Metrics for Migdal et al, Equation (64)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 21 to 14 computations (33.3% saved)

sample1.5s (18.2%)

Memory

-179.2MiB live, 1 911.1MiB allocated

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 654.0ms

ival-cos: 233.0ms (35.6% of total)

ival-mult: 198.0ms (30.3% of total)

ival-sqrt: 117.0ms (17.9% of total)

ival-div: 52.0ms (7.9% of total)

ival-add: 40.0ms (6.1% of total)

ival-true: 6.0ms (0.9% of total)

exact: 6.0ms (0.9% of total)

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

Bogosity

explain219.0ms (2.6%)

Memory

39.6MiB live, 308.1MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

128.0ms

512×

valid

Compiler

Compiled 135 to 40 computations (70.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-cos: 22.0ms (50.5% of total)

ival-mult: 12.0ms (27.6% of total)

ival-sqrt: 4.0ms (9.2% of total)

ival-div: 3.0ms (6.9% of total)

ival-add: 2.0ms (4.6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess150.0ms (1.8%)

Memory

-6.6MiB live, 72.3MiB 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 19 to 12 computations (36.8% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify5.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize65.0ms (0.8%)

Memory

-18.7MiB live, 61.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
accuracy	0.19140625	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
accuracy	0.217128759768442	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
accuracy	0.7138862793053261	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

35.0ms

256×

valid

Compiler

Compiled 58 to 14 computations (75.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-cos: 6.0ms (38% of total)

ival-mult: 6.0ms (38% of total)

ival-sqrt: 2.0ms (12.7% of total)

ival-div: 1.0ms (6.3% of total)

ival-add: 1.0ms (6.3% of total)

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

exact: 0.0ms (0% of total)

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

series33.0ms (0.4%)

Memory

-2.6MiB live, 36.6MiB allocated

Counts

5 → 108

Calls

Call 1

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

Outputs
#s(alt (/ (* (pow 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
15.0ms	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)))
3.0ms	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)))

simplify273.0ms (3.3%)

Memory

-15.5MiB live, 230.0MiB 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 a1) (/.f64 a2 a1) #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 a1) (/.f64 a2 a1) #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 a1) (/.f64 a2 a1) #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 a1) (/.f64 a2 a1) #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 a1) (/.f64 a2 a1) #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 a1) (/.f64 a2 a1) #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 (pow.f64 th #s(literal 4 binary64)) (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) (.f64 (fma.f64 #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 (fma.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 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 th th) (/.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 a2) (/.f64 a1 a2) #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 a2) (/.f64 a1 a2) #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 a2) (/.f64 a1 a2) #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 a2) (/.f64 a1 a2) #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 a2) (/.f64 a1 a2) #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 a2) (/.f64 a1 a2) #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))))

rewrite180.0ms (2.2%)

Memory

21.8MiB live, 186.6MiB 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)))
(.f64 (/.f64 (.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -2 binary64)) (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64)))) (.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -3 binary64)) (-.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))))) (fma.f64 (pow.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) #s(literal 2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64)) #s(literal 1/2 binary64))))
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(-.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (.f64 (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(-.f64 (.f64 (.f64 (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (.f64 (.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))
(+.f64 (.f64 (.f64 (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (neg.f64 (.f64 (.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))
(+.f64 (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th)))
(+.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th)) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
(.f64 (/.f64 (.f64 a1 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 (.f64 a1 a1) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 a1 (cos.f64 th)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (.f64 a1 a1) (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 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a1 a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a1 (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (*.f64 a1 (cos.f64 th)) (neg.f64 a1)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (*.f64 a1 (cos.f64 th)) a1) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a1)
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (.f64 a1 a1) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 a1 (cos.f64 th)) a1))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th)))
(.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 a1 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
(.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a1 a1)) #s(literal -1 binary64))
(/.f64 (/.f64 (.f64 (.f64 a1 (cos.f64 th)) (neg.f64 a1)) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) (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 a1 (cos.f64 th)) (neg.f64 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (*.f64 a1 a1)) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 a1 a1)) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.f64 (.f64 (.f64 (*.f64 a1 (cos.f64 th)) a1) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 a1 a1) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.f64 (.f64 (.f64 (*.f64 a1 (cos.f64 th)) a1) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 (cos.f64 th) #s(literal -1 binary64)))
(/.f64 (.f64 (.f64 a1 (cos.f64 th)) (neg.f64 a1)) (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)) (*.f64 a1 a1))))
(/.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a1 a1)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a1 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 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 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) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 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 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1 binary64)))
(/.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)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.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 (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.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) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2)
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 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 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 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) (pow.f64 (cos.f64 th) #s(literal -1 binary64)))
(/.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 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 a2))))
(/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 a2)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 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))))

eval118.0ms (1.4%)

Memory: -1.5MiB live, 122.0MiB allocated
Compiler: Compiled 12 965 to 1 060 computations (91.8% saved)

prune55.0ms (0.7%)

Memory

-26.8MiB live, 56.8MiB allocated

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	475	15	490
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	476	15	491

Accuracy

100.0%

Counts

491 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (fma.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)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (cos.f64 th) #s(literal -1 binary64)))
▶	99.7%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	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))))
▶	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))))
	99.6%	(.f64 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64))
	99.6%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
	99.6%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
	99.7%	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	99.6%	(.f64 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (neg.f64 (cos.f64 th))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
▶	66.8%	#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)))
	61.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	60.9%	#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))))
▶	98.9%	#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 454 to 364 computations (19.8% saved)

simplify15.0ms (0.2%)

Memory

18.3MiB live, 18.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

284×	`lower-*.f32`
272×	`lower-*.f64`
248×	`times-frac`
176×	`lower-/.f32`
160×	`lower-/.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	33	253
0	51	235
1	87	235
2	140	235
3	265	233
4	364	233
5	551	227
6	664	227
0	664	227

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize154.0ms (1.8%)

Memory

-27.7MiB live, 171.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1953125	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.330127232799804	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))))
accuracy	0.5641093161642965	(/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.7138862793053261	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.08822250976844202	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
accuracy	0.203125	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.15234375	(*.f64 (cos.f64 th) a2)
accuracy	0.15625	(.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.44921875	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.4861156154526852	#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)))))
accuracy	0.125	(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
accuracy	0.44921875	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.453125	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.148695122553423	#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	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.14453125	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
accuracy	0.24285126953688405	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))

Samples

73.0ms

256×

valid

Compiler

Compiled 242 to 30 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-mult: 22.0ms (48.9% of total)

ival-div: 11.0ms (24.5% of total)

ival-cos: 6.0ms (13.3% of total)

ival-add: 3.0ms (6.7% of total)

ival-sqrt: 2.0ms (4.4% of total)

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

exact: 0.0ms (0% of total)

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

series62.0ms (0.8%)

Memory

6.9MiB live, 84.6MiB allocated

Counts

20 → 468

Calls

Call 1

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

Calls

9 calls:

Time	Variable		Point	Expression
12.0ms	a2	@	0	((/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ (sqrt 2) (cos th)) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (/ 1 (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))))) (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (/ (cos th) (sqrt 2)))
6.0ms	th	@	-inf	((/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ (sqrt 2) (cos th)) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (/ 1 (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))))) (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (/ (cos th) (sqrt 2)))
3.0ms	a2	@	inf	((/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ (sqrt 2) (cos th)) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (/ 1 (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))))) (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (/ (cos th) (sqrt 2)))
3.0ms	th	@	inf	((/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ (sqrt 2) (cos th)) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (/ 1 (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))))) (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (/ (cos th) (sqrt 2)))
3.0ms	a1	@	inf	((/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ (sqrt 2) (cos th)) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (/ 1 (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))))) (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (/ (cos th) (sqrt 2)))

simplify228.0ms (2.7%)

Memory

12.2MiB live, 249.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10 506×	`lower-fma.f64`
10 506×	`lower-fma.f32`
6 722×	`lower-*.f64`
6 722×	`lower-*.f32`
3 084×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	307	7296
1	1012	6607
2	3782	6309
0	8053	5932

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 467

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

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

rewrite596.0ms (7.2%)

Memory

11.0MiB live, 484.0MiB allocated

Rules

5 248×	`lower-/.f32`
5 232×	`lower-/.f64`
4 080×	`lower-fma.f32`
4 076×	`lower-fma.f64`
3 968×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	198
0	51	180
1	172	178
2	1198	178
0	8135	178

Stop Event

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

Counts

20 → 2 840

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a2 a1)) (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (-.f64 a2 a1)))
(.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1))) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(.f64 (/.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64)))))
(.f64 (/.f64 (fma.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))) #s(literal 1 binary64)) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))))))
(.f64 (/.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))) #s(literal 1 binary64)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 (pow.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (/.f64 (pow.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)))))
(.f64 (/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (cos.f64 th) #s(literal -1 binary64)) (/.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (+.f64 a2 a1)) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (-.f64 a2 a1)))
(.f64 (/.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal -1 binary64))) (/.f64 (neg.f64 (cos.f64 th)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))))
(.f64 (/.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) #s(literal -1 binary64))) (/.f64 (neg.f64 (cos.f64 th)) (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64)))))
(.f64 (/.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (neg.f64 (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal -1 binary64))) (/.f64 (cos.f64 th) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) #s(literal -1 binary64))) (/.f64 (cos.f64 th) (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64)))))
(.f64 (/.f64 (neg.f64 (cos.f64 th)) (pow.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal -1 binary64))) (/.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))))
(.f64 (/.f64 (neg.f64 (cos.f64 th)) (pow.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) #s(literal -1 binary64))) (/.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64)))))
(.f64 (/.f64 (neg.f64 (cos.f64 th)) #s(literal 1 binary64)) (/.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1 binary64))))
(.f64 (/.f64 (neg.f64 (cos.f64 th)) #s(literal 1 binary64)) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal -1 binary64))) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) #s(literal -1 binary64))) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64)))))
(.f64 (/.f64 (cos.f64 th) (pow.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal -1 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))))
(.f64 (/.f64 (cos.f64 th) (pow.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) #s(literal -1 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))))) (fma.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (pow.f64 (.f64 (.f64 (cos.f64 th) a1) a1) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (cos.f64 th) a1) a1) (.f64 (.f64 (cos.f64 th) a2) a2))) #s(literal 2 binary64))) (fma.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (neg.f64 (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(neg.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 a1 a1) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a1 #s(literal 1 binary64)) (.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (neg.f64 a2) #s(literal -1 binary64)) (.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 (/.f64 (.f64 (cos.f64 th) a2) #s(literal -1 binary64)) (/.f64 (neg.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 (.f64 a2 a2) #s(literal -1 binary64)) (/.f64 (neg.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 (/.f64 (.f64 a2 a2) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.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 (/.f64 (.f64 (cos.f64 th) a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (cos.f64 th) a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a2 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a2 #s(literal 1 binary64)) (.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 (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (/.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 (.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 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 (.f64 a1 a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a1 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 a1 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a1 (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a1 a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 a1 a1)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (neg.f64 a2) (.f64 (cos.f64 th) a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 #s(literal 1 binary64) (.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 (neg.f64 (cos.f64 th)) (.f64 a2 a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 #s(literal 1 binary64) (.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 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (.f64 a1 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (.f64 (cos.f64 th) a2) (neg.f64 a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 (.f64 (cos.f64 th) a2) #s(literal 1 binary64)) (/.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 (.f64 a2 a2) (neg.f64 (cos.f64 th))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.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 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a1 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a2 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (.f64 a1 a1) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (.f64 a2 a2) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 (cos.f64 th) #s(literal 1 binary64)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (cos.f64 th) #s(literal 1 binary64)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(fma.f64 (neg.f64 (.f64 (.f64 (cos.f64 th) a2) a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(fma.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) a1 (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 a2 #s(literal -1 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 (cos.f64 th) (/.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 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (.f64 a1 a1) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (.f64 (cos.f64 th) a2) (pow.f64 a2 #s(literal -1 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (pow.f64 a2 #s(literal -1 binary64))) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 #s(literal 1 binary64) (.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 #s(literal 1 binary64) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(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 (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) #s(literal 1 binary64) (.f64 (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64)))
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(fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (cos.f64 th) (pow.f64 a2 #s(literal -1 binary64))) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) a2) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(/.f64 (fma.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (neg.f64 (.f64 a1 a1)))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.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))))
(/.f64 (fma.f64 a2 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 a1 a1))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(/.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal 2 binary64)) (/.f64 (*.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (/.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64))) #s(literal 2 binary64))) (neg.f64 (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (+.f64 (/.f64 (pow.f64 a2 #s(literal 6 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (/.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))))) (neg.f64 (fma.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64) (/.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (*.f64 a1 a2) #s(literal 2 binary64))) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (+.f64 (/.f64 (pow.f64 a2 #s(literal 6 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (/.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))))) (neg.f64 (fma.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64) (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 (*.f64 a1 a2) #s(literal 2 binary64))) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2))) #s(literal 2 binary64))
(/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))) #s(literal 2 binary64))
(/.f64 (/.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64))) #s(literal 2 binary64)) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (+.f64 (/.f64 (pow.f64 a2 #s(literal 6 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (/.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)))) (fma.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64) (/.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (*.f64 a1 a2) #s(literal 2 binary64))) #s(literal 2 binary64))))
(/.f64 (+.f64 (/.f64 (pow.f64 a2 #s(literal 6 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (/.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)))) (fma.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64) (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 (*.f64 a1 a2) #s(literal 2 binary64))) #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fma.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64) (/.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (*.f64 a1 a2) #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 a2 #s(literal 6 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (/.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #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(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #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))))
(fma.f64 (/.f64 a2 #s(literal -1 binary64)) (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (/.f64 a1 #s(literal -1 binary64)) (/.f64 (neg.f64 a1) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (/.f64 (neg.f64 a1) #s(literal -1 binary64)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (/.f64 (neg.f64 a2) #s(literal -1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (/.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (.f64 (neg.f64 a2) a2) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (.f64 #s(literal 1 binary64) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (.f64 #s(literal 1 binary64) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (.f64 a2 (neg.f64 a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (.f64 a2 #s(literal 1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (.f64 a1 (neg.f64 a1)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (.f64 a1 #s(literal 1 binary64)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (.f64 (neg.f64 a1) a1) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (neg.f64 (.f64 a2 a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (neg.f64 (.f64 a1 a1)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 a1 (pow.f64 a1 #s(literal -1 binary64))) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 a2 (pow.f64 a2 #s(literal -1 binary64))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 #s(literal 1 binary64) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 #s(literal 1 binary64) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 a2 #s(literal -1 binary64))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 a1 #s(literal -1 binary64))) (*.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))
(fma.f64 (.f64 a1 a1) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(-.f64 (/.f64 (.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(+.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 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))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(*.f64 (/.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 a1 #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (neg.f64 (neg.f64 a1)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 a1 #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) a1)
(*.f64 (neg.f64 a1) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
(*.f64 #s(literal 1 binary64) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (neg.f64 a1))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (*.f64 a1 #s(literal 1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 a1 #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (neg.f64 a1)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 (/.f64 (neg.f64 a1) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 a1 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) #s(literal -1 binary64)))
(*.f64 (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) (sqrt.f64 #s(literal 2 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 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.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 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (neg.f64 a2) #s(literal -1 binary64)) (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (.f64 (cos.f64 th) a2) #s(literal -1 binary64)) (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))))
(.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 a2) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(.f64 (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 (cos.f64 th) a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (cos.f64 th) a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 a2 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 a2 #s(literal 1 binary64)) (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 (neg.f64 a2) (*.f64 (cos.f64 th) a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 (cos.f64 th) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (neg.f64 (cos.f64 th)) (*.f64 a2 a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (*.f64 (cos.f64 th) a2) (neg.f64 a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (*.f64 (cos.f64 th) a2) #s(literal 1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (*.f64 a2 a2) (neg.f64 (cos.f64 th))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (*.f64 a2 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2)
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(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))))) (fma.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (pow.f64 (.f64 (.f64 (cos.f64 th) a1) a1) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (cos.f64 th) a1) a1) (.f64 (.f64 (cos.f64 th) a2) a2))) #s(literal 2 binary64))) (fma.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (neg.f64 (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(neg.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 a1 a1) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 a1 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (.f64 (cos.f64 th) a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a1 #s(literal 1 binary64)) (.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (neg.f64 a2) #s(literal -1 binary64)) (.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 (/.f64 (.f64 (cos.f64 th) a2) #s(literal -1 binary64)) (/.f64 (neg.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 (.f64 a2 a2) #s(literal -1 binary64)) (/.f64 (neg.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 (/.f64 (.f64 a2 a2) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.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 (/.f64 (.f64 (cos.f64 th) a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (cos.f64 th) a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a2 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a2 #s(literal 1 binary64)) (.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 (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (/.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 (.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 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 (.f64 a1 a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a1 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 a1 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a1 (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a1 a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 a1 a1)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (neg.f64 a2) (.f64 (cos.f64 th) a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 #s(literal 1 binary64) (.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 (neg.f64 (cos.f64 th)) (.f64 a2 a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 #s(literal 1 binary64) (.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 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (.f64 a1 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (.f64 (cos.f64 th) a2) (neg.f64 a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 (.f64 (cos.f64 th) a2) #s(literal 1 binary64)) (/.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 (.f64 a2 a2) (neg.f64 (cos.f64 th))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.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 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a1 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a2 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (.f64 a1 a1) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (.f64 a2 a2) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 (cos.f64 th) #s(literal 1 binary64)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (cos.f64 th) #s(literal 1 binary64)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(fma.f64 (neg.f64 (.f64 (.f64 (cos.f64 th) a2) a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(fma.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) a1 (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 a2 #s(literal -1 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (.f64 (cos.f64 th) (/.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 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (.f64 a1 a1) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (.f64 (cos.f64 th) a2) (pow.f64 a2 #s(literal -1 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (pow.f64 a2 #s(literal -1 binary64))) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 #s(literal 1 binary64) (.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 #s(literal 1 binary64) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(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 (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) #s(literal 1 binary64) (.f64 (.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64)))
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(fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (cos.f64 th) (pow.f64 a2 #s(literal -1 binary64))) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) a2) (.f64 (cos.f64 th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1))))
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(*.f64 #s(literal 1 binary64) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 a2 #s(literal 1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 a2))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (*.f64 a2 #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (neg.f64 a2)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (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)) a2)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #s(literal -1 binary64)))
(*.f64 (/.f64 a2 #s(literal -1 binary64)) (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (neg.f64 a2) #s(literal -1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 (neg.f64 a2) a2) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 a2 (neg.f64 a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 a2 #s(literal 1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 (.f64 a2 a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 a2 (pow.f64 a2 #s(literal -1 binary64))))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 a2 #s(literal -1 binary64))))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (neg.f64 a2) a2)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 a2 (neg.f64 a2))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 a2 a2))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 a2 #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) a2)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (*.f64 (neg.f64 a2) a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (*.f64 a2 (neg.f64 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 a2 #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (neg.f64 (*.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 a2) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 a2) a2)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 #s(literal 1 binary64) a2)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (neg.f64 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 a2 #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(exp.f64 (-.f64 (.f64 (log.f64 a2) #s(literal 2 binary64)) (.f64 (log.f64 #s(literal 2 binary64)) #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 (pow.f64 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (neg.f64 (cos.f64 th)))
(.f64 (.f64 (cos.f64 th) #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (neg.f64 (neg.f64 (cos.f64 th))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (cos.f64 th) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (cos.f64 th))
(*.f64 (neg.f64 (cos.f64 th)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (cos.f64 th) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 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 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(/.f64 (*.f64 (cos.f64 th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (cos.f64 th))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1 binary64)))
(/.f64 (neg.f64 (cos.f64 th)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 (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))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #s(literal -1 binary64)))

eval783.0ms (9.4%)

Memory: 37.2MiB live, 928.3MiB allocated
Compiler: Compiled 90 628 to 5 269 computations (94.2% saved)

prune178.0ms (2.1%)

Memory

-8.1MiB live, 332.8MiB allocated

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	3 587	30	3 617
Fresh	10	0	10
Picked	4	1	5
Done	0	0	0
Total	3 601	31	3 632

Accuracy

100.0%

Counts

3 632 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	60.3%	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	66.8%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
✓	99.7%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	60.9%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) (.f64 th th) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	62.6%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	98.9%	(/.f64 (.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	99.3%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1))))
	62.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
	66.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))))
	66.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
	29.7%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (fma.f64 (.f64 (.f64 th th) #s(literal -1/2 binary64)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))))
	66.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
▶	66.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2)))
	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.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)))))
	54.1%	#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)))))
	66.8%	#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))))
	98.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2))))
	66.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #s(literal 1/2 binary64)))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
▶	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (*.f64 (cos.f64 th) a2) a2) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) a2)))
	61.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.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) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
	60.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.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) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
	61.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
	66.4%	#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))))))
▶	15.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	62.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (.f64 a2 a2) (fma.f64 (*.f64 th (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))))

Compiler

Compiled 918 to 744 computations (19% saved)

simplify37.0ms (0.5%)

Memory

-19.6MiB live, 59.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
cost-diff	0	(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2)
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2))
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 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
cost-diff	1344	(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2))
cost-diff	0	#s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (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)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
cost-diff	0	(*.f64 a1 a1)
cost-diff	0	(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff	384	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	6080	(*.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))

Rules

524×	`lower-*.f32`
508×	`lower-*.f64`
300×	`lower-/.f32`
292×	`times-frac`
288×	`lower-/.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	46	321
0	70	302
1	112	290
2	168	286
3	258	286
4	424	286
5	539	274
6	738	274
7	764	274
8	816	274
9	904	274
10	951	274
11	970	274
12	977	274
13	986	274
0	986	274

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize106.0ms (1.3%)

Memory

1.6MiB live, 239.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.125	(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2)
accuracy	0.19921875	(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
accuracy	0.44921875	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.4861156154526852	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2))
accuracy	0.2265625	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
accuracy	0.453125	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.484375	(/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
accuracy	21.148695122553423	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.1328125	(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.14453125	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	32.776564731260926	#s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.1484375	(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.453125	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.148695122553423	#s(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	52.265772717124456	#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	0.09765625	(pow.f64 (cos.f64 th) #s(literal -1 binary64))
accuracy	0.14453125	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.2109375	(*.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))

Samples

76.0ms

256×

valid

Compiler

Compiled 257 to 39 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-mult: 22.0ms (40.7% of total)

ival-div: 13.0ms (24.1% of total)

ival-cos: 6.0ms (11.1% of total)

ival-add: 5.0ms (9.3% of total)

ival-pow: 5.0ms (9.3% of total)

ival-sqrt: 2.0ms (3.7% of total)

exact: 1.0ms (1.9% of total)

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

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

series42.0ms (0.5%)

Memory

3.4MiB live, 120.0MiB allocated

Counts

22 → 432

Calls

Call 1

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

Calls

9 calls:

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

simplify170.0ms (2%)

Memory

-10.2MiB live, 302.9MiB allocated

Algorithm

1×	egg-herbie

Rules

13 484×	`lower-fma.f64`
13 484×	`lower-fma.f32`
5 390×	`lower-*.f64`
5 390×	`lower-*.f32`
3 196×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	182	5499
1	582	4698
2	2055	4479
3	4867	4242
0	8265	3953

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 432

Calls

Call 1

Inputs
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(pow 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) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (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 a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (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) (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) (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) (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)))))
(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) (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) (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 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)))
(/ a2 (sqrt 2))
(+ (* -1/2 (/ (* a2 (pow th 2)) (sqrt 2))) (/ a2 (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ a2 (sqrt 2))) (* 1/24 (/ (* a2 (pow th 2)) (sqrt 2))))) (/ a2 (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ a2 (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* a2 (pow th 2)) (sqrt 2))) (* 1/24 (/ a2 (sqrt 2))))))) (/ a2 (sqrt 2)))
1
(+ 1 (* 1/2 (pow th 2)))
(+ 1 (* (pow th 2) (+ 1/2 (* 5/24 (pow th 2)))))
(+ 1 (* (pow th 2) (+ 1/2 (* (pow th 2) (+ 5/24 (* 61/720 (pow th 2)))))))
1
(+ 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)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(/ (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)))
(/ (* (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))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(cos th)
(cos th)
(cos th)
(cos th)
(* 1/2 (* (pow th 2) (sqrt 2)))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(/ (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)))
(/ (* (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))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(cos th)
(cos th)
(cos th)
(cos th)
(* 1/2 (* (pow th 2) (sqrt 2)))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(* (pow th 2) (+ (* 1/2 (sqrt 2)) (/ (sqrt 2) (pow th 2))))
(/ (* (pow 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) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (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)))
(/ 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 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 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (* (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) (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)))))
(/ 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) (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 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (* (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) (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)))))
(/ 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) (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 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ (* a2 (cos th)) (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)

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

rewrite205.0ms (2.5%)

Memory

0.2MiB live, 446.0MiB allocated

Rules

4 892×	`lower-/.f32`
4 880×	`lower-/.f64`
4 770×	`lower-fma.f32`
4 764×	`lower-fma.f64`
4 368×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	261
0	70	228
1	227	228
2	1431	228
0	8217	228

Stop Event

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

Counts

22 → 1 076

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) (.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1 binary64)))
(*.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #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 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (cos.f64 th)))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (cos.f64 th)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (neg.f64 (neg.f64 (cos.f64 th)))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (cos.f64 th))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (neg.f64 (cos.f64 th))))
(/.f64 (neg.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (cos.f64 th)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.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 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 (log.f64 (cos.f64 th)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log.f64 (cos.f64 th)) #s(literal -1 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (+.f64 a2 a1)) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (-.f64 a2 a1)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a2 a1)) (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (-.f64 a2 a1)))
(.f64 (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (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 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (cos.f64 th) #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (*.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 (pow.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)) (*.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (/.f64 (pow.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (*.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)) (*.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1))) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (+.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 a2 #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (-.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 (.f64 a1 a2) #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 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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(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 a1 #s(literal -1 binary64))) (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(fma.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (*.f64 a1 a1) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (pow.f64 a2 #s(literal -1 binary64))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 #s(literal -1 binary64) (/.f64 a2 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(-.f64 (/.f64 (/.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 2 binary64)) (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 2 binary64)) (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a2 a1)) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 2 binary64)) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (/.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 2 binary64)) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
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(*.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (neg.f64 a2))
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(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) a2)
(*.f64 (neg.f64 a2) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
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(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(pow.f64 (exp.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal -2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 a2))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 a2 #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 a2))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 a2)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 a2 #s(literal -1 binary64)))
(/.f64 (neg.f64 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2))
(neg.f64 (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(neg.f64 (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #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 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(.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 a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))))
(.f64 (/.f64 (.f64 a2 a2) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 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 #s(literal 1 binary64) (pow.f64 (neg.f64 a2) #s(literal -1 binary64))) (/.f64 (.f64 a2 (cos.f64 th)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a2 (cos.f64 th)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 (cos.f64 th)) (neg.f64 (pow.f64 a2 #s(literal -1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)))) (/.f64 (*.f64 a2 a2) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))) (/.f64 (.f64 a2 a2) (*.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)))) (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))))
(*.f64 (/.f64 a2 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))) (/.f64 a2 (.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a2 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))))
(.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (.f64 a2 (cos.f64 th)) (pow.f64 (neg.f64 a2) #s(literal -1 binary64))))
(.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (.f64 a2 a2) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))))
(*.f64 (pow.f64 (cos.f64 th) #s(literal 1 binary64)) (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(*.f64 (/.f64 (cos.f64 th) #s(literal 1 binary64)) (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(.f64 (/.f64 a2 #s(literal 1 binary64)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(.f64 (.f64 (*.f64 a2 (cos.f64 th)) a2) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(.f64 (.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2)
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (.f64 a2 (cos.f64 th)) (/.f64 (pow.f64 a2 #s(literal -1 binary64)) #s(literal 1 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (.f64 a2 (cos.f64 th)) (pow.f64 a2 #s(literal -1 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 (cos.f64 th)) #s(literal 1 binary64)))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (cos.f64 th)))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (pow.f64 (cos.f64 th) #s(literal 1 binary64)))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (cos.f64 th))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 a2 (cos.f64 th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 a2 (cos.f64 th)) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2)))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (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 (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 (neg.f64 a2) (.f64 a2 (cos.f64 th)))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 a2 (cos.f64 th)))) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2))
(/.f64 (neg.f64 (.f64 #s(literal -1 binary64) (.f64 a2 (cos.f64 th)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.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 (.f64 a2 (.f64 a2 (cos.f64 th)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 a2 (cos.f64 th)) a2))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (neg.f64 a2) (.f64 a2 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 a2 (cos.f64 th))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 a2 (cos.f64 th))) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2))
(/.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (.f64 (.f64 a2 (cos.f64 th)) a2)) (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 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 2 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)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2))))
(*.f64 (/.f64 (cos.f64 th) (pow.f64 (neg.f64 a2) #s(literal -1 binary64))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 a2) #s(literal -1 binary64))) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 (cos.f64 th) #s(literal -1 binary64)) (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (cos.f64 th) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(*.f64 (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cos.f64 th) (pow.f64 a2 #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (cos.f64 th) (neg.f64 (pow.f64 a2 #s(literal -1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)))) (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))) (/.f64 a2 (.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))))
(*.f64 (/.f64 a2 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(.f64 (.f64 (cos.f64 th) #s(literal 1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
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(*.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 a2 #s(literal -1 binary64))))
(*.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 a2) #s(literal -1 binary64))))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (cos.f64 th) (pow.f64 (neg.f64 a2) #s(literal -1 binary64))))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 a2 (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))))
(*.f64 (pow.f64 (cos.f64 th) #s(literal 1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (cos.f64 th) #s(literal 1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
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(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 a2 #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 a2 #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (pow.f64 a2 #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a2 #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2))
(pow.f64 (/.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 a2))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (neg.f64 (neg.f64 a2))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) a2)
(/.f64 (neg.f64 (pow.f64 a2 #s(literal -1 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 a2))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (neg.f64 a2)))
(/.f64 (pow.f64 a2 #s(literal -1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(/.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal -1 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal 1 binary64) (neg.f64 a2)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 a2))
(/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 #s(literal 1 binary64) (neg.f64 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (neg.f64 a2))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 a2)) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #s(literal -1 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #s(literal 1 binary64)))

eval223.0ms (2.7%)

Memory: 9.5MiB live, 574.1MiB allocated
Compiler: Compiled 33 440 to 3 837 computations (88.5% saved)

prune85.0ms (1%)

Memory

12.2MiB live, 291.6MiB allocated

Pruning

37 alts after pruning (34 fresh and 3 done)

	Pruned	Kept	Total
New	1 669	16	1 685
Fresh	7	18	25
Picked	3	2	5
Done	0	1	1
Total	1 679	37	1 716

Accuracy

100.0%

Counts

1 716 → 37

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
	57.8%	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 #s(approx (pow (cos th) -1) (fma.f64 (fma.f64 #s(literal 5/24 binary64) (.f64 th th) #s(literal 1/2 binary64)) (.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	66.8%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
✓	99.7%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	62.6%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	98.9%	(/.f64 (.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	99.3%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1))))
	59.9%	(/.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	62.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
	66.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))))
▶	66.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
	62.6%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (fma.f64 #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)))))
	66.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
✓	66.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2)))
	66.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) a2)))
	66.6%	#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)))))
	54.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
	54.1%	#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)))))
	66.8%	#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))))
	98.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2))))
	66.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #s(literal 1/2 binary64)))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 a2 (*.f64 a2 (cos.f64 th)))))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) a2))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
	98.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 a2 (cos.f64 th))) a2))
	61.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (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)))) a2))
	60.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (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)))) a2))
▶	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	61.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
	66.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 #s(approx ( (/ a2 (sqrt 2)) (cos th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a2))
▶	15.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	15.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	15.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
✓	15.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	15.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))))
▶	62.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (.f64 a2 a2) (fma.f64 (*.f64 th (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))))

Compiler

Compiled 1 027 to 853 computations (16.9% saved)

simplify41.0ms (0.5%)

Memory

-4.2MiB live, 37.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

964×	`lower-*.f32`
950×	`lower-*.f64`
496×	`times-frac`
480×	`associate-r`
358×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	369
0	75	348
1	131	344
2	217	340
3	465	340
4	828	334
5	1163	334
6	1237	334
7	1314	324
8	1366	324
9	1406	324
10	1439	324
11	1451	324
0	1451	320

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize103.0ms (1.2%)

Memory

6.4MiB live, 282.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.09375	(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))
accuracy	0.125	(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
accuracy	0.44921875	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.4861156154526852	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
accuracy	0.4861156154526852	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (.f64 a2 a2) (fma.f64 (*.f64 th (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	3.668960517579692	(.f64 (.f64 a2 a2) (fma.f64 (*.f64 th (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	24.491643708685896	#s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (.f64 a2 a2) (fma.f64 (*.f64 th (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.330127232799804	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
accuracy	0.642675912551442	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
accuracy	14.226120715997736	#s(approx (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.21875	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.148695122553423	#s(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	52.265772717124456	#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	0.1015625	(/.f64 #s(literal 1 binary64) (cos.f64 th))
accuracy	0.14453125	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.2109375	(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))

Samples

76.0ms

256×

valid

Compiler

Compiled 277 to 40 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 21.0ms (39.9% of total)

ival-div: 18.0ms (34.2% of total)

ival-cos: 6.0ms (11.4% of total)

ival-add: 5.0ms (9.5% of total)

ival-sqrt: 2.0ms (3.8% of total)

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

exact: 0.0ms (0% of total)

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

series51.0ms (0.6%)

Memory

-28.7MiB live, 137.9MiB allocated

Counts

22 → 456

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	a1	@	0	((/ (+ (* a2 a2) (* a1 a1)) (* (/ 1 (cos th)) (sqrt 2))) (* (/ 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)) (/ 1 (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))))) (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (sqrt 2) (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (* a2 a2) (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2)))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (/ a2 (sqrt 2)) a2) (cos th)) (* (/ a2 (sqrt 2)) a2) (/ a2 (sqrt 2)) (/ 1 (cos th)) (cos th) (/ 1 (sqrt 2)))
5.0ms	a2	@	0	((/ (+ (* a2 a2) (* a1 a1)) (* (/ 1 (cos th)) (sqrt 2))) (* (/ 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)) (/ 1 (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))))) (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (sqrt 2) (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (* a2 a2) (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2)))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (/ a2 (sqrt 2)) a2) (cos th)) (* (/ a2 (sqrt 2)) a2) (/ a2 (sqrt 2)) (/ 1 (cos th)) (cos th) (/ 1 (sqrt 2)))
3.0ms	a2	@	inf	((/ (+ (* a2 a2) (* a1 a1)) (* (/ 1 (cos th)) (sqrt 2))) (* (/ 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)) (/ 1 (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))))) (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (sqrt 2) (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (* a2 a2) (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2)))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (/ a2 (sqrt 2)) a2) (cos th)) (* (/ a2 (sqrt 2)) a2) (/ a2 (sqrt 2)) (/ 1 (cos th)) (cos th) (/ 1 (sqrt 2)))
3.0ms	a2	@	-inf	((/ (+ (* a2 a2) (* a1 a1)) (* (/ 1 (cos th)) (sqrt 2))) (* (/ 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)) (/ 1 (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))))) (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (sqrt 2) (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (* a2 a2) (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2)))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (/ a2 (sqrt 2)) a2) (cos th)) (* (/ a2 (sqrt 2)) a2) (/ a2 (sqrt 2)) (/ 1 (cos th)) (cos th) (/ 1 (sqrt 2)))
3.0ms	th	@	inf	((/ (+ (* a2 a2) (* a1 a1)) (* (/ 1 (cos th)) (sqrt 2))) (* (/ 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)) (/ 1 (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))))) (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (sqrt 2) (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (* a2 a2) (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2)))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (/ a2 (sqrt 2)) a2) (cos th)) (* (/ a2 (sqrt 2)) a2) (/ a2 (sqrt 2)) (/ 1 (cos th)) (cos th) (/ 1 (sqrt 2)))

simplify162.0ms (2%)

Memory

5.6MiB live, 319.5MiB allocated

Algorithm

1×	egg-herbie

Rules

10 316×	`lower-fma.f64`
10 316×	`lower-fma.f32`
6 668×	`lower-*.f64`
6 668×	`lower-*.f32`
2 886×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	346	7482
1	1080	6803
2	3804	6769
0	8269	6420

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 456

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))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(/ (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) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
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(pow a1 2)
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
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(/ (pow a1 2) (sqrt 2))
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
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(/ (pow a1 2) (sqrt 2))
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(sqrt 2)
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(/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))
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(/ 1 (sqrt 2))
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(+ (* (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 a2 2) (sqrt 2))
(+ (* -1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (/ (pow a2 2) (sqrt 2)))
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(+ (* (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)))
1
(+ 1 (* 1/2 (pow th 2)))
(+ 1 (* (pow th 2) (+ 1/2 (* 5/24 (pow th 2)))))
(+ 1 (* (pow th 2) (+ 1/2 (* (pow th 2) (+ 5/24 (* 61/720 (pow th 2)))))))
1
(+ 1 (* -1/2 (pow th 2)))
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(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
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(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
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(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
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(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (sqrt 2) (* (cos th) (+ (pow a1 2) (pow a2 2))))
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(/ (sqrt 2) (* (cos th) (+ (pow a1 2) (pow a2 2))))
(/ (sqrt 2) (* (cos th) (+ (pow a1 2) (pow a2 2))))
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(cos th)
(cos th)
(cos th)
(cos th)
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(+ (/ (* (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))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(cos th)
(cos th)
(cos th)
(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)
(+ (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) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(+ (* (pow a2 2) (- (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 6) (cos th))) (/ (sqrt 2) (* (pow a1 4) (cos th))))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(+ (* (pow a2 2) (- (* (pow a2 2) (- (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a1 6) (cos th)))))) (/ (sqrt 2) (* (pow a1 4) (cos th))))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(/ (sqrt 2) (pow a1 2))
(+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 4))) (/ (sqrt 2) (pow a1 2)))
(+ (* (pow a2 2) (- (/ (* (pow a2 2) (sqrt 2)) (pow a1 6)) (/ (sqrt 2) (pow a1 4)))) (/ (sqrt 2) (pow a1 2)))
(+ (* (pow a2 2) (- (* (pow a2 2) (- (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 8))) (* -1 (/ (sqrt 2) (pow a1 6))))) (/ (sqrt 2) (pow a1 4)))) (/ (sqrt 2) (pow a1 2)))
(/ (* (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) (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2))))
(* (pow a2 2) (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2))))
(* (pow a2 2) (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2))))
(* (pow a2 2) (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (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) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ (* (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) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(/ (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) (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) (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2))))
(* (pow a2 2) (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2))))
(* (pow a2 2) (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2))))
(* (pow a2 2) (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (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) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ (* (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) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(/ (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) (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) (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2))))
(* (pow a2 2) (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2))))
(* (pow a2 2) (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2))))
(* (pow a2 2) (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (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) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))

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

rewrite167.0ms (2%)

Memory

16.3MiB live, 382.3MiB allocated

Rules

4 376×	`lower-/.f32`
4 360×	`lower-/.f64`
4 262×	`lower-*.f32`
4 248×	`lower-*.f64`
3 072×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	315
0	75	294
1	260	281
2	1892	281
0	8143	279

Stop Event

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

Counts

22 → 632

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1 binary64)) (neg.f64 (cos.f64 th))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 (pow.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
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(/.f64 (.f64 (.f64 a2 a2) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th) #s(literal 3 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)))) (-.f64 (fma.f64 (pow.f64 (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th) #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (pow.f64 a2 #s(literal 4 binary64)))) (-.f64 (.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(/.f64 (fma.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)) #s(literal 3 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)) (pow.f64 a2 #s(literal 6 binary64)))) (+.f64 (pow.f64 (.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 a2 #s(literal 4 binary64))) (.f64 (.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))))
(fma.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)))
(fma.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (.f64 (.f64 a2 a2) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)) #s(literal -1/2 binary64) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (.f64 (.f64 a2 a2) th) (.f64 #s(literal -1/2 binary64) (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)) a2) a2 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)) (.f64 a2 a2) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 a2 a2) (.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (*.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)))
(fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th) (.f64 a2 a2)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th) (.f64 #s(literal -1/2 binary64) (.f64 a2 a2)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (.f64 a2 a2) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (*.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)))
(fma.f64 th (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) (.f64 a2 a2)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 #s(literal 1 binary64) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (*.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)))
(fma.f64 a2 (.f64 a2 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th))) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)))
(+.f64 (.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(+.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (.f64 (.f64 (.f64 a2 a2) #s(literal -1/2 binary64)) (*.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2)
(.f64 (.f64 (*.f64 (cos.f64 th) a2) a2) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(.f64 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a2)
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))
(.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) a2))
(.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(.f64 a2 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (cos.f64 th) a2)))
(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(.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 (.f64 (neg.f64 (cos.f64 th)) (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (neg.f64 a2) (.f64 (cos.f64 th) a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 (cos.f64 th) a2) (neg.f64 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 (cos.f64 th) a2) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.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 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.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 (.f64 (*.f64 a2 a2) #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 a2 a2))
(.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)) #s(literal -1 binary64))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (.f64 (.f64 a2 a2) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 a2 (neg.f64 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 a2 #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (*.f64 (neg.f64 a2) a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))
(/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(exp.f64 (log.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(.f64 (.f64 a2 #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (neg.f64 a2) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 a2 #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) a2)
(*.f64 #s(literal 1 binary64) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal -1 binary64))
(/.f64 (*.f64 a2 #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 a2 #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (neg.f64 a2)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (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)) a2)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 th) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log.f64 (cos.f64 th))) #s(literal -1 binary64))
(pow.f64 (*.f64 (cos.f64 th) (cos.f64 th)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (cos.f64 th) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 (cos.f64 th))) #s(literal -1 binary64))
(pow.f64 (cos.f64 th) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 th)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (cos.f64 th))))
(/.f64 #s(literal 1 binary64) (cos.f64 th))
(neg.f64 (/.f64 #s(literal -1 binary64) (cos.f64 th)))
(exp.f64 (*.f64 (log.f64 (cos.f64 th)) #s(literal -1 binary64)))
(*.f64 (cos.f64 th) #s(literal 1 binary64))
(pow.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (cos.f64 th) #s(literal 1 binary64))
(/.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64))
(/.f64 (cos.f64 th) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 th) #s(literal -1 binary64)))
(cos.f64 th)
(exp.f64 (neg.f64 (*.f64 (log.f64 (cos.f64 th)) #s(literal -1 binary64))))
(*.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) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.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 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 2 binary64))))

eval164.0ms (2%)

Memory: 5.0MiB live, 475.3MiB allocated
Compiler: Compiled 24 223 to 2 668 computations (89% saved)

prune66.0ms (0.8%)

Memory

-8.0MiB live, 230.8MiB allocated

Pruning

39 alts after pruning (33 fresh and 6 done)

	Pruned	Kept	Total
New	1 189	7	1 196
Fresh	3	26	29
Picked	2	3	5
Done	0	3	3
Total	1 194	39	1 233

Accuracy

100.0%

Counts

1 233 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	57.8%	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 #s(approx (pow (cos th) -1) (fma.f64 (fma.f64 #s(literal 5/24 binary64) (.f64 th th) #s(literal 1/2 binary64)) (.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	66.8%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))))
✓	99.7%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	62.6%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	98.9%	(/.f64 (.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	99.3%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1))))
	98.9%	(/.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (.f64 a2 a2)) (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
	59.9%	(/.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (.f64 a2 a2)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	62.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
✓	66.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
	66.3%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) #s(approx (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
	11.6%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2)))) #s(approx (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (/.f64 (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a1) (/.f64 a2 a1))) (*.f64 a1 a1)))))
	62.6%	#s(approx (/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2) (cos th))) (.f64 (fma.f64 #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)))))
✓	66.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2)))
	66.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) a2)))
	66.6%	#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)))))
	54.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
	54.1%	#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)))))
	66.8%	#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))))
	98.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2))))
	66.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #s(literal 1/2 binary64)))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 a2 (*.f64 a2 (cos.f64 th)))))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) a2))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
	98.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 a2 (cos.f64 th))) a2))
	61.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (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)))) a2))
	60.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (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)))) a2))
✓	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
	62.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	66.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 #s(approx ( (/ a2 (sqrt 2)) (cos th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a2))
✓	15.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	15.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	15.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
✓	15.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	15.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))))
	49.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)) a2) a2 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
	66.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (.f64 a2 a2) #s(approx (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
	18.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (.f64 a2 a2) #s(approx (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2))) (.f64 (.f64 th th) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))))))

Compiler

Compiled 1 595 to 734 computations (54% saved)

regimes162.0ms (2%)

Memory

8.2MiB live, 456.0MiB allocated

Counts

69 → 1

Calls

Call 1

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

Calls

8 calls:

27.0ms	a2
20.0ms	a1
19.0ms	th
19.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
19.0ms	(*.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 35 to 40 computations (-14.3% saved)

regimes125.0ms (1.5%)

Memory

-17.1MiB live, 381.2MiB allocated

Counts

54 → 1

Calls

Call 1

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

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

Calls

8 calls:

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

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 35 to 40 computations (-14.3% saved)

regimes116.0ms (1.4%)

Memory

7.7MiB live, 285.8MiB allocated

Counts

48 → 1

Calls

Call 1

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

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

Calls

8 calls:

16.0ms	th
16.0ms	a1
15.0ms	a2
15.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
14.0ms	(cos.f64 th)

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes108.0ms (1.3%)

Memory

11.5MiB live, 251.4MiB allocated

Counts

43 → 1

Calls

Call 1

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

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

Calls

8 calls:

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

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes105.0ms (1.3%)

Memory

-3.1MiB live, 230.3MiB allocated

Counts

42 → 1

Calls

Call 1

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

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:

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

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes104.0ms (1.3%)

Memory

-21.7MiB live, 220.8MiB allocated

Counts

41 → 2

Calls

Call 1

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

Outputs

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

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

Calls

8 calls:

16.0ms	(cos.f64 th)
13.0ms	a2
13.0ms	a1
13.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
13.0ms	(*.f64 a2 a2)

Results

Accuracy	Segments	Branch
66.8%	1	`th`
66.8%	1	`a1`
68.8%	2	`a2`
80.6%	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)))`
79.7%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
79.7%	2	`(cos.f64 th)`
66.8%	1	`(*.f64 a1 a1)`
66.8%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes7.0ms (0.1%)

Memory

16.8MiB live, 16.8MiB allocated

Counts

21 → 2

Calls

Call 1

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

Outputs

#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (*.f64 #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) a2) (/.f64 a2 (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
80.6%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes4.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Counts

10 → 2

Calls

Call 1

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

Outputs

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

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
80.6%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes31.0ms (0.4%)

Memory

-14.7MiB live, 63.4MiB 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 (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 #s(approx ( (/ a2 (sqrt 2)) (cos th)) (/.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 (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (.f64 a2 a2) #s(approx (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2))) (/.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 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:

5.0ms	(cos.f64 th)
5.0ms	th
3.0ms	a2
3.0ms	a1
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes22.0ms (0.3%)

Memory

9.8MiB live, 48.9MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs

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

Calls

8 calls:

4.0ms	th
3.0ms	a1
3.0ms	a2
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
2.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Results

Accuracy	Segments	Branch
66.4%	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)))`
66.4%	1	`a1`
66.4%	1	`th`
66.4%	1	`(*.f64 a1 a1)`
66.4%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
66.4%	1	`(cos.f64 th)`
66.4%	1	`a2`
66.4%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes13.0ms (0.2%)

Memory

-14.6MiB live, 27.8MiB 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:

3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
1.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
1.0ms	th
1.0ms	a2
1.0ms	a1

Results

Accuracy	Segments	Branch
15.6%	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)))`
15.6%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
15.6%	1	`(cos.f64 th)`
15.6%	1	`a1`
15.6%	1	`th`
15.6%	1	`(*.f64 a1 a1)`
15.6%	1	`a2`
15.6%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-6.951520586016186e-105	-1.0175879126025359e-143

Compiler

Compiled 22 to 18 computations (18.2% saved)

bsearch0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-6.951520586016186e-105	-1.0175879126025359e-143

Compiler

Compiled 22 to 18 computations (18.2% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-6.951520586016186e-105	-1.0175879126025359e-143

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify25.0ms (0.3%)

Memory

16.5MiB live, 55.6MiB allocated

Algorithm

1×	egg-herbie

Rules

28×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`
2×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	462
1	96	462

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(.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 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (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)))))
(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 -6455624695217271/1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915717951585986373746688 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(approx (cos th) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 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 -6455624695217271/1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915717951585986373746688 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(approx (cos th) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) a2) (/.f64 a2 (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 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) #s(literal -6455624695217271/1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915717951585986373746688 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (.f64 a2 a2) #s(approx (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2))) (.f64 (.f64 th th) (/.f64 #s(literal -1/2 binary64) (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))))
#s(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 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(.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 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (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)))))
(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 -6455624695217271/1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915717951585986373746688 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(approx (cos th) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
(if (<=.f64 (+.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) #s(literal -6455624695217271/1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915717951585986373746688 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(approx (cos th) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 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 -6455624695217271/1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915717951585986373746688 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(approx (cos th) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) a2) (/.f64 a2 (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 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) #s(literal -6455624695217271/1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915717951585986373746688 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(approx (cos th) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) a2) (/.f64 a2 (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 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) #s(literal -6455624695217271/1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915717951585986373746688 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (.f64 a2 a2) #s(approx (+ (* (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2))) (.f64 (.f64 th th) (/.f64 #s(literal -1/2 binary64) (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 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) #s(literal -6455624695217271/1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915717951585986373746688 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 #s(approx (+ ( (* th (/ th (sqrt 2))) -1/2) (/ 1 (sqrt 2))) (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 th th))) (.f64 a2 a2)))) (/.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))))
#s(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)))

soundness1.1s (12.9%)

Memory

1.6MiB live, 787.5MiB allocated

Rules

34 694×	`lower-fma.f64`
34 694×	`lower-fma.f32`
10 506×	`lower-fma.f64`
10 506×	`lower-fma.f32`
10 316×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	346	7482
1	1080	6803
2	3804	6769
0	8269	6420
0	33	198
0	51	180
1	172	178
2	1198	178
0	8135	178
0	12	44
0	20	38
1	58	38
2	411	38
3	7331	38
0	8434	37
0	111	1498
1	343	1366
2	1206	1262
3	3900	1233
0	8428	1172
0	307	7296
1	1012	6607
2	3782	6309
0	8053	5932

Stop Event

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

Compiler

Compiled 516 to 274 computations (46.9% saved)

preprocess152.0ms (1.8%)

Memory

3.8MiB live, 211.9MiB allocated

Remove

(sort a1 a2)

(abs a1)

(abs a2)

(abs th)

Compiler

Compiled 774 to 376 computations (51.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	33	253
0	51	235
1	87	235
2	140	235
3	265	233
4	364	233
5	551	227
6	664	227
0	664	227

Iter	Nodes	Cost
0	46	321
0	70	302
1	112	290
2	168	286
3	258	286
4	424	286
5	539	274
6	738	274
7	764	274
8	816	274
9	904	274
10	951	274
11	970	274
12	977	274
13	986	274
0	986	274

Iter	Nodes	Cost
0	33	253
0	51	235
1	87	235
2	140	235
3	265	233
4	364	233
5	551	227
6	664	227
0	664	227

Iter	Nodes	Cost
0	46	321
0	70	302
1	112	290
2	168	286
3	258	286
4	424	286
5	539	274
6	738	274
7	764	274
8	816	274
9	904	274
10	951	274
11	970	274
12	977	274
13	986	274
0	986	274

start0.0ms (0%)

analyze0.0ms (0%)

sample1.5s (18.2%)

explain219.0ms (2.6%)

preprocess150.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize65.0ms (0.8%)

series33.0ms (0.4%)

simplify273.0ms (3.3%)

rewrite180.0ms (2.2%)

eval118.0ms (1.4%)

prune55.0ms (0.7%)

simplify15.0ms (0.2%)

localize154.0ms (1.8%)

series62.0ms (0.8%)

simplify228.0ms (2.7%)

rewrite596.0ms (7.2%)

eval783.0ms (9.4%)

prune178.0ms (2.1%)

simplify37.0ms (0.5%)

localize106.0ms (1.3%)

series42.0ms (0.5%)

simplify170.0ms (2%)

rewrite205.0ms (2.5%)

eval223.0ms (2.7%)

prune85.0ms (1%)

simplify41.0ms (0.5%)

localize103.0ms (1.2%)

series51.0ms (0.6%)

simplify162.0ms (2%)

rewrite167.0ms (2%)

eval164.0ms (2%)

prune66.0ms (0.8%)

regimes162.0ms (2%)

regimes125.0ms (1.5%)

regimes116.0ms (1.4%)

regimes108.0ms (1.3%)

regimes105.0ms (1.3%)

regimes104.0ms (1.3%)

regimes7.0ms (0.1%)

regimes4.0ms (0.1%)

regimes31.0ms (0.4%)

regimes22.0ms (0.3%)

regimes13.0ms (0.2%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify25.0ms (0.3%)

soundness1.1s (12.9%)

preprocess152.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	33	253
0	51	235
1	87	235
2	140	235
3	265	233
4	364	233
5	551	227
6	664	227
0	664	227

Iter	Nodes	Cost
0	46	321
0	70	302
1	112	290
2	168	286
3	258	286
4	424	286
5	539	274
6	738	274
7	764	274
8	816	274
9	904	274
10	951	274
11	970	274
12	977	274
13	986	274
0	986	274