 2)) (pow a2 2))) (sqrt 2))) (/ (* (cos th) (+ (* -1 (pow a2 3)) (pow a2 3))) (* a1 (sqrt 2)))) a1))) a1)) (/ (cos th) (sqrt 2))))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(* a1 (sqrt 2))
(pow a1 4)
(* (pow a1 4) (+ 1 (+ (* -1 (/ a2 a1)) (/ a2 a1))))
(* (pow a1 4) (+ 1 (* -1 (/ (+ (* -1 (+ a2 (* -1 a2))) (+ (* -1 (/ (pow a2 2) a1)) (/ (pow a2 2) a1))) a1))))
(* (pow a1 4) (+ 1 (* -1 (/ (+ (* -1 (+ a2 (* -1 a2))) (* -1 (/ (+ (* -1 (+ (* -1 (pow a2 2)) (pow a2 2))) (+ (* -1 (/ (pow a2 3) a1)) (/ (pow a2 3) a1))) a1))) a1))))
(+ (* (pow a1 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)
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(+ (sqrt 2) (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(+ (sqrt 2) (* (pow th 2) (- (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/720 (sqrt 2)) (+ (* 1/48 (sqrt 2)) (* 1/2 (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(/ (+ (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))))
(/ (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2))) (sqrt 2))
(+ (* -1/2 (/ (* (pow th 2) (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2)))) (sqrt 2))) (/ (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2))) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2))) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2)))) (sqrt 2))))) (/ (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2))) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2))) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2)))) (sqrt 2))) (* 1/24 (/ (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2))) (sqrt 2))))))) (/ (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2))) (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)))
(+ (* (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 (+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* 1/2 (+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* 1/2 (+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* 1/2 (+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(cos th)
(cos th)
(cos th)
(cos th)
(+ (/ (* (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)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (* (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) (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2)))) (sqrt 2))
(/ (* (cos th) (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2)))) (sqrt 2))
(/ (* (cos th) (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2)))) (sqrt 2))
(/ (* (cos th) (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2)))) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 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))))
(* 1/2 (+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* 1/2 (+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* 1/2 (+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* 1/2 (+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(cos th)
(cos th)
(cos th)
(cos th)
(+ (/ (* (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)))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (* (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) (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2)))) (sqrt 2))
(/ (* (cos th) (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2)))) (sqrt 2))
(/ (* (cos th) (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2)))) (sqrt 2))
(/ (* (cos th) (* (+ a1 a2) (* (+ (pow a1 2) (pow a2 2)) (- a1 a2)))) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 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))))
(* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(/ (* (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 a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (* (pow 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 a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(pow a1 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 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 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 a1 4) (cos th)) (sqrt 2))
(+ (/ (* a2 (* (cos th) (+ (* -1 (pow a1 3)) (pow a1 3)))) (sqrt 2)) (/ (* (pow a1 4) (cos th)) (sqrt 2)))
(+ (* a2 (+ (/ (* a2 (* (cos th) (+ (* -1 (pow a1 2)) (pow a1 2)))) (sqrt 2)) (/ (* (cos th) (+ (* -1 (pow a1 3)) (pow a1 3))) (sqrt 2)))) (/ (* (pow a1 4) (cos th)) (sqrt 2)))
(+ (* a2 (+ (* a2 (+ (/ (* a2 (* (cos th) (+ a1 (* -1 a1)))) (sqrt 2)) (/ (* (cos th) (+ (* -1 (pow a1 2)) (pow a1 2))) (sqrt 2)))) (/ (* (cos th) (+ (* -1 (pow a1 3)) (pow a1 3))) (sqrt 2)))) (/ (* (pow a1 4) (cos th)) (sqrt 2)))
(* a2 (sqrt 2))
(* a2 (sqrt 2))
(* a2 (sqrt 2))
(* a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(pow a1 4)
(+ (* a2 (+ (* -1 (pow a1 3)) (pow a1 3))) (pow a1 4))
(+ (* a2 (+ (* -1 (pow a1 3)) (+ (* a2 (+ (* -1 (pow a1 2)) (pow a1 2))) (pow a1 3)))) (pow a1 4))
(+ (* a2 (+ (* -1 (pow a1 3)) (+ (* a2 (+ (* -1 (pow a1 2)) (+ (* a2 (+ a1 (* -1 a1))) (pow a1 2)))) (pow a1 3)))) (pow a1 4))
(* (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))))
(* 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)))))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(/ (* (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) (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)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2)))
(* (pow a2 4) (+ (* -1 (/ (cos th) (sqrt 2))) (/ (* (cos th) (+ a1 (* -1 a1))) (* a2 (sqrt 2)))))
(* (pow a2 4) (+ (* -1 (/ (cos th) (sqrt 2))) (+ (/ (* (cos th) (+ a1 (* -1 a1))) (* a2 (sqrt 2))) (/ (* (cos th) (+ (* -1 (pow a1 2)) (pow a1 2))) (* (pow a2 2) (sqrt 2))))))
(* (pow a2 4) (+ (* -1 (/ (cos th) (sqrt 2))) (+ (/ (* (cos th) (+ a1 (* -1 a1))) (* a2 (sqrt 2))) (+ (/ (* (cos th) (+ (* -1 (pow a1 2)) (pow a1 2))) (* (pow a2 2) (sqrt 2))) (/ (* (cos th) (+ (* -1 (pow a1 3)) (pow a1 3))) (* (pow a2 3) (sqrt 2)))))))
(* a2 (sqrt 2))
(* a2 (sqrt 2))
(* a2 (sqrt 2))
(* a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(* -1 (pow a2 4))
(* (pow a2 4) (- (+ (* -1 (/ a1 a2)) (/ a1 a2)) 1))
(* (pow a2 4) (- (+ (* -1 (/ a1 a2)) (+ (* -1 (/ (pow a1 2) (pow a2 2))) (+ (/ a1 a2) (/ (pow a1 2) (pow a2 2))))) 1))
(* (pow a2 4) (- (+ (* -1 (/ a1 a2)) (+ (* -1 (/ (pow a1 2) (pow a2 2))) (+ (* -1 (/ (pow a1 3) (pow a2 3))) (+ (/ a1 a2) (+ (/ (pow a1 2) (pow a2 2)) (/ (pow a1 3) (pow a2 3))))))) 1))
(* (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))))
(* 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)))))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(* a2 (cos th))
(/ (* (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) (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)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2)))
(* (pow a2 4) (+ (* -1 (/ (cos th) (sqrt 2))) (* -1 (/ (* (cos th) (+ a1 (* -1 a1))) (* a2 (sqrt 2))))))
(* (pow a2 4) (+ (* -1 (/ (cos th) (sqrt 2))) (* -1 (/ (+ (* -1 (/ (* (cos th) (+ (* -1 (pow a1 2)) (pow a1 2))) (* a2 (sqrt 2)))) (/ (* (cos th) (+ a1 (* -1 a1))) (sqrt 2))) a2))))
(* (pow a2 4) (+ (* -1 (/ (cos th) (sqrt 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (cos th) (+ (* -1 (pow a1 3)) (pow a1 3))) (* a2 (sqrt 2)))) (/ (* (cos th) (+ (* -1 (pow a1 2)) (pow a1 2))) (sqrt 2))) a2)) (/ (* (cos th) (+ a1 (* -1 a1))) (sqrt 2))) a2))))
(* 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))
(* -1 (pow a2 4))
(* (pow a2 4) (- (* -1 (/ (+ a1 (* -1 a1)) a2)) 1))
(* (pow a2 4) (- (* -1 (/ (+ a1 (+ (* -1 a1) (* -1 (/ (+ (* -1 (pow a1 2)) (pow a1 2)) a2)))) a2)) 1))
(* (pow a2 4) (- (* -1 (/ (+ a1 (+ (* -1 a1) (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow a1 3)) (pow a1 3)) a2)) (+ (* -1 (pow a1 2)) (pow a1 2))) a2)))) a2)) 1))

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

rewrite234.0ms (2.6%)

Memory

21.8MiB live, 460.7MiB allocated

Rules

5 726×	`lower-/.f32`
5 712×	`lower-/.f64`
5 072×	`lower-fma.f32`
5 066×	`lower-fma.f64`
3 930×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	226
0	67	219
1	227	207
2	1874	207
0	8600	205

Stop Event

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

Counts

22 → 1 159

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

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

eval243.0ms (2.7%)

Memory: -15.7MiB live, 570.6MiB allocated
Compiler: Compiled 50 942 to 3 031 computations (94.1% saved)

prune224.0ms (2.5%)

Memory

3.4MiB live, 652.4MiB allocated

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	1 851	29	1 880
Fresh	8	3	11
Picked	5	0	5
Done	0	0	0
Total	1 864	32	1 896

Accuracy

100.0%

Counts

1 896 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	55.6%	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (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)))))
	62.6%	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
▶	99.6%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
	53.1%	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (fma.f64 (fma.f64 (fma.f64 (neg.f64 th) (.f64 th (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/360 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/48 binary64)))) (.f64 #s(literal 5/24 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 th th) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))
	56.6%	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	61.7%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
	14.8%	(/.f64 #s(approx (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/.f64 (.f64 (.f64 (-.f64 a1 a2) (fma.f64 a1 a1 (.f64 a2 a2))) (+.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))))
	98.5%	(.f64 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 #s(approx (cos th) #s(literal 1 binary64))) (.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))))
▶	61.1%	(.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))))
	55.6%	(.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))))
	62.6%	(.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))))
	28.0%	(.f64 (/.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 a1 a1) a1) a1) (.f64 (.f64 (.f64 a2 a2) a2) a2)) (.f64 (-.f64 a1 a2) (+.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	99.2%	(.f64 (/.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) (cos.f64 th))
	61.7%	(.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))
	99.2%	(.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))
▶	99.2%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
	61.7%	#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))))
	61.7%	#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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
	61.7%	#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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
▶	61.6%	#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)))
	61.7%	#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 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	61.6%	#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)))))
	51.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
	61.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	30.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)))))
	62.6%	#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))))
	30.3%	#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))))
	61.4%	#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))))))
▶	13.3%	#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 1 328 to 786 computations (40.8% saved)

simplify32.0ms (0.3%)

Memory

12.8MiB live, 52.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (cos.f64 th) a2)
cost-diff	0	(.f64 (.f64 (cos.f64 th) a2) a2)
cost-diff	0	(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) 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)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(.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))))
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 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2)))
cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2)
cost-diff	1344	(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))
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 a1 a1)
cost-diff	0	(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff	384	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))

Rules

852×	`lower-fma.f32`
842×	`lower-fma.f64`
646×	`lower-*.f32`
630×	`lower-*.f64`
312×	`associate-r`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	51	354
0	81	345
1	131	331
2	200	329
3	393	329
4	755	329
5	1039	314
6	1166	314
7	1194	314
8	1217	314
9	1229	314
0	1229	314

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize112.0ms (1.2%)

Memory

-0.6MiB live, 317.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0546875	(.f64 (.f64 (cos.f64 th) a2) a2)
accuracy	0.140625	(*.f64 (cos.f64 th) a2)
accuracy	0.22722626953688405	(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.22914589688607095	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.09603500976844201	(.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))))
accuracy	0.24056625976844204	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.3149730304024824	(fma.f64 #s(literal -1/720 binary64) (*.f64 th th) #s(literal 1/24 binary64))
accuracy	32.99516537230372	#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)))
accuracy	0.41796875	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2)
accuracy	0.46484375	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	24.401830135439017	#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)))
accuracy	0.12890625	(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.46484375	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	24.401830135439017	#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	54.43907961434165	#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0	(cos.f64 th)
accuracy	0.21712875976844204	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.58203125	(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.721035009768442	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

83.0ms

256×

valid

Compiler

Compiled 282 to 45 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-mult: 23.0ms (39% of total)

ival-div: 15.0ms (25.5% of total)

ival-add: 7.0ms (11.9% of total)

ival-cos: 6.0ms (10.2% of total)

const: 6.0ms (10.2% of total)

ival-sqrt: 2.0ms (3.4% of total)

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

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

exact: 0.0ms (0% of total)

series40.0ms (0.4%)

Memory

-3.6MiB live, 116.9MiB allocated

Counts

22 → 456

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	a1	@	-inf	((/ 1 (/ (cos th) (sqrt 2))) (/ (+ (* a2 a2) (* a1 a1)) (/ 1 (/ (cos th) (sqrt 2)))) (+ (* 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)) (* a1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2)) (+ (* (/ a1 (sqrt 2)) a1) (* (* (/ 1 (sqrt 2)) a2) a2)) (* (/ 1 (sqrt 2)) a2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (* (* (cos th) a2) a2) (sqrt 2)) (* (* (cos th) a2) a2) (* (cos th) a2) (/ (cos th) (sqrt 2)) (cos th) (/ 1 (sqrt 2)) (cos th) (+ (* -1/720 (* th th)) 1/24))
3.0ms	a2	@	-inf	((/ 1 (/ (cos th) (sqrt 2))) (/ (+ (* a2 a2) (* a1 a1)) (/ 1 (/ (cos th) (sqrt 2)))) (+ (* 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)) (* a1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2)) (+ (* (/ a1 (sqrt 2)) a1) (* (* (/ 1 (sqrt 2)) a2) a2)) (* (/ 1 (sqrt 2)) a2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (* (* (cos th) a2) a2) (sqrt 2)) (* (* (cos th) a2) a2) (* (cos th) a2) (/ (cos th) (sqrt 2)) (cos th) (/ 1 (sqrt 2)) (cos th) (+ (* -1/720 (* th th)) 1/24))
3.0ms	a2	@	inf	((/ 1 (/ (cos th) (sqrt 2))) (/ (+ (* a2 a2) (* a1 a1)) (/ 1 (/ (cos th) (sqrt 2)))) (+ (* 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)) (* a1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2)) (+ (* (/ a1 (sqrt 2)) a1) (* (* (/ 1 (sqrt 2)) a2) a2)) (* (/ 1 (sqrt 2)) a2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (* (* (cos th) a2) a2) (sqrt 2)) (* (* (cos th) a2) a2) (* (cos th) a2) (/ (cos th) (sqrt 2)) (cos th) (/ 1 (sqrt 2)) (cos th) (+ (* -1/720 (* th th)) 1/24))
2.0ms	th	@	inf	((/ 1 (/ (cos th) (sqrt 2))) (/ (+ (* a2 a2) (* a1 a1)) (/ 1 (/ (cos th) (sqrt 2)))) (+ (* 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)) (* a1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2)) (+ (* (/ a1 (sqrt 2)) a1) (* (* (/ 1 (sqrt 2)) a2) a2)) (* (/ 1 (sqrt 2)) a2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (* (* (cos th) a2) a2) (sqrt 2)) (* (* (cos th) a2) a2) (* (cos th) a2) (/ (cos th) (sqrt 2)) (cos th) (/ 1 (sqrt 2)) (cos th) (+ (* -1/720 (* th th)) 1/24))
2.0ms	th	@	-inf	((/ 1 (/ (cos th) (sqrt 2))) (/ (+ (* a2 a2) (* a1 a1)) (/ 1 (/ (cos th) (sqrt 2)))) (+ (* 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)) (* a1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2)) (+ (* (/ a1 (sqrt 2)) a1) (* (* (/ 1 (sqrt 2)) a2) a2)) (* (/ 1 (sqrt 2)) a2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (* (* (cos th) a2) a2) (sqrt 2)) (* (* (cos th) a2) a2) (* (cos th) a2) (/ (cos th) (sqrt 2)) (cos th) (/ 1 (sqrt 2)) (cos th) (+ (* -1/720 (* th th)) 1/24))

simplify183.0ms (2%)

Memory

-1.5MiB live, 313.7MiB allocated

Algorithm

1×	egg-herbie

Rules

14 636×	`lower-fma.f64`
14 636×	`lower-fma.f32`
5 384×	`lower-*.f64`
5 384×	`lower-*.f32`
3 338×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	194	5710
1	615	4921
2	2131	4685
3	4970	4446
0	8398	4139

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 455

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

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

rewrite202.0ms (2.2%)

Memory

33.1MiB live, 420.6MiB allocated

Rules

5 280×	`lower-/.f32`
5 266×	`lower-/.f64`
4 892×	`lower-*.f32`
4 876×	`lower-*.f64`
4 136×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	269
0	81	243
1	273	242
2	1813	242
0	8851	242

Stop Event

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

Counts

22 → 1 048

Calls

Call 1

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

Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))
(.f64 (pow.f64 (.f64 (cos.f64 th) #s(literal 1 binary64)) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (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 #s(literal 1 binary64) (neg.f64 (cos.f64 th))) (pow.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th))))
(*.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (/.f64 #s(literal -1 binary64) (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 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) #s(literal 1 binary64)))
(*.f64 (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)))
(pow.f64 (exp.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1 binary64))
(pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (neg.f64 (neg.f64 (cos.f64 th)))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (neg.f64 (cos.f64 th))))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th))) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (neg.f64 (cos.f64 th))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th)))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (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 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 th))) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (+.f64 a2 a1)) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (-.f64 a2 a1)))
(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a2 a1)) (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (-.f64 a2 a1)))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 a2 a2) a2) a2 (.f64 (.f64 a1 a1) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (fma.f64 (.f64 (.f64 a2 a2) a2) a2 (.f64 (.f64 a1 a1) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))))
(.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1/2 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))))
(.f64 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))))
(.f64 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.f64 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(.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))) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 a2 a2) a2) a2 (.f64 (.f64 a1 a1) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1/2 binary64))))
(.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))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 a2 a2) a2) a2 (.f64 (.f64 a1 a1) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.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))) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 a2 a2) a2) a2 (.f64 (.f64 a1 a1) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))) (sqrt.f64 #s(literal 2 binary64))))
(.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))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 a2 a2) a2) a2 (.f64 (.f64 a1 a1) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 th)))))
(.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))) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 a2 a2) a2) a2 (.f64 (.f64 a1 a1) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))))
(.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))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 a2 a2) a2) a2 (.f64 (.f64 a1 a1) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))) #s(literal 1 binary64)))
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(fma.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 #s(literal 1 binary64) (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (/.f64 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 th) a1) a1) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 a2 a2) a2) a2) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1)))) (/.f64 (.f64 (.f64 (.f64 a1 a1) a1) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1)))))
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(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a1 (/.f64 #s(literal 1 binary64) a1)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
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(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
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(/.f64 (neg.f64 (neg.f64 (neg.f64 (cos.f64 th)))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (cos.f64 th) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 (cos.f64 th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(/.f64 (neg.f64 (neg.f64 (cos.f64 th))) (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (cos.f64 th))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (cos.f64 th)) (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (cos.f64 th)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(neg.f64 (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (cos.f64 th) (.f64 #s(literal 1 binary64) (neg.f64 (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 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64)))
(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) (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 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 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 (neg.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
#s(approx (cos th) (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))
(.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(.f64 (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 th th) #s(literal -1/17280 binary64))))))
(pow.f64 (/.f64 (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/576 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) #s(literal -1/17280 binary64)))) (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th))))) (neg.f64 (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 th th) #s(literal -1/720 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/576 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) #s(literal -1/17280 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th))) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/576 binary64))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(/.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)))) (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 th th) #s(literal -1/720 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/576 binary64))) (neg.f64 (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 (*.f64 th th) #s(literal -1/17280 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) #s(literal -1/17280 binary64))))))
(/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/576 binary64)) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 (*.f64 th th) #s(literal -1/17280 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) #s(literal -1/17280 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/576 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) #s(literal -1/17280 binary64)))) (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1/576 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 th th) #s(literal -1/17280 binary64)))) (fma.f64 (.f64 (.f64 th th) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))))
(fma.f64 (*.f64 #s(literal -1/720 binary64) th) th #s(literal 1/24 binary64))
(fma.f64 (*.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 th th) #s(literal 1/24 binary64))
(fma.f64 th (*.f64 #s(literal -1/720 binary64) th) #s(literal 1/24 binary64))
(-.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 th th) #s(literal -1/720 binary64)))) (/.f64 (.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th))) (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 th th) #s(literal -1/720 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (.f64 (.f64 th th) (.f64 th th))) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(+.f64 (.f64 (.f64 th th) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 (.f64 th th) #s(literal -1/720 binary64)))

eval240.0ms (2.6%)

Memory: 9.6MiB live, 602.7MiB allocated
Compiler: Compiled 38 010 to 2 912 computations (92.3% saved)

prune269.0ms (2.9%)

Memory

-49.3MiB live, 769.2MiB allocated

Pruning

40 alts after pruning (37 fresh and 3 done)

	Pruned	Kept	Total
New	1 622	22	1 644
Fresh	12	15	27
Picked	2	3	5
Done	0	0	0
Total	1 636	40	1 676

Accuracy

100.0%

Counts

1 676 → 40

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.6%	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	99.2%	(/.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
	14.8%	(/.f64 #s(approx (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/.f64 (.f64 (.f64 (-.f64 a1 a2) (fma.f64 a1 a1 (.f64 a2 a2))) (+.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
	98.5%	(.f64 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 #s(approx (cos th) #s(literal 1 binary64))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64))
	28.0%	(.f64 (/.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 a1 a1) a1) a1) (.f64 (.f64 (.f64 a2 a2) a2) a2)) (.f64 (-.f64 a1 a2) (+.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	99.2%	(.f64 (/.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
▶	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) (cos.f64 th))
	15.7%	(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) 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))))
	61.7%	(.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))
	99.2%	(.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))
✓	99.2%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
	60.8%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
	55.3%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
	61.6%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
▶	62.3%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
	61.4%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	98.9%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2))))
▶	99.2%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
	99.2%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 a2 #s(literal -1 binary64)) (/.f64 (neg.f64 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))))
	99.1%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2))
	62.3%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
	61.4%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
	61.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
	61.7%	#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))))
	61.7%	#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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
	61.7%	#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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
	61.7%	#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 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) a2) a2)))
✓	61.6%	#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)))
	61.7%	#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 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	61.6%	#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)))))
	51.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
	61.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	30.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
▶	13.3%	#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)))))
	13.3%	#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 (sqrt.f64 #s(literal 2 binary64)) a1))))
	13.3%	#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)))))
▶	30.3%	#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))))
✓	13.3%	#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))))))
	13.3%	#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)))))
	13.3%	#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))))

Compiler

Compiled 1 416 to 863 computations (39.1% saved)

simplify141.0ms (1.5%)

Memory

9.9MiB live, 203.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 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 a2 a2))
cost-diff	0	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.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	704	(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	1600	(.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 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))
cost-diff	0	#s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2)))
cost-diff	0	(/.f64 #s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(*.f64 a1 a1)
cost-diff	0	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
cost-diff	0	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) (cos.f64 th))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))

Rules

7 798×	`lower-*.f32`
7 780×	`lower-*.f64`
5 206×	`lower-fma.f32`
5 200×	`lower-fma.f64`
2 348×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	419
0	78	396
1	125	394
2	204	390
3	436	374
4	926	356
5	1695	356
6	2062	356
7	2338	356
8	3023	356
9	3398	356
10	3880	356
11	4793	356
12	7738	356
0	8121	355

Stop Event

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

Calls

Call 1

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

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

localize108.0ms (1.2%)

Memory

18.5MiB live, 215.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 th)
accuracy	0.22914589688607095	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
accuracy	0.2584762695368841	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
accuracy	0.721035009768442	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
accuracy	3.6512808493390327	(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	6.522190060440041	(/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
accuracy	24.401830135439017	#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	26.005777436354666	(.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	0.22722626953688405	(/.f64 #s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.22914589688607095	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
accuracy	2.964499113125465	(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))
accuracy	24.229912874651365	#s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.205410009768442	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
accuracy	24.401830135439017	#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)))))
accuracy	54.43907961434165	#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0	(cos.f64 th)
accuracy	0.09603500976844201	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) (cos.f64 th))
accuracy	0.3156228096636605	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
accuracy	0.3886860673852279	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))

Samples

80.0ms

256×

valid

Compiler

Compiled 296 to 43 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 26.0ms (45.3% of total)

ival-div: 17.0ms (29.6% of total)

ival-add: 6.0ms (10.5% of total)

ival-cos: 6.0ms (10.5% of total)

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

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

exact: 0.0ms (0% of total)

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

series62.0ms (0.7%)

Memory

7.0MiB live, 126.2MiB allocated

Counts

21 → 492

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
8.0ms	th	@	inf	((/ 1 (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (* (/ 1 (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (cos th)) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (sqrt 2) (+ (* (/ (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 a1) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (* (* (cos th) a2) a2) (sqrt 2)) (* (* (cos th) a2) a2) (* (+ (* -1/2 (* th th)) 1) (* 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)) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (* (/ (cos th) (sqrt 2)) (* a2 a2)) (/ (cos th) (sqrt 2)) (cos th) (/ a2 (* (* a1 (sqrt 2)) a1)))
7.0ms	a1	@	inf	((/ 1 (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (* (/ 1 (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (cos th)) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (sqrt 2) (+ (* (/ (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 a1) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (* (* (cos th) a2) a2) (sqrt 2)) (* (* (cos th) a2) a2) (* (+ (* -1/2 (* th th)) 1) (* 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)) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (* (/ (cos th) (sqrt 2)) (* a2 a2)) (/ (cos th) (sqrt 2)) (cos th) (/ a2 (* (* a1 (sqrt 2)) a1)))
6.0ms	a2	@	inf	((/ 1 (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (* (/ 1 (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (cos th)) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (sqrt 2) (+ (* (/ (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 a1) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (* (* (cos th) a2) a2) (sqrt 2)) (* (* (cos th) a2) a2) (* (+ (* -1/2 (* th th)) 1) (* 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)) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (* (/ (cos th) (sqrt 2)) (* a2 a2)) (/ (cos th) (sqrt 2)) (cos th) (/ a2 (* (* a1 (sqrt 2)) a1)))
4.0ms	a2	@	0	((/ 1 (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (* (/ 1 (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (cos th)) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (sqrt 2) (+ (* (/ (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 a1) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (* (* (cos th) a2) a2) (sqrt 2)) (* (* (cos th) a2) a2) (* (+ (* -1/2 (* th th)) 1) (* 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)) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (* (/ (cos th) (sqrt 2)) (* a2 a2)) (/ (cos th) (sqrt 2)) (cos th) (/ a2 (* (* a1 (sqrt 2)) a1)))
4.0ms	a2	@	-inf	((/ 1 (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (* (/ 1 (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (cos th)) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (sqrt 2) (+ (* (/ (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 a1) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/ (* (* (cos th) a2) a2) (sqrt 2)) (* (* (cos th) a2) a2) (* (+ (* -1/2 (* th th)) 1) (* 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)) (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (* (/ (cos th) (sqrt 2)) (* a2 a2)) (/ (cos th) (sqrt 2)) (cos th) (/ a2 (* (* a1 (sqrt 2)) a1)))

simplify215.0ms (2.4%)

Memory

12.2MiB live, 325.0MiB allocated

Algorithm

1×	egg-herbie

Rules

16 170×	`lower-fma.f64`
16 170×	`lower-fma.f32`
5 070×	`lower-*.f64`
5 070×	`lower-*.f32`
3 958×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	227	7129
1	690	6349
2	2272	6099
3	5553	6099
0	8661	5750

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 492

Calls

Call 1

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

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

rewrite195.0ms (2.1%)

Memory

-2.0MiB live, 273.8MiB allocated

Rules

5 198×	`lower-/.f32`
5 184×	`lower-/.f64`
4 570×	`lower-*.f32`
4 552×	`lower-*.f64`
3 082×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	349
0	78	333
1	262	309
2	1987	309
0	8851	309

Stop Event

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

Counts

21 → 954

Calls

Call 1

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

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

eval211.0ms (2.3%)

Memory: 5.4MiB live, 349.4MiB allocated
Compiler: Compiled 35 973 to 3 109 computations (91.4% saved)

prune249.0ms (2.7%)

Memory

29.0MiB live, 380.1MiB allocated

Pruning

44 alts after pruning (38 fresh and 6 done)

	Pruned	Kept	Total
New	1 544	10	1 554
Fresh	4	28	32
Picked	2	3	5
Done	0	3	3
Total	1 550	44	1 594

Accuracy

100.0%

Counts

1 594 → 44

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.6%	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	99.2%	(/.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
	14.8%	(/.f64 #s(approx (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/.f64 (.f64 (.f64 (-.f64 a1 a2) (fma.f64 a1 a1 (.f64 a2 a2))) (+.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
	98.5%	(.f64 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 #s(approx (cos th) #s(literal 1 binary64))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64))
	28.0%	(.f64 (/.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 a1 a1) a1) a1) (.f64 (.f64 (.f64 a2 a2) a2) a2)) (.f64 (-.f64 a1 a2) (+.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	99.2%	(.f64 (/.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	61.7%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) #s(approx (cos th) #s(literal 1 binary64)))
	98.9%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (+ ( a1 a1) (* a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))) (cos.f64 th))
	15.7%	(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) 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))))
	61.7%	(.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))
	99.2%	(.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))
✓	99.2%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
	60.8%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
	55.3%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
	61.6%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
✓	62.3%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
	61.4%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	21.0%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (sqrt.f64 #s(literal 2 binary64))))
	98.9%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2))))
✓	99.2%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
	61.3%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
	99.2%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 a2 #s(literal -1 binary64)) (/.f64 (neg.f64 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))))
	61.5%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx ( (* (cos th) a2) a2) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) a2) a2))))
	99.1%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2))
	62.3%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
	61.4%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
	39.3%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (fma.f64 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) a2 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a1) a1)))
	61.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
	61.7%	#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))))
	61.7%	#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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
	61.7%	#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 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) a2) a2)))
✓	61.6%	#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)))
	61.6%	#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)))))
	51.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
	61.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	30.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
✓	13.3%	#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)))))
	13.3%	#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 (sqrt.f64 #s(literal 2 binary64)) a1))))
	13.3%	#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)))))
	26.0%	#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 (fma.f64 a2 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) #s(literal 1 binary64))) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) (sqrt.f64 #s(literal 2 binary64)))) (.f64 a1 a1))))
	25.7%	#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 #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))))
✓	13.3%	#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))))))
	13.3%	#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)))))
	13.3%	#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))))

Compiler

Compiled 2 158 to 733 computations (66% saved)

regimes186.0ms (2%)

Memory

-38.2MiB live, 260.5MiB allocated

Counts

78 → 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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (*.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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 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))
#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 (sqrt.f64 #s(literal 2 binary64)) a1))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) 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 #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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx ( (* (cos th) a2) a2) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) a2) a2))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) #s(approx (cos th) #s(literal 1 binary64)))
(.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 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (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)))
#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))))
#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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) 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))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (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)))))
#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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (fma.f64 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) a2 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.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))))
#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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(.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))))
(/.f64 #s(approx (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/.f64 (.f64 (.f64 (-.f64 a1 a2) (fma.f64 a1 a1 (.f64 a2 a2))) (+.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (/.f64 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 (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))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 a2 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) #s(literal 1 binary64))) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) (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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (fma.f64 (fma.f64 (fma.f64 (neg.f64 th) (.f64 th (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/360 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/48 binary64)))) (.f64 #s(literal 5/24 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 th th) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 th th) (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))
#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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 #s(literal 1 binary64) (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 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) a2) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2))))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (+ ( a1 a1) (* a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))) (cos.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) (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 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 a2 #s(literal -1 binary64)) (/.f64 (neg.f64 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) (cos.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))))
(/.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (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 #s(approx (cos th) #s(literal 1 binary64))) (.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))) (.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 (.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)))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
(.f64 (/.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 a1 a1) a1) a1) (.f64 (.f64 (.f64 a2 a2) a2) a2)) (.f64 (-.f64 a1 a2) (+.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 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))) (/.f64 (cos.f64 th) (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 (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)))

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))

Calls

8 calls:

23.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
23.0ms	th
22.0ms	a2
22.0ms	a1
21.0ms	(*.f64 a1 a1)

Results

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

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes165.0ms (1.8%)

Memory

14.8MiB live, 206.9MiB 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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (*.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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 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))
#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 (sqrt.f64 #s(literal 2 binary64)) a1))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) 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 #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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx ( (* (cos th) a2) a2) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) a2) a2))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) #s(approx (cos th) #s(literal 1 binary64)))
(.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 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (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)))
#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))))
#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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) 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))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (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)))))
#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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (fma.f64 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) a2 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.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))))
#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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(.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))))
(/.f64 #s(approx (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/.f64 (.f64 (.f64 (-.f64 a1 a2) (fma.f64 a1 a1 (.f64 a2 a2))) (+.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (/.f64 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 (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))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 a2 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) #s(literal 1 binary64))) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) (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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (fma.f64 (fma.f64 (fma.f64 (neg.f64 th) (.f64 th (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/360 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/48 binary64)))) (.f64 #s(literal 5/24 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 th th) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 th th) (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))
#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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 #s(literal 1 binary64) (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 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) a2) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2))))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (+ ( a1 a1) (* a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))) (cos.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) (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 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 a2 #s(literal -1 binary64)) (/.f64 (neg.f64 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) (cos.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))))
(/.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (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 #s(approx (cos th) #s(literal 1 binary64))) (.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))) (.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 (.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)))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
(.f64 (/.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 a1 a1) a1) a1) (.f64 (.f64 (.f64 a2 a2) a2) a2)) (.f64 (-.f64 a1 a2) (+.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 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))) (/.f64 (cos.f64 th) (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 (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))))

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

Calls

8 calls:

21.0ms	a1
21.0ms	th
21.0ms	(cos.f64 th)
20.0ms	(*.f64 a2 a2)
20.0ms	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)

regimes127.0ms (1.4%)

Memory

7.1MiB live, 161.6MiB allocated

Counts

57 → 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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (*.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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 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))
#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 (sqrt.f64 #s(literal 2 binary64)) a1))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) 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 #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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx ( (* (cos th) a2) a2) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) a2) a2))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) #s(approx (cos th) #s(literal 1 binary64)))
(.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 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (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)))
#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))))
#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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) 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))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (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)))))
#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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (fma.f64 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) a2 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.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))))
#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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(.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))))
(/.f64 #s(approx (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/.f64 (.f64 (.f64 (-.f64 a1 a2) (fma.f64 a1 a1 (.f64 a2 a2))) (+.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (/.f64 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 (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))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 a2 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) #s(literal 1 binary64))) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) (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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (fma.f64 (fma.f64 (fma.f64 (neg.f64 th) (.f64 th (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/360 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/48 binary64)))) (.f64 #s(literal 5/24 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 th th) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 th th) (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))
#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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 #s(literal 1 binary64) (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))))

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

Calls

8 calls:

17.0ms	(*.f64 a2 a2)
16.0ms	a2
16.0ms	(cos.f64 th)
15.0ms	a1
15.0ms	th

Results

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

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes127.0ms (1.4%)

Memory

-1.6MiB live, 156.9MiB allocated

Counts

55 → 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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (*.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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 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))
#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 (sqrt.f64 #s(literal 2 binary64)) a1))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) 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 #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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx ( (* (cos th) a2) a2) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) a2) a2))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) #s(approx (cos th) #s(literal 1 binary64)))
(.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 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (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)))
#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))))
#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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) 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))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (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)))))
#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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (fma.f64 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) a2 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.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))))
#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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(.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))))
(/.f64 #s(approx (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/.f64 (.f64 (.f64 (-.f64 a1 a2) (fma.f64 a1 a1 (.f64 a2 a2))) (+.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (/.f64 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 (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))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 a2 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) #s(literal 1 binary64))) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) (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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (fma.f64 (fma.f64 (fma.f64 (neg.f64 th) (.f64 th (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/360 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/48 binary64)))) (.f64 #s(literal 5/24 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 th th) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 th th) (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))
#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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2))

Outputs
#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)))))

Calls

8 calls:

19.0ms	(*.f64 a1 a1)
16.0ms	th
15.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
15.0ms	(*.f64 a2 a2)
15.0ms	a2

Results

Accuracy	Segments	Branch
99.2%	1	`a2`
99.2%	1	`(*.f64 a2 a2)`
99.2%	1	`a1`
99.2%	1	`th`
99.2%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
99.2%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.2%	1	`(cos.f64 th)`
99.2%	1	`(*.f64 a1 a1)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes114.0ms (1.2%)

Memory

-9.1MiB live, 145.2MiB allocated

Counts

50 → 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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (*.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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 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))
#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 (sqrt.f64 #s(literal 2 binary64)) a1))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) 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 #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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx ( (* (cos th) a2) a2) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) a2) a2))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) #s(approx (cos th) #s(literal 1 binary64)))
(.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 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (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)))
#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))))
#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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) 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))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (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)))))
#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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (fma.f64 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) a2 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.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))))
#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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(.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))))
(/.f64 #s(approx (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/.f64 (.f64 (.f64 (-.f64 a1 a2) (fma.f64 a1 a1 (.f64 a2 a2))) (+.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (/.f64 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 (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))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 a2 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) #s(literal 1 binary64))) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) (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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (fma.f64 (fma.f64 (fma.f64 (neg.f64 th) (.f64 th (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/360 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/48 binary64)))) (.f64 #s(literal 5/24 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 th th) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 th th) (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))

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:

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

Results

Accuracy	Segments	Branch
99.2%	1	`a1`
99.2%	1	`a2`
99.2%	1	`th`
99.2%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
99.2%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.2%	1	`(cos.f64 th)`
99.2%	1	`(*.f64 a1 a1)`
99.2%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes110.0ms (1.2%)

Memory

24.7MiB live, 141.2MiB allocated

Counts

49 → 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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (*.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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 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))
#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 (sqrt.f64 #s(literal 2 binary64)) a1))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) 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 #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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx ( (* (cos th) a2) a2) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) a2) a2))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))) #s(approx (cos th) #s(literal 1 binary64)))
(.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 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (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)))
#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))))
#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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 (.f64 (.f64 #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))) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) 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))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (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)))))
#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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (fma.f64 (/.f64 a2 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) a2 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a1) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.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))))
#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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(.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))))
(/.f64 #s(approx (* (/ (cos th) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2)))) (/.f64 (.f64 (.f64 (-.f64 a1 a2) (fma.f64 a1 a1 (.f64 a2 a2))) (+.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (/.f64 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 (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))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (.f64 (/.f64 (fma.f64 a2 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) #s(literal 1 binary64))) (.f64 (/.f64 (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) a2) (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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (fma.f64 (fma.f64 (fma.f64 (neg.f64 th) (.f64 th (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/360 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/48 binary64)))) (.f64 #s(literal 5/24 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 th th) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))

Outputs

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

Calls

8 calls:

14.0ms	a1
14.0ms	(*.f64 a1 a1)
13.0ms	(+.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)))
13.0ms	a2
13.0ms	th

Results

Accuracy	Segments	Branch
65.3%	2	`th`
66.5%	2	`a1`
67.3%	2	`a2`
75.6%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
75.5%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
75.5%	2	`(cos.f64 th)`
66.5%	2	`(*.f64 a1 a1)`
67.3%	2	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes9.0ms (0.1%)

Memory

-26.5MiB live, 11.9MiB allocated

Counts

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

Outputs

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

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

Calls

1 calls:

6.0ms

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

Results

Accuracy	Segments	Branch
75.5%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 22 to 12 computations (45.5% saved)

regimes35.0ms (0.4%)

Memory

8.4MiB live, 49.1MiB 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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) #s(approx (/ (* (* (cos th) a2) a2) (sqrt 2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) (*.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 (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 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))
#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 (sqrt.f64 #s(literal 2 binary64)) a1))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))

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

Calls

8 calls:

6.0ms	a1
4.0ms	th
4.0ms	a2
4.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
4.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Results

Accuracy	Segments	Branch
61.7%	1	`th`
61.7%	1	`a1`
61.7%	1	`(*.f64 a1 a1)`
61.7%	1	`a2`
61.7%	1	`(*.f64 a2 a2)`
61.7%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
61.7%	1	`(cos.f64 th)`
61.7%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes29.0ms (0.3%)

Memory

10.9MiB live, 48.6MiB allocated

Counts

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

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

8 calls:

4.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
3.0ms	a1
3.0ms	th
3.0ms	a2
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)))

Results

Accuracy	Segments	Branch
61.7%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
61.7%	1	`th`
61.7%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
61.7%	1	`(cos.f64 th)`
61.7%	1	`a1`
61.7%	1	`(*.f64 a1 a1)`
61.7%	1	`a2`
61.7%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes27.0ms (0.3%)

Memory

7.2MiB live, 43.6MiB allocated

Counts

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

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:

7.0ms	(cos.f64 th)
3.0ms	a1
3.0ms	th
3.0ms	a2
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
61.4%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
61.4%	1	`th`
61.4%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
61.4%	1	`(cos.f64 th)`
61.4%	1	`a1`
61.4%	1	`(*.f64 a1 a1)`
61.4%	1	`a2`
61.4%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes14.0ms (0.2%)

Memory

-14.2MiB live, 24.0MiB 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:

4.0ms	th
1.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
1.0ms	(cos.f64 th)
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

Results

Accuracy	Segments	Branch
13.3%	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)))`
13.3%	1	`th`
13.3%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
13.3%	1	`(cos.f64 th)`
13.3%	1	`a1`
13.3%	1	`(*.f64 a1 a1)`
13.3%	1	`a2`
13.3%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.6841533045290775e-121	-1.9813900364350736e-143

Compiler

Compiled 25 to 18 computations (28% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.6841533045290775e-121	-1.9813900364350736e-143

Compiler

Compiled 25 to 18 computations (28% saved)

simplify7.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	411
1	116	411

Stop Event

1×

saturated

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))
(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (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))
(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 -1162941958872971/11629419588729710248789180926208072549658261770997088964503843186890228609814366773219056811420217048972200345700258846936553626057834496 binary64)) #s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (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))))
(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 -1162941958872971/11629419588729710248789180926208072549658261770997088964503843186890228609814366773219056811420217048972200345700258846936553626057834496 binary64)) #s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (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))
#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 (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 #s(literal 1/2 binary64) (fma.f64 (.f64 (cos.f64 th) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 (cos.f64 th)))))
(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) a2)))
(.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 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) #s(literal 1/2 binary64))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) #s(literal -1162941958872971/11629419588729710248789180926208072549658261770997088964503843186890228609814366773219056811420217048972200345700258846936553626057834496 binary64)) #s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (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))))
(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 -1162941958872971/11629419588729710248789180926208072549658261770997088964503843186890228609814366773219056811420217048972200345700258846936553626057834496 binary64)) #s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (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))))
(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 -1162941958872971/11629419588729710248789180926208072549658261770997088964503843186890228609814366773219056811420217048972200345700258846936553626057834496 binary64)) #s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 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 -1162941958872971/11629419588729710248789180926208072549658261770997088964503843186890228609814366773219056811420217048972200345700258846936553626057834496 binary64)) #s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (/.f64 #s(approx (* (* (cos th) a2) a2) #s(approx (* (+ (* -1/2 (* th th)) 1) (* a2 a2)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) th) th))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (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))
#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)))

soundness1.5s (16.3%)

Memory

4.1MiB live, 889.0MiB allocated

Rules

34 694×	`lower-fma.f64`
34 694×	`lower-fma.f32`
16 170×	`lower-fma.f64`
16 170×	`lower-fma.f32`
14 636×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	227	7129
1	690	6349
2	2272	6099
3	5553	6099
0	8661	5750
0	194	5710
1	615	4921
2	2131	4685
3	4970	4446
0	8398	4139
0	12	44
0	20	38
1	58	38
2	411	38
3	7331	38
0	8434	37
0	494	6819
1	1757	6376
2	6824	6313
0	8078	5942
0	111	1498
1	343	1366
2	1206	1262
3	3900	1233
0	8428	1172

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

Compiler

Compiled 625 to 281 computations (55% saved)

preprocess96.0ms (1.1%)

Memory

-10.3MiB live, 220.8MiB allocated

Remove

(sort a1 a2)

(abs a1)

(abs a2)

(abs th)

Compiler

Compiled 1 556 to 788 computations (49.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.3s (14.7%)

explain263.0ms (2.9%)

preprocess172.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize44.0ms (0.5%)

series36.0ms (0.4%)

simplify366.0ms (4%)

rewrite322.0ms (3.5%)

eval97.0ms (1.1%)

prune269.0ms (2.9%)

simplify180.0ms (2%)

localize232.0ms (2.5%)

series170.0ms (1.9%)

simplify132.0ms (1.4%)

rewrite234.0ms (2.6%)

eval243.0ms (2.7%)

prune224.0ms (2.5%)

simplify32.0ms (0.3%)

localize112.0ms (1.2%)

series40.0ms (0.4%)

simplify183.0ms (2%)

rewrite202.0ms (2.2%)

eval240.0ms (2.6%)

prune269.0ms (2.9%)

simplify141.0ms (1.5%)

localize108.0ms (1.2%)

series62.0ms (0.7%)

simplify215.0ms (2.4%)

rewrite195.0ms (2.1%)

eval211.0ms (2.3%)

prune249.0ms (2.7%)

regimes186.0ms (2%)

regimes165.0ms (1.8%)

regimes127.0ms (1.4%)

regimes127.0ms (1.4%)

regimes114.0ms (1.2%)

regimes110.0ms (1.2%)

regimes9.0ms (0.1%)

regimes35.0ms (0.4%)

regimes29.0ms (0.3%)

regimes27.0ms (0.3%)

regimes14.0ms (0.2%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

soundness1.5s (16.3%)

preprocess96.0ms (1.1%)

end0.0ms (0%)

Profiling