Metrics for Migdal et al, Equation (64)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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)

sample1.6s (16.3%)

Memory

80.3MiB live, 1 758.3MiB allocated

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 914.0ms

ival-mult: 400.0ms (43.8% of total)

ival-cos: 275.0ms (30.1% of total)

ival-div: 95.0ms (10.4% of total)

ival-add: 67.0ms (7.3% of total)

ival-sqrt: 62.0ms (6.8% of total)

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

exact: 6.0ms (0.7% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain236.0ms (2.5%)

Memory

-51.1MiB live, 213.1MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

61.0ms

512×

valid

Compiler

Compiled 135 to 40 computations (70.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-div: 12.0ms (28% of total)

ival-cos: 12.0ms (28% of total)

ival-mult: 12.0ms (28% of total)

ival-sqrt: 4.0ms (9.3% of total)

ival-add: 2.0ms (4.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess135.0ms (1.4%)

Memory

10.8MiB live, 47.6MiB 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	9

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 (hypot.f64 a2 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB 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

7.3MiB live, 7.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 th)
cost-diff	0	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
cost-diff	2432	(+.f64 (.f64 (/.f64 (cos.f64 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	46

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 (hypot.f64 a2 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

localize57.0ms (0.6%)

Memory

-16.2MiB live, 62.1MiB 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

31.0ms

256×

valid

Compiler

Compiled 58 to 14 computations (75.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-cos: 12.0ms (54.3% of total)

ival-mult: 5.0ms (22.6% of total)

ival-div: 2.0ms (9% of total)

ival-sqrt: 2.0ms (9% of total)

ival-add: 1.0ms (4.5% of total)

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

exact: 0.0ms (0% of total)

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

series27.0ms (0.3%)

Memory

-2.8MiB live, 33.8MiB 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
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)))
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)))

simplify329.0ms (3.4%)

Memory

17.2MiB live, 399.5MiB 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	1068

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

rewrite177.0ms (1.8%)

Memory

12.2MiB live, 321.4MiB 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	34

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

eval60.0ms (0.6%)

Memory: 35.8MiB live, 154.8MiB allocated
Compiler: Compiled 12 726 to 1 066 computations (91.6% saved)

prune78.0ms (0.8%)

Memory

-68.9MiB live, 89.7MiB allocated

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	477	13	490
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	478	13	491

Accuracy

100.0%

Counts

491 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(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 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th)))
▶	99.6%	(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th)))
	99.7%	(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
▶	99.7%	(fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th)))
	99.6%	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 2 binary64))))
▶	99.7%	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
	99.6%	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
	96.9%	(+.f64 #s(approx (* (/ (cos th) (sqrt 2)) (* a1 a1)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
	99.6%	(.f64 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64))
▶	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)))
	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 478 to 350 computations (26.8% saved)

simplify9.0ms (0.1%)

Memory

16.1MiB live, 16.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 a2 (cos.f64 th))
cost-diff	0	(.f64 (.f64 a2 (cos.f64 th)) a2)
cost-diff	0	(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))
cost-diff	6720	(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
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	2304	(fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th)))
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	(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
cost-diff	0	(/.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	384	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
cost-diff	2432	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))

Rules

152×	`lower-*.f32`
130×	`lower-*.f64`
108×	`lower-fma.f32`
102×	`lower-fma.f64`
54×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	293
0	61	282
1	105	270
2	143	270
3	174	268
4	192	268
5	193	268
0	193	251

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

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

localize142.0ms (1.5%)

Memory

7.2MiB live, 161.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1484375	(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
accuracy	0.15234375	(*.f64 a2 (cos.f64 th))
accuracy	0.21941376953688405	(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th)))
accuracy	0.453125	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.1484375	(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
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	0.453125	(/.f64 a1 (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	0.1484375	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
accuracy	0.217128759768442	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
accuracy	0.24285126953688405	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
accuracy	0.7138862793053261	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

112.0ms

256×

valid

Compiler

Compiled 275 to 34 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-mult: 42.0ms (60.3% of total)

ival-div: 7.0ms (10% of total)

ival-cos: 6.0ms (8.6% of total)

ival-add: 5.0ms (7.2% of total)

ival-sqrt: 5.0ms (7.2% of total)

ival-pow: 4.0ms (5.7% of total)

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

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

exact: 0.0ms (0% of total)

series50.0ms (0.5%)

Memory

-25.4MiB live, 94.9MiB allocated

Counts

22 → 456

Calls

Call 1

Inputs
#s(alt (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (patch (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) #<representation:binary64>) () ())
#s(alt (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (patch (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #<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 #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) #<representation:binary64>) () ())
#s(alt (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (patch (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) #<representation:binary64>) () ())
#s(alt (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) #<representation:binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation:binary64>) () ())
#s(alt #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 (fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) (patch (fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) #<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 (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) (patch (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) #<representation:binary64>) () ())
#s(alt (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (patch (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #<representation:binary64>) () ())
#s(alt (.f64 (.f64 a2 (cos.f64 th)) a2) (patch (.f64 (.f64 a2 (cos.f64 th)) a2) #<representation:binary64>) () ())
#s(alt (.f64 a2 (cos.f64 th)) (patch (.f64 a2 (cos.f64 th)) #<representation:binary64>) () ())
#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #<representation:binary64>) () ())
#s(alt (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (patch (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #<representation:binary64>) () ())
#s(alt (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (patch (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) #<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 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (patch (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) #<representation:binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (patch (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) #<representation:binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (patch (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) #<representation:binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (patch (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) #<representation:binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor 0 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 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 (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) (patch (fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (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 (fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) (patch (fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (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 (fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) (patch (fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (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 (fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) (patch (fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (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 (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 (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor -inf a2) (#s(alt (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) (patch (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) (patch (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) (patch (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) (patch (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th))) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (cos th)) (taylor -inf a2) (#s(alt (.f64 (.f64 a2 (cos.f64 th)) a2) (patch (.f64 (.f64 a2 (cos.f64 th)) a2) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (cos th)) (taylor -inf a2) (#s(alt (.f64 (.f64 a2 (cos.f64 th)) a2) (patch (.f64 (.f64 a2 (cos.f64 th)) a2) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (cos th)) (taylor -inf a2) (#s(alt (.f64 (.f64 a2 (cos.f64 th)) a2) (patch (.f64 (.f64 a2 (cos.f64 th)) a2) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (cos th)) (taylor -inf a2) (#s(alt (.f64 (.f64 a2 (cos.f64 th)) a2) (patch (.f64 (.f64 a2 (cos.f64 th)) a2) #<representation:binary64>) () ())) ())
#s(alt (* a2 (cos th)) (taylor -inf a2) (#s(alt (.f64 a2 (cos.f64 th)) (patch (.f64 a2 (cos.f64 th)) #<representation:binary64>) () ())) ())
#s(alt (* a2 (cos th)) (taylor -inf a2) (#s(alt (.f64 a2 (cos.f64 th)) (patch (.f64 a2 (cos.f64 th)) #<representation:binary64>) () ())) ())
#s(alt (* a2 (cos th)) (taylor -inf a2) (#s(alt (.f64 a2 (cos.f64 th)) (patch (.f64 a2 (cos.f64 th)) #<representation:binary64>) () ())) ())
#s(alt (* a2 (cos th)) (taylor -inf a2) (#s(alt (.f64 a2 (cos.f64 th)) (patch (.f64 a2 (cos.f64 th)) #<representation:binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor -inf a2) (#s(alt (.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
6.0ms	a2	@	inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (* a2 a2) (/ (sqrt 2) (cos th)))) (/ (* a2 a2) (/ (sqrt 2) (cos th))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (+ (* (* (/ a2 (sqrt 2)) (cos th)) a2) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (/ a2 (sqrt 2)) (cos th)) (/ a2 (sqrt 2)) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (pow 2 -1/2) (* (* a2 (cos th)) a2) (* a2 (cos th)) (/ (sqrt 2) (cos th)) (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1))
4.0ms	a1	@	-inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (* a2 a2) (/ (sqrt 2) (cos th)))) (/ (* a2 a2) (/ (sqrt 2) (cos th))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (+ (* (* (/ a2 (sqrt 2)) (cos th)) a2) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (/ a2 (sqrt 2)) (cos th)) (/ a2 (sqrt 2)) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (pow 2 -1/2) (* (* a2 (cos th)) a2) (* a2 (cos th)) (/ (sqrt 2) (cos th)) (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1))
3.0ms	a2	@	-inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (* a2 a2) (/ (sqrt 2) (cos th)))) (/ (* a2 a2) (/ (sqrt 2) (cos th))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (+ (* (* (/ a2 (sqrt 2)) (cos th)) a2) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (/ a2 (sqrt 2)) (cos th)) (/ a2 (sqrt 2)) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (pow 2 -1/2) (* (* a2 (cos th)) a2) (* a2 (cos th)) (/ (sqrt 2) (cos th)) (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1))
3.0ms	th	@	inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (* a2 a2) (/ (sqrt 2) (cos th)))) (/ (* a2 a2) (/ (sqrt 2) (cos th))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (+ (* (* (/ a2 (sqrt 2)) (cos th)) a2) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (/ a2 (sqrt 2)) (cos th)) (/ a2 (sqrt 2)) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (pow 2 -1/2) (* (* a2 (cos th)) a2) (* a2 (cos th)) (/ (sqrt 2) (cos th)) (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1))
3.0ms	th	@	-inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (* a2 a2) (/ (sqrt 2) (cos th)))) (/ (* a2 a2) (/ (sqrt 2) (cos th))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (+ (* (* (/ a2 (sqrt 2)) (cos th)) a2) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (/ a2 (sqrt 2)) (cos th)) (/ a2 (sqrt 2)) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (pow 2 -1/2) (* (* a2 (cos th)) a2) (* a2 (cos th)) (/ (sqrt 2) (cos th)) (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1))

simplify283.0ms (2.9%)

Memory

39.5MiB live, 359.7MiB allocated

Algorithm

1×	egg-herbie

Rules

20 208×	`lower-fma.f64`
20 208×	`lower-fma.f32`
6 078×	`lower-*.f64`
6 078×	`lower-*.f32`
4 288×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	228	6156
1	724	5619
2	2557	5202
3	5549	5048
0	8146	4342

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 454

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

rewrite230.0ms (2.4%)

Memory

6.5MiB live, 430.2MiB allocated

Rules

10 608×	`lower-fma.f32`
10 602×	`lower-fma.f64`
4 650×	`lower-*.f32`
4 628×	`lower-*.f64`
3 616×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	214
0	61	185
1	202	185
2	1483	185
0	8317	163

Stop Event

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

Counts

22 → 1 224

Calls

Call 1

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

Outputs
(.f64 (/.f64 (.f64 (hypot.f64 a2 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2))) (fma.f64 a1 a1 (*.f64 (neg.f64 a2) a2))))
(.f64 (/.f64 (.f64 (hypot.f64 a2 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (cos.f64 th)) (/.f64 (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 th))) (/.f64 (hypot.f64 a2 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 (hypot.f64 a2 a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 (neg.f64 (cos.f64 th)) (hypot.f64 a2 a1)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (hypot.f64 a2 a1) (/.f64 #s(literal -1 binary64) (cos.f64 th))))
(.f64 (neg.f64 (/.f64 (-.f64 (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 (neg.f64 a2) a2)))))
(.f64 (fma.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) #s(literal -1/2 binary64) (.f64 (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 (cos.f64 th)) (/.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (neg.f64 (fma.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -3 binary64)) (pow.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a2 #s(literal -2 binary64))) #s(literal -3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.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 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))))))
(.f64 (neg.f64 (fma.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -3 binary64)) (pow.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a2 #s(literal -2 binary64))) #s(literal -3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.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 (.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2))))))))
(.f64 (fma.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a1 (cos.f64 th)) a1))) #s(literal 1/2 binary64))
(.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a2 #s(literal -2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) a1))) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a2 #s(literal -2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (fma.f64 (.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (.f64 (.f64 a1 (cos.f64 th)) a1))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (.f64 a1 (cos.f64 th)) a1))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2))) #s(literal 1/2 binary64))
(.f64 (fma.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a2 #s(literal -2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a2 #s(literal -2 binary64))))))
(.f64 (fma.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 a2) a2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))))
(.f64 (fma.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))))
(*.f64 (hypot.f64 a2 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 (neg.f64 a2) a2))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (/.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (hypot.f64 a2 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (fma.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -3 binary64)) (pow.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a2 #s(literal -2 binary64))) #s(literal -3 binary64))) (pow.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 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal -3 binary64)) (pow.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a2 #s(literal -2 binary64))) #s(literal -3 binary64))) (pow.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 (.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2))))) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (/.f64 (hypot.f64 a2 a1) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (hypot.f64 a2 a1))
(*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (cos.f64 th) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (hypot.f64 a2 a1)))
(*.f64 (cos.f64 th) (hypot.f64 (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (hypot.f64 a2 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2)))) (.f64 (/.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2))))) (.f64 (.f64 (/.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2)))) (.f64 (/.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2)))))) (fma.f64 (/.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2))) (.f64 (/.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2))))))
(/.f64 (-.f64 (.f64 (/.f64 (.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 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (/.f64 (.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 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))) (.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (/.f64 (.f64 (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 th)) (/.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))))
(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2)))) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2)))) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2)))) (.f64 (/.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2)))) (fma.f64 (.f64 (/.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2)))) (.f64 (/.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2)))) (.f64 (.f64 (/.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2)))) (.f64 (/.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (fma.f64 a1 a1 (*.f64 (neg.f64 a2) a2))))))))
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(fma.f64 (.f64 (neg.f64 a1) (.f64 a1 (cos.f64 th))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 (.f64 (.f64 (neg.f64 a2) (cos.f64 th)) a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 (.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) a1 (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 (.f64 (.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64) (.f64 (.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th) (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
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(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)))))
(fma.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th) (.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (cos.f64 th)) (.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 a1 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 a1 (.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
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(fma.f64 (cos.f64 th) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (.f64 a1 a1)) (.f64 (.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 (*.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (.f64 (/.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2)))) (.f64 (/.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (fma.f64 a1 a1 (*.f64 (neg.f64 a2) a2)))))
(-.f64 (/.f64 (.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 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (/.f64 (.f64 (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))))
(-.f64 (.f64 (.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 (neg.f64 a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (cos.f64 th)))
(+.f64 (.f64 (/.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 (neg.f64 a2) a2)))) (neg.f64 (.f64 (/.f64 (pow.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) #s(literal 2 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (fma.f64 a1 a1 (*.f64 (neg.f64 a2) a2))))))
(+.f64 (/.f64 (.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 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (neg.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))))
(+.f64 (.f64 (.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (.f64 (.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 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 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) #s(literal 2 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) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (neg.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal -1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(.f64 (.f64 (*.f64 a2 (cos.f64 th)) a2) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 a2 (cos.f64 th)) a2))
(.f64 (.f64 a2 (cos.f64 th)) a2)
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 #s(literal 1 binary64) (.f64 a2 (cos.f64 th)))
(.f64 (.f64 a2 (cos.f64 th)) #s(literal 1 binary64))
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) a2))
(/.f64 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (cos.f64 th)))
(/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) (/.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 th)))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (cos.f64 th) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 th)) (pow.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (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 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (cos.f64 th)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (cos.f64 th) #s(literal -1 binary64)))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1 binary64))
(pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 th)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (pow.f64 (cos.f64 th) #s(literal -1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) #s(literal -1 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (cos.f64 th)))
(/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) #s(literal 1 binary64))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(neg.f64 (/.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) #s(literal 1 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)))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 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 #s(literal -1 binary64)) (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 a2 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) (*.f64 a2 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(.f64 (.f64 (neg.f64 a2) a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (/.f64 a2 (pow.f64 a2 #s(literal -1 binary64))))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
(.f64 (.f64 a2 a2) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 a2 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a2 #s(literal -2 binary64))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a2 #s(literal -2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a2 #s(literal -2 binary64))) #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)) (pow.f64 a2 #s(literal -2 binary64))))
(/.f64 (*.f64 (neg.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 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(neg.f64 (*.f64 (neg.f64 a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (neg.f64 a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (-.f64 (.f64 (log.f64 a2) #s(literal 2 binary64)) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 a2) #s(literal 2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(*.f64 (/.f64 a1 #s(literal -1 binary64)) (/.f64 (neg.f64 a1) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (neg.f64 a1) #s(literal -1 binary64)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 a1 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) (*.f64 a1 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))))
(.f64 (.f64 (neg.f64 a1) a1) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (/.f64 a1 (pow.f64 a1 #s(literal -1 binary64))))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 a1 #s(literal -1 binary64))))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
(.f64 (.f64 a1 a1) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 a1 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (neg.f64 a1) a1)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (neg.f64 a1) a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))
(/.f64 (neg.f64 a1) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(neg.f64 (/.f64 (*.f64 (neg.f64 a1) a1) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 (*.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (*.f64 (neg.f64 a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (-.f64 (.f64 (log.f64 a1) #s(literal 2 binary64)) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 a1) #s(literal 2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))))

eval299.0ms (3.1%)

Memory: 27.7MiB live, 684.4MiB allocated
Compiler: Compiled 49 459 to 2 851 computations (94.2% saved)

prune59.0ms (0.6%)

Memory

-41.4MiB live, 185.3MiB allocated

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	2 048	21	2 069
Fresh	8	0	8
Picked	4	1	5
Done	0	0	0
Total	2 060	22	2 082

Accuracy

100.0%

Counts

2 082 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	42.6%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (fma.f64 (.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64))) (.f64 th th) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))))
	66.8%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
	98.9%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
	99.6%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 a2 a2)))
▶	99.6%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (cos.f64 th) (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))))
▶	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 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 a2 (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 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (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 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 2 binary64))))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (*.f64 (neg.f64 a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (cos.f64 th))))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 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) (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 (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 (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 #s(literal -1/2 binary64) (*.f64 th th) #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 (/.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 (sqrt.f64 #s(literal 2 binary64))) a1)))
▶	42.2%	#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 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (.f64 (.f64 (.f64 (.f64 a2 a2) th) (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64))))))

Compiler

Compiled 649 to 540 computations (16.8% saved)

simplify268.0ms (2.8%)

Memory

20.7MiB live, 138.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 a2 (cos.f64 th))
cost-diff	0	(.f64 (.f64 a2 (cos.f64 th)) a2)
cost-diff	0	(/.f64 (.f64 (.f64 a2 (cos.f64 th)) 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 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (.f64 (.f64 (.f64 (.f64 a2 a2) th) (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 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))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (.f64 (.f64 (.f64 (.f64 a2 a2) th) (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64))))))
cost-diff	1664	(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (.f64 (.f64 (.f64 (.f64 a2 a2) th) (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
cost-diff	0	#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
cost-diff	0	(fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
cost-diff	0	(cos.f64 th)
cost-diff	0	(.f64 (cos.f64 th) (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
cost-diff	0	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (cos.f64 th) (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))))

Rules

9 472×	`lower-fma.f32`
9 464×	`lower-fma.f64`
5 156×	`lower-*.f32`
5 136×	`lower-*.f64`
2 328×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	447
0	87	421
1	154	421
2	318	418
3	869	415
4	1847	415
5	2456	406
6	2787	406
7	3488	406
8	4599	406
9	5773	406
10	6307	406
11	6527	406
12	6623	406
13	6651	406
14	6651	406
15	6838	406
16	6998	406
17	7141	406
18	7217	406
19	7261	406
20	7769	406
21	7782	406
22	7792	406
0	8714	386

Stop Event

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

Calls

Call 1

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

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

localize168.0ms (1.7%)

Memory

-4.1MiB live, 154.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.07421875	(.f64 (.f64 a2 (cos.f64 th)) a2)
accuracy	0.15234375	(*.f64 a2 (cos.f64 th))
accuracy	0.203125	(/.f64 (.f64 (.f64 a2 (cos.f64 th)) 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 (cos.f64 th)) a2) (sqrt.f64 #s(literal 2 binary64))))
accuracy	2.816375973661162	(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (.f64 (.f64 (.f64 (.f64 a2 a2) th) (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64))))
accuracy	4.578754027221312	(.f64 (.f64 (*.f64 a2 a2) th) (/.f64 th (sqrt.f64 #s(literal 2 binary64))))
accuracy	7.281719919143085	(.f64 (.f64 a2 a2) th)
accuracy	24.846226850245543	#s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (.f64 (.f64 (.f64 (.f64 a2 a2) th) (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)))))
accuracy	0.00390625	(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.197597509768442	(/.f64 (*.f64 a2 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 a2) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.1484375	(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
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 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
accuracy	52.265772717124456	#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
accuracy	0.12109375	(fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
accuracy	0.1484375	(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
accuracy	0.41796875	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2)
accuracy	0.453125	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))

Samples

111.0ms

256×

valid

Compiler

Compiled 331 to 46 computations (86.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-mult: 26.0ms (37.2% of total)

const: 13.0ms (18.6% of total)

ival-div: 9.0ms (12.9% of total)

ival-add: 7.0ms (10% of total)

ival-cos: 6.0ms (8.6% of total)

ival-pow: 4.0ms (5.7% of total)

ival-sqrt: 3.0ms (4.3% of total)

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

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

exact: 0.0ms (0% of total)

series71.0ms (0.7%)

Memory

-4.3MiB live, 72.8MiB allocated

Counts

23 → 528

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
14.0ms	a1	@	-inf	((+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (cos th) (+ (* (* (sqrt 1/2) a2) a2) (* (/ a1 (sqrt 2)) a1))) (cos th) (+ (* (* (sqrt 1/2) a2) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* (/ a1 (sqrt 2)) a1) (/ a1 (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (/ (* a2 a2) (sqrt 2))) (sqrt 2) (+ (* (/ a2 (sqrt 2)) a2) (* (* (* (* a2 a2) th) (/ th (sqrt 2))) (+ (* 1/24 (* th th)) -1/2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a2 (cos th)) a2) (sqrt 2)) (* (* a2 (cos th)) a2) (* a2 (cos th)) (* (sqrt 1/2) a2) (/ (* a2 a2) (sqrt 2)) (* (* a2 a2) th) (* (* (* a2 a2) th) (/ th (sqrt 2))))
5.0ms	a2	@	0	((+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (cos th) (+ (* (* (sqrt 1/2) a2) a2) (* (/ a1 (sqrt 2)) a1))) (cos th) (+ (* (* (sqrt 1/2) a2) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* (/ a1 (sqrt 2)) a1) (/ a1 (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (/ (* a2 a2) (sqrt 2))) (sqrt 2) (+ (* (/ a2 (sqrt 2)) a2) (* (* (* (* a2 a2) th) (/ th (sqrt 2))) (+ (* 1/24 (* th th)) -1/2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a2 (cos th)) a2) (sqrt 2)) (* (* a2 (cos th)) a2) (* a2 (cos th)) (* (sqrt 1/2) a2) (/ (* a2 a2) (sqrt 2)) (* (* a2 a2) th) (* (* (* a2 a2) th) (/ th (sqrt 2))))
4.0ms	a2	@	inf	((+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (cos th) (+ (* (* (sqrt 1/2) a2) a2) (* (/ a1 (sqrt 2)) a1))) (cos th) (+ (* (* (sqrt 1/2) a2) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* (/ a1 (sqrt 2)) a1) (/ a1 (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (/ (* a2 a2) (sqrt 2))) (sqrt 2) (+ (* (/ a2 (sqrt 2)) a2) (* (* (* (* a2 a2) th) (/ th (sqrt 2))) (+ (* 1/24 (* th th)) -1/2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a2 (cos th)) a2) (sqrt 2)) (* (* a2 (cos th)) a2) (* a2 (cos th)) (* (sqrt 1/2) a2) (/ (* a2 a2) (sqrt 2)) (* (* a2 a2) th) (* (* (* a2 a2) th) (/ th (sqrt 2))))
4.0ms	a2	@	-inf	((+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (cos th) (+ (* (* (sqrt 1/2) a2) a2) (* (/ a1 (sqrt 2)) a1))) (cos th) (+ (* (* (sqrt 1/2) a2) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* (/ a1 (sqrt 2)) a1) (/ a1 (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (/ (* a2 a2) (sqrt 2))) (sqrt 2) (+ (* (/ a2 (sqrt 2)) a2) (* (* (* (* a2 a2) th) (/ th (sqrt 2))) (+ (* 1/24 (* th th)) -1/2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a2 (cos th)) a2) (sqrt 2)) (* (* a2 (cos th)) a2) (* a2 (cos th)) (* (sqrt 1/2) a2) (/ (* a2 a2) (sqrt 2)) (* (* a2 a2) th) (* (* (* a2 a2) th) (/ th (sqrt 2))))
4.0ms	th	@	inf	((+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (cos th) (+ (* (* (sqrt 1/2) a2) a2) (* (/ a1 (sqrt 2)) a1))) (cos th) (+ (* (* (sqrt 1/2) a2) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (* (/ a1 (sqrt 2)) a1) (/ a1 (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (/ (* a2 a2) (sqrt 2))) (sqrt 2) (+ (* (/ a2 (sqrt 2)) a2) (* (* (* (* a2 a2) th) (/ th (sqrt 2))) (+ (* 1/24 (* th th)) -1/2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a2 (cos th)) a2) (sqrt 2)) (* (* a2 (cos th)) a2) (* a2 (cos th)) (* (sqrt 1/2) a2) (/ (* a2 a2) (sqrt 2)) (* (* a2 a2) th) (* (* (* a2 a2) th) (/ th (sqrt 2))))

simplify299.0ms (3.1%)

Memory

-19.5MiB live, 272.4MiB allocated

Algorithm

1×	egg-herbie

Rules

17 602×	`lower-fma.f64`
17 602×	`lower-fma.f32`
5 744×	`lower-*.f64`
5 744×	`lower-*.f32`
3 370×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	198	7413
1	647	6553
2	2216	6128
3	4641	5958
4	7520	5938
0	8274	5103

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 527

Calls

Call 1

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

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

rewrite264.0ms (2.7%)

Memory

-9.6MiB live, 308.6MiB allocated

Rules

9 948×	`lower-fma.f32`
9 940×	`lower-fma.f64`
4 516×	`lower-*.f32`
4 516×	`lower-/.f32`
4 506×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	367
0	87	341
1	283	334
2	2057	326
0	8507	302

Stop Event

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

Counts

23 → 598

Calls

Call 1

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

Outputs
#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (cos.f64 th)))
(.f64 (.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)))) (cos.f64 th)) (pow.f64 (fma.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64) (-.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))) #s(literal -1 binary64)))
(.f64 (.f64 (cos.f64 th) (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal 2 binary64))) (pow.f64 (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) #s(literal -1 binary64)))
(.f64 (.f64 (cos.f64 th) (fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64))))) (pow.f64 (fma.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64) (-.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) (.f64 (*.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
(.f64 (fma.f64 (pow.f64 (.f64 (cos.f64 th) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) #s(literal 2 binary64)) (-.f64 (.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 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) (.f64 (*.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (cos.f64 th))
(.f64 (cos.f64 th) (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(/.f64 (neg.f64 (.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal 2 binary64)) (cos.f64 th))) (neg.f64 (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)))) (cos.f64 th))) (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)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (.f64 (cos.f64 th) (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))))
(/.f64 (neg.f64 (.f64 (cos.f64 th) (fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 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)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64))))) (neg.f64 (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) (.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 (.f64 (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal 2 binary64)) (cos.f64 th)) (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(/.f64 (.f64 (fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)))) (cos.f64 th)) (fma.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64) (-.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 (.f64 (cos.f64 th) (/.f64 (-.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
(/.f64 (.f64 (cos.f64 th) (fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64))))) (fma.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64) (-.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) #s(literal 2 binary64)) (.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 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) (.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (cos.f64 th) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) #s(literal 2 binary64)) (-.f64 (.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 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) (.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (.f64 (/.f64 a1 (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)) (cos.f64 th))))
(/.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)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))) (.f64 (fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (*.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)))) (cos.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (.f64 (cos.f64 th) (/.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 (fma.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64) (-.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))) (.f64 (cos.f64 th) (fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (*.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) (.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (-.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 th) #s(literal 2 binary64)) (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) #s(literal 2 binary64)) (-.f64 (.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 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) (.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))) (fma.f64 (pow.f64 (.f64 (cos.f64 th) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))))
(/.f64 (fma.f64 (pow.f64 (.f64 (cos.f64 th) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 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 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th))))))
(/.f64 (fma.f64 (pow.f64 (.f64 (cos.f64 th) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) #s(literal 2 binary64)) (-.f64 (.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 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)) (.f64 (.f64 (cos.f64 th) a1) (/.f64 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 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)))
(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 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)))
(fma.f64 (/.f64 (neg.f64 a1) #s(literal -1 binary64)) (.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)))
(fma.f64 (/.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)))
(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 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)))
(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 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)))
(fma.f64 (/.f64 a1 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (cos.f64 th) a1) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)))
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(fma.f64 (.f64 a1 (neg.f64 a1)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))
(fma.f64 (.f64 a1 #s(literal 1 binary64)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))
(fma.f64 (neg.f64 (.f64 a1 a1)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))
(fma.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (/.f64 a1 (pow.f64 a1 #s(literal -1 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))
(fma.f64 #s(literal 1 binary64) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))
(fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (.f64 a1 a1) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))
(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 a1 #s(literal -1 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))
(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))
(fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 a2 a2) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))
(fma.f64 a2 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(-.f64 (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (-.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))) (/.f64 (.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (-.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))))
(-.f64 (/.f64 (.f64 (pow.f64 a2 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))) (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))))
(+.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(+.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))
#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
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(.f64 (.f64 #s(literal 1 binary64) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 a1 (neg.f64 a1)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
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(.f64 (.f64 a1 a1) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
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(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 a1 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) #s(literal 2 binary64))
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(/.f64 (neg.f64 (*.f64 a1 (neg.f64 a1))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 a1 #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
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(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) a1)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
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(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 (neg.f64 a1))))
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(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))
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(/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
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(.f64 (.f64 a1 #s(literal 1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(*.f64 (neg.f64 (neg.f64 a1)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
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(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 a1 #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) a1)
(*.f64 #s(literal 1 binary64) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 a1) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
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(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) #s(literal -1 binary64))
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(/.f64 (neg.f64 (*.f64 a1 #s(literal 1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
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(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
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(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)))
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(.f64 (neg.f64 (fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)) (pow.f64 a2 #s(literal 6 binary64)) (.f64 (pow.f64 a1 #s(literal 6 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64))))) (/.f64 #s(literal 1 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))))))
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(.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 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #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 1/2 binary64))
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(.f64 (fma.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 a2) a2))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #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 1/2 binary64))
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(.f64 (/.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 (-.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))))
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(+.f64 (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (.f64 (.f64 (.f64 th th) #s(literal 1/24 binary64)) (/.f64 (pow.f64 (.f64 th a2) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 (pow.f64 (.f64 th a2) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (.f64 (.f64 th th) #s(literal 1/24 binary64)) (/.f64 (pow.f64 (.f64 th a2) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (.f64 th a2) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(+.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (.f64 (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (.f64 th a2) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (.f64 th a2) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (.f64 th a2) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (.f64 th a2) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(*.f64 (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 a2 #s(literal 1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(*.f64 (neg.f64 (neg.f64 a2)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 a2 #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) a2)
(*.f64 #s(literal 1 binary64) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 a2) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 a2 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) 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 (neg.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 #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 (neg.f64 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.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)))
#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (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 (cos.f64 th) #s(literal -1 binary64)) (/.f64 (.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (neg.f64 (.f64 (cos.f64 th) a2)) #s(literal -1 binary64)) (/.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 (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 (neg.f64 a2) #s(literal -1 binary64)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(.f64 (/.f64 a2 #s(literal -1 binary64)) (/.f64 (neg.f64 (.f64 (cos.f64 th) a2)) (sqrt.f64 #s(literal 2 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 (cos.f64 th) a2) a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.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 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 (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 (cos.f64 th) a2)) (/.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 (.f64 (cos.f64 th) a2) a2) #s(literal 1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(.f64 (.f64 (*.f64 (cos.f64 th) a2) #s(literal 1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (cos.f64 th) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(.f64 (.f64 (cos.f64 th) (*.f64 (neg.f64 a2) a2)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))
(.f64 (neg.f64 (.f64 (neg.f64 a2) (*.f64 (cos.f64 th) a2))) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (*.f64 a2 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (cos.f64 th) a2)))))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (/.f64 #s(literal 1 binary64) (pow.f64 a2 #s(literal -1 binary64))))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2)
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2)))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (/.f64 (.f64 (cos.f64 th) a2) (pow.f64 a2 #s(literal -1 binary64))))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (/.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 (.f64 (*.f64 (cos.f64 th) a2) a2) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (.f64 (*.f64 (cos.f64 th) a2) a2))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
(.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 (/.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 (*.f64 (cos.f64 th) a2) a2) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (cos.f64 th) (pow.f64 a2 #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 (cos.f64 th) a2))
(.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 #s(literal 1 binary64) (pow.f64 a2 #s(literal -2 binary64))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (pow.f64 a2 #s(literal -1 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 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (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 #s(literal 1 binary64) (.f64 (cos.f64 th) a2))) (neg.f64 (/.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 (.f64 (*.f64 (cos.f64 th) a2) a2) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 (.f64 (cos.f64 th) a2) #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 (neg.f64 a2) a2))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (.f64 (neg.f64 a2) (.f64 (cos.f64 th) a2)))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 a2 a2))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(/.f64 (neg.f64 (*.f64 (cos.f64 th) #s(literal 1 binary64))) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)))
(/.f64 (neg.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(/.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 #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 (*.f64 (cos.f64 th) a2) a2) #s(literal 1 binary64)) (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 (cos.f64 th) #s(literal 1 binary64)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))
(/.f64 (.f64 (cos.f64 th) (.f64 (neg.f64 a2) a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 (cos.f64 th) a2)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (neg.f64 (.f64 (neg.f64 a2) (.f64 (cos.f64 th) a2))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (cos.f64 th) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 (cos.f64 th)) (.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (*.f64 (cos.f64 th) a2) a2) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (.f64 (cos.f64 th) a2) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2) (*.f64 (cos.f64 th) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (cos.f64 th) (.f64 (neg.f64 a2) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 #s(literal 1 binary64) (.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 (.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 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2) (cos.f64 th)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (cos.f64 th) a2)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (cos.f64 th) a2)))
(/.f64 (neg.f64 (cos.f64 th)) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)))
(/.f64 (.f64 (neg.f64 a2) (.f64 (cos.f64 th) a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 (neg.f64 a2) a2) (neg.f64 (/.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 (cos.f64 th) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))
(neg.f64 (/.f64 (.f64 (neg.f64 a2) (.f64 (cos.f64 th) a2)) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (cos.f64 th) a2))) #s(literal -1 binary64)))
(.f64 (.f64 (cos.f64 th) a2) a2)
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 (cos.f64 th) a2))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2)
(*.f64 a2 (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (/.f64 (neg.f64 a2) #s(literal -1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 a2 #s(literal -1 binary64)) (/.f64 (neg.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 #s(literal 1 binary64) (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 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 #s(literal 1 binary64) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 a2 #s(literal 1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 (.f64 (neg.f64 a2) a2)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(.f64 (.f64 (*.f64 a2 a2) #s(literal 1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (/.f64 a2 (pow.f64 a2 #s(literal -1 binary64))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 a2 #s(literal -2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (.f64 a2 a2))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(.f64 (.f64 (neg.f64 a2) a2) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 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 (.f64 a2 a2) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) a2) #s(literal 2 binary64))
(pow.f64 (*.f64 a2 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) a2)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (neg.f64 (*.f64 a2 #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (neg.f64 a2) a2))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64))) (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 #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (neg.f64 (*.f64 (neg.f64 a2) a2)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) 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 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 a2 #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 a2) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))
(/.f64 (*.f64 (neg.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 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(neg.f64 (/.f64 (*.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 (*.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (-.f64 (.f64 (log.f64 a2) #s(literal 2 binary64)) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64) (*.f64 (log.f64 a2) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 a2) #s(literal 2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)) #s(literal -1 binary64)))
(.f64 (.f64 th a2) a2)
(.f64 (.f64 a2 a2) th)
(.f64 th (.f64 a2 a2))
(.f64 a2 (.f64 th a2))
(.f64 (/.f64 (neg.f64 th) #s(literal -1 binary64)) (/.f64 (.f64 (*.f64 a2 a2) th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 (*.f64 a2 a2) th) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 th #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (*.f64 a2 a2) th) #s(literal -1 binary64)) (/.f64 (neg.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (*.f64 th th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (.f64 (*.f64 a2 a2) th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 th (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 th (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (*.f64 a2 a2) th) (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 (*.f64 th a2) th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (.f64 th a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (pow.f64 th #s(literal -1 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (.f64 a2 a2) th)) (/.f64 th (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (neg.f64 th) (.f64 (.f64 a2 a2) th)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (.f64 (.f64 a2 a2) th) #s(literal 1 binary64)) (/.f64 th (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (.f64 (.f64 a2 a2) th) (neg.f64 th)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) th)
(.f64 (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) a2) (*.f64 th a2))
(.f64 (neg.f64 (pow.f64 (.f64 th a2) #s(literal 2 binary64))) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 th a2) #s(literal 2 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(.f64 (.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th) (*.f64 a2 a2))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (/.f64 (.f64 (*.f64 a2 a2) th) (pow.f64 th #s(literal -1 binary64))))
(.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 th a2) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 th (pow.f64 th #s(literal -1 binary64))))
(.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) (pow.f64 th #s(literal -1 binary64))))
(.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 a2 a2) th))
(.f64 (.f64 (*.f64 a2 a2) th) (/.f64 th (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 th a2) (pow.f64 th #s(literal -1 binary64))))
(.f64 (.f64 a2 a2) (*.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th))
(.f64 th (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (.f64 (.f64 a2 a2) th)))
(.f64 th (.f64 (*.f64 a2 a2) (/.f64 th (sqrt.f64 #s(literal 2 binary64)))))
(.f64 a2 (.f64 (*.f64 th a2) (/.f64 th (sqrt.f64 #s(literal 2 binary64)))))
(.f64 a2 (.f64 a2 (*.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th)))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 th a2) #s(literal 2 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 (*.f64 a2 a2) th))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) th)))
(/.f64 (neg.f64 (.f64 (neg.f64 th) (.f64 (*.f64 a2 a2) th))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 (*.f64 a2 a2) th) #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) th)))
(/.f64 (neg.f64 (.f64 (.f64 (*.f64 a2 a2) th) (neg.f64 th))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 th a2) #s(literal 2 binary64)))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (*.f64 a2 a2) th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) th))
(/.f64 (.f64 (neg.f64 th) (.f64 (*.f64 a2 a2) th)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 (*.f64 a2 a2) th) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) th))
(/.f64 (.f64 (.f64 (*.f64 a2 a2) th) (neg.f64 th)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 (.f64 a2 a2) th)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) th)))
(/.f64 (neg.f64 (pow.f64 (*.f64 th a2) #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 th a2) #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 th a2) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) th) (.f64 #s(literal 1 binary64) (.f64 (*.f64 a2 a2) th))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 th) (.f64 (*.f64 a2 a2) th))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) th) (.f64 (.f64 (*.f64 a2 a2) th) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (*.f64 a2 a2) th) (neg.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 th a2) #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) th) (.f64 (.f64 a2 a2) th)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 th a2) #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 a2 a2) th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) th))

eval288.0ms (3%)

Memory: 27.5MiB live, 337.4MiB allocated
Compiler: Compiled 24 901 to 2 819 computations (88.7% saved)

prune127.0ms (1.3%)

Memory

9.1MiB live, 174.6MiB allocated

Pruning

32 alts after pruning (29 fresh and 3 done)

	Pruned	Kept	Total
New	1 277	20	1 297
Fresh	7	9	16
Picked	2	3	5
Done	1	0	1
Total	1 287	32	1 319

Accuracy

100.0%

Counts

1 319 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.9%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
▶	98.9%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
▶	99.6%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 a2 a2)))
	99.6%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (cos.f64 th) (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))))
	98.9%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (cos.f64 th) #s(approx (+ ( (* (sqrt 1/2) a2) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 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 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))))
	66.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 a2) #s(literal 1 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 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (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))))
✓	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 (cos.f64 th)) 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 (.f64 a2 #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) (sqrt.f64 #s(literal 2 binary64))))
	60.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 #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) (sqrt.f64 #s(literal 2 binary64))))
▶	61.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) a2) (sqrt.f64 #s(literal 2 binary64))))
	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (*.f64 (neg.f64 a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (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 (sqrt.f64 #s(literal 2 binary64)) a2)))
	62.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (* (* a2 (cos th)) a2) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
	66.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (* (* a2 (cos th)) a2) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.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)))
	66.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))) #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 (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))) #s(approx (/ (* (* a2 (cos th)) a2) (sqrt 2)) (*.f64 (/.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 (/.f64 a1 (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 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) a1)))

Compiler

Compiled 883 to 751 computations (14.9% saved)

simplify292.0ms (3%)

Memory

-13.4MiB live, 182.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))
cost-diff	0	(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
cost-diff	0	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
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 #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	0	(.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
cost-diff	0	(.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) a2)
cost-diff	0	(/.f64 (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) 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 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) a2) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(*.f64 a1 a1)
cost-diff	0	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(cos.f64 th)
cost-diff	0	(*.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 a2 a2)))
cost-diff	1408	(.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 a2 a2))

Rules

4 962×	`lower-*.f32`
4 942×	`lower-*.f64`
3 578×	`lower-/.f32`
3 564×	`lower-/.f64`
2 562×	`associate-/r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	417
0	86	399
1	154	389
2	280	389
3	606	383
4	1306	383
5	2852	377
6	2959	377
7	3283	377
8	3450	377
9	3486	377
10	3572	377
11	4896	377
12	4945	377
13	4997	377
14	5115	377
15	5165	377
16	5217	377
17	5272	377
18	5330	377
19	5391	377
20	5455	377
21	5522	377
22	5592	377
23	5665	377
24	5741	377
25	5820	377
26	5902	377
27	7978	377
0	8024	345

Stop Event

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

Calls

Call 1

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

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

localize165.0ms (1.7%)

Memory

9.1MiB live, 207.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 th)
accuracy	0.19140625	(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
accuracy	0.209316259768442	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))
accuracy	0.4861156154526852	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 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	0.15234375	(.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
accuracy	0.203125	(/.f64 (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) 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 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) a2) (sqrt.f64 #s(literal 2 binary64))))
accuracy	32.75742518128696	#s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))
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	0.18359375	(.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 a2 a2))
accuracy	0.1953125	(*.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	0.23046875	(/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2)
accuracy	0.453125	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))

Samples

122.0ms

256×

valid

Compiler

Compiled 306 to 46 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 92.0ms

ival-mult: 31.0ms (33.6% of total)

ival-pow: 27.0ms (29.2% of total)

ival-div: 17.0ms (18.4% of total)

ival-add: 6.0ms (6.5% of total)

ival-cos: 6.0ms (6.5% of total)

ival-sqrt: 3.0ms (3.2% of total)

exact: 1.0ms (1.1% of total)

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

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

series105.0ms (1.1%)

Memory

-11.2MiB live, 113.6MiB allocated

Counts

23 → 492

Calls

Call 1

Inputs
#s(alt (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2)) (patch (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2)) #<representation:binary64>) () ())
#s(alt #s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2))) (patch #s(approx (+ ( (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 a2 a2))) #<representation:binary64>) () ())
#s(alt (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation:binary64>) () ())
#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation:binary64>) () ())
#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))) #<representation:binary64>) () ())
#s(alt #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (+ ( (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))) #<representation:binary64>) () ())
#s(alt (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) #<representation:binary64>) () ())
#s(alt (.f64 a1 a1) (patch (.f64 a1 a1) #<representation:binary64>) () ())
#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))) a2) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) a2) (sqrt.f64 #s(literal 2 binary64)))) #<representation:binary64>) () ())
#s(alt (/.f64 (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))) a2) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))) a2) (sqrt.f64 #s(literal 2 binary64))) #<representation:binary64>) () ())
#s(alt (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))) a2) (patch (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))) a2) #<representation:binary64>) () ())
#s(alt (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))) (patch (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))) #<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 (/.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 (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2))) (patch #s(approx (+ ( (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))) #<representation:binary64>) () ())
#s(alt (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (patch (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2)) #<representation:binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) #<representation:binary64>) () ())
#s(alt (sqrt.f64 #s(literal 1/2 binary64)) (patch (sqrt.f64 #s(literal 1/2 binary64)) #<representation:binary64>) () ())
#s(alt (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (patch (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) #<representation:binary64>) () ())
#s(alt #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))) (patch #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))) #<representation:binary64>) () ())
#s(alt (/.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 1/2))) (taylor 0 a1) (#s(alt (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2)) (patch (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2)) #<representation:binary64>) () ())) ())
#s(alt (+ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (/ (* (pow a1 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2)) (patch (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2)) #<representation:binary64>) () ())) ())
#s(alt (+ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (/ (* (pow a1 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2)) (patch (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2)) #<representation:binary64>) () ())) ())
#s(alt (+ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (/ (* (pow a1 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2)) (patch (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2)) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2))) (patch #s(approx (+ ( (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 a2 a2))) #<representation:binary64>) () ())) ())
#s(alt (+ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (/ (* (pow a1 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2))) (patch #s(approx (+ ( (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 a2 a2))) #<representation:binary64>) () ())) ())
#s(alt (+ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (/ (* (pow a1 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2))) (patch #s(approx (+ ( (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 a2 a2))) #<representation:binary64>) () ())) ())
#s(alt (+ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (/ (* (pow a1 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2))) (patch #s(approx (+ ( (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 a2 a2))) #<representation:binary64>) () ())) ())
#s(alt (* (cos th) (sqrt 1/2)) (taylor 0 a1) (#s(alt (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))) (taylor 0 a1) (#s(alt (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))) (taylor 0 a1) (#s(alt (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))) (taylor 0 a1) (#s(alt (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (.f64 (cos.f64 th) (fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (+ ( (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (+ ( (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (+ ( (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (+ ( (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ (pow a1 2) (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) #<representation:binary64>) () ())) ())
#s(alt (/ (pow a1 2) (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) #<representation:binary64>) () ())) ())
#s(alt (/ (pow a1 2) (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) #<representation:binary64>) () ())) ())
#s(alt (/ (pow a1 2) (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) #<representation:binary64>) () ())) ())
#s(alt (pow a1 2) (taylor 0 a1) (#s(alt (.f64 a1 a1) (patch (.f64 a1 a1) #<representation:binary64>) () ())) ())
#s(alt (pow a1 2) (taylor 0 a1) (#s(alt (.f64 a1 a1) (patch (.f64 a1 a1) #<representation:binary64>) () ())) ())
#s(alt (pow a1 2) (taylor 0 a1) (#s(alt (.f64 a1 a1) (patch (.f64 a1 a1) #<representation:binary64>) () ())) ())
#s(alt (pow a1 2) (taylor 0 a1) (#s(alt (.f64 a1 a1) (patch (.f64 a1 a1) #<representation:binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))) a2) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) a2) (sqrt.f64 #s(literal 2 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)))) a2) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (+ ( (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) a2) (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))) (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 1/2))) (taylor -inf a2) (#s(alt #s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2))) (patch #s(approx (+ ( (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt #s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2))) (patch #s(approx (+ ( (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt #s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2))) (patch #s(approx (+ ( (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt #s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2))) (patch #s(approx (+ ( (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor -inf a2) (#s(alt (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (patch (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2)) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor -inf a2) (#s(alt (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (patch (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2)) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor -inf a2) (#s(alt (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (patch (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2)) #<representation:binary64>) () ())) ())
#s(alt (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor -inf a2) (#s(alt (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (patch (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2)) #<representation:binary64>) () ())) ())
#s(alt (/ a1 (* a2 (sqrt 2))) (taylor -inf a2) (#s(alt (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (patch (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) #<representation:binary64>) () ())) ())
#s(alt (/ a1 (* a2 (sqrt 2))) (taylor -inf a2) (#s(alt (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (patch (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) #<representation:binary64>) () ())) ())
#s(alt (/ a1 (* a2 (sqrt 2))) (taylor -inf a2) (#s(alt (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (patch (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) #<representation:binary64>) () ())) ())
#s(alt (/ a1 (* a2 (sqrt 2))) (taylor -inf a2) (#s(alt (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (patch (/.f64 (/.f64 a1 (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>) () ())) ())
#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
33.0ms	a1	@	inf	((* (* (cos th) (+ (* (/ (/ a1 (sqrt 2)) a2) (/ a1 a2)) (sqrt 1/2))) (* a2 a2)) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (cos th) (+ (* (/ (/ a1 (sqrt 2)) a2) (/ a1 a2)) (sqrt 1/2))) (cos th) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/ (* a1 a1) (sqrt 2)) (* a1 a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a2 (cos th)) a2) (sqrt 2)) (* (* a2 (cos th)) a2) (* a2 (cos th)) (/ 1 (/ (sqrt 2) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (sqrt 1/2) (/ (/ a1 (sqrt 2)) a2) (cos th) (/ (sqrt 2) a2))
18.0ms	a2	@	inf	((* (* (cos th) (+ (* (/ (/ a1 (sqrt 2)) a2) (/ a1 a2)) (sqrt 1/2))) (* a2 a2)) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (cos th) (+ (* (/ (/ a1 (sqrt 2)) a2) (/ a1 a2)) (sqrt 1/2))) (cos th) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/ (* a1 a1) (sqrt 2)) (* a1 a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a2 (cos th)) a2) (sqrt 2)) (* (* a2 (cos th)) a2) (* a2 (cos th)) (/ 1 (/ (sqrt 2) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (sqrt 1/2) (/ (/ a1 (sqrt 2)) a2) (cos th) (/ (sqrt 2) a2))
4.0ms	a2	@	-inf	((* (* (cos th) (+ (* (/ (/ a1 (sqrt 2)) a2) (/ a1 a2)) (sqrt 1/2))) (* a2 a2)) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (cos th) (+ (* (/ (/ a1 (sqrt 2)) a2) (/ a1 a2)) (sqrt 1/2))) (cos th) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/ (* a1 a1) (sqrt 2)) (* a1 a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a2 (cos th)) a2) (sqrt 2)) (* (* a2 (cos th)) a2) (* a2 (cos th)) (/ 1 (/ (sqrt 2) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (sqrt 1/2) (/ (/ a1 (sqrt 2)) a2) (cos th) (/ (sqrt 2) a2))
4.0ms	a2	@	0	((* (* (cos th) (+ (* (/ (/ a1 (sqrt 2)) a2) (/ a1 a2)) (sqrt 1/2))) (* a2 a2)) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (cos th) (+ (* (/ (/ a1 (sqrt 2)) a2) (/ a1 a2)) (sqrt 1/2))) (cos th) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/ (* a1 a1) (sqrt 2)) (* a1 a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a2 (cos th)) a2) (sqrt 2)) (* (* a2 (cos th)) a2) (* a2 (cos th)) (/ 1 (/ (sqrt 2) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (sqrt 1/2) (/ (/ a1 (sqrt 2)) a2) (cos th) (/ (sqrt 2) a2))
3.0ms	a1	@	-inf	((* (* (cos th) (+ (* (/ (/ a1 (sqrt 2)) a2) (/ a1 a2)) (sqrt 1/2))) (* a2 a2)) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (cos th) (+ (* (/ (/ a1 (sqrt 2)) a2) (/ a1 a2)) (sqrt 1/2))) (cos th) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (/ (* a1 a1) (sqrt 2)) (* a1 a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (* (* a2 (cos th)) a2) (sqrt 2)) (* (* a2 (cos th)) a2) (* a2 (cos th)) (/ 1 (/ (sqrt 2) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (sqrt 1/2) (/ (/ a1 (sqrt 2)) a2) (cos th) (/ (sqrt 2) a2))

simplify327.0ms (3.4%)

Memory

27.8MiB live, 336.7MiB allocated

Algorithm

1×	egg-herbie

Rules

21 500×	`lower-fma.f64`
21 500×	`lower-fma.f32`
5 122×	`lower-*.f64`
5 122×	`lower-*.f32`
4 418×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	228	7180
1	747	6698
2	2750	6072
3	6537	5881
0	8409	5142

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 491

Calls

Call 1

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

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

rewrite592.0ms (6.1%)

Memory

-34.7MiB live, 329.6MiB allocated

Rules

4 948×	`lower-*.f32`
4 928×	`lower-*.f64`
4 276×	`lower-/.f32`
4 262×	`lower-/.f64`
4 142×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	332
0	86	308
1	287	294
2	2092	294
0	8303	274

Stop Event

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

Counts

23 → 304

Calls

Call 1

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

Outputs
(.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (fma.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(.f64 (.f64 (.f64 a2 a2) (fma.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (cos.f64 th))
(.f64 (.f64 (fma.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 a2 (cos.f64 th))) a2)
(.f64 (.f64 a2 a2) (.f64 (fma.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
(.f64 (.f64 (fma.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)) (.f64 a2 a2))
(.f64 (fma.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 a2 (cos.f64 th)) a2))
(.f64 a2 (.f64 (fma.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 a2 (cos.f64 th))))
(.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (fma.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) (.f64 a2 a2) (.f64 (.f64 (*.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (.f64 a2 a2) (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) (.f64 (.f64 (*.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 1/2 binary64))))
(+.f64 (.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) (.f64 a2 a2)) (.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 1/2 binary64))))
(+.f64 (.f64 (.f64 a2 a2) (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th))) (.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (fma.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(.f64 (fma.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(.f64 (cos.f64 th) (fma.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (.f64 (-.f64 (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (pow.f64 a2 #s(literal 4 binary64))) #s(literal 1/2 binary64)) (cos.f64 th))) (neg.f64 (-.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (pow.f64 a1 #s(literal 6 binary64))) (pow.f64 a2 #s(literal 6 binary64)))) (cos.f64 th))) (neg.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)))) (/.f64 (*.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (pow.f64 a2 #s(literal 4 binary64))))))
(/.f64 (neg.f64 (.f64 (cos.f64 th) (-.f64 (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (pow.f64 a2 #s(literal 4 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (-.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (cos.f64 th) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (pow.f64 a1 #s(literal 6 binary64))) (pow.f64 a2 #s(literal 6 binary64)))))) (neg.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)))) (/.f64 (*.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (pow.f64 a2 #s(literal 4 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) #s(literal 2 binary64)) (pow.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (cos.f64 th) #s(literal 3 binary64)) (/.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (pow.f64 a1 #s(literal 6 binary64))) (pow.f64 a2 #s(literal 6 binary64))) (pow.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))))))
(/.f64 (.f64 (-.f64 (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (pow.f64 a2 #s(literal 4 binary64))) #s(literal 1/2 binary64)) (cos.f64 th)) (-.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (pow.f64 a1 #s(literal 6 binary64))) (pow.f64 a2 #s(literal 6 binary64)))) (cos.f64 th)) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)))) (/.f64 (*.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (pow.f64 a2 #s(literal 4 binary64)))))
(/.f64 (.f64 (cos.f64 th) (-.f64 (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (pow.f64 a2 #s(literal 4 binary64))) #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (.f64 (cos.f64 th) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (pow.f64 a1 #s(literal 6 binary64))) (pow.f64 a2 #s(literal 6 binary64))))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64)))) (/.f64 (*.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 1/2 binary64)) (pow.f64 a2 #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) #s(literal 2 binary64)) (pow.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))))
(/.f64 (fma.f64 (pow.f64 (cos.f64 th) #s(literal 3 binary64)) (/.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (pow.f64 a1 #s(literal 6 binary64))) (pow.f64 a2 #s(literal 6 binary64))) (pow.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))))))
(fma.f64 (.f64 (cos.f64 th) (/.f64 a1 a2)) (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))
(fma.f64 (.f64 (cos.f64 th) (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2)) (/.f64 a1 a2) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))
(fma.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (.f64 (.f64 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)))
(fma.f64 (/.f64 a1 a2) (.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))
(fma.f64 (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (.f64 (/.f64 a1 a2) (cos.f64 th)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))
(fma.f64 (cos.f64 th) (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))) (/.f64 (pow.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))))
(+.f64 (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 (.f64 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (pow.f64 a2 #s(literal -2 binary64))) (cos.f64 th)))
(cos.f64 th)
#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
#s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 a1 #s(literal -2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (.f64 a1 a1))
(.f64 (.f64 (neg.f64 a1) a1) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
(.f64 (.f64 a1 a1) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) a1) #s(literal 2 binary64))
(pow.f64 (*.f64 a1 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a1 #s(literal -2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a1 #s(literal -2 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (*.f64 (neg.f64 a1) a1))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 a1 a1) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) a1)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(/.f64 (neg.f64 (*.f64 a1 #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(/.f64 (neg.f64 (*.f64 (neg.f64 a1) a1)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 (.f64 a1 a1) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
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(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
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(pow.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))
(pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1/2 binary64))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (/.f64 a2 (neg.f64 a1)) #s(literal -1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 a2 #s(literal -1 binary64)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (neg.f64 a1) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (neg.f64 a2) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2))
(*.f64 (/.f64 a1 a2) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 a2 #s(literal -1 binary64)))
(.f64 a1 (pow.f64 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 a1 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) a2))
(pow.f64 (/.f64 (/.f64 a2 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a1) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2) #s(literal -1 binary64))
(pow.f64 (/.f64 a2 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (neg.f64 a1) (pow.f64 a2 #s(literal -1 binary64)))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))) (neg.f64 a2))
(/.f64 (neg.f64 (.f64 (neg.f64 a1) #s(literal 1 binary64))) (neg.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2)))
(/.f64 (neg.f64 (.f64 a1 #s(literal 1 binary64))) (neg.f64 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (/.f64 a1 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 (neg.f64 a1) (pow.f64 a2 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (pow.f64 a2 #s(literal -1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1)))
(/.f64 (neg.f64 (neg.f64 a1)) (neg.f64 (*.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 a1)) (neg.f64 (neg.f64 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) a2)
(/.f64 (.f64 (neg.f64 a1) #s(literal 1 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2))
(/.f64 (.f64 a1 #s(literal 1 binary64)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (pow.f64 a2 #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))
(/.f64 (neg.f64 a1) (*.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 a1) (neg.f64 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 (neg.f64 a1) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (neg.f64 (neg.f64 a2))))
(/.f64 (/.f64 (neg.f64 a1) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 a2))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 a2 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a1)))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 a2 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 a2 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 a2 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a1))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2))
(/.f64 #s(literal 1 binary64) (/.f64 a2 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 a1 a2) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (neg.f64 a2)))
(/.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2)
(/.f64 a1 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 (/.f64 (neg.f64 a1) (sqrt.f64 #s(literal 2 binary64))) a2))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 a1 (.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 a1 (neg.f64 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 a2)) (/.f64 (/.f64 (neg.f64 a1) (sqrt.f64 #s(literal 2 binary64))) a2))
(exp.f64 (*.f64 (log.f64 (/.f64 a2 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal -1 binary64)))
#s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (neg.f64 a2) #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 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (neg.f64 a2) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 a2 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal -1/2 binary64)) #s(literal -1 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 a2) #s(literal -1 binary64)))
(*.f64 (pow.f64 (neg.f64 a2) #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 a2) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 a2 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (neg.f64 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) (pow.f64 (/.f64 #s(literal -1 binary64) (/.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))
(*.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 (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)))
(pow.f64 (/.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64))
(pow.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #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 (neg.f64 (pow.f64 a2 #s(literal -1 binary64))) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 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 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) a2)
(/.f64 (pow.f64 a2 #s(literal -1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 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 #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)))))
(/.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)
(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 (sqrt.f64 #s(literal 2 binary64)) a2)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)))

eval110.0ms (1.1%)

Memory: 35.9MiB live, 273.6MiB allocated
Compiler: Compiled 14 954 to 1 888 computations (87.4% saved)

prune66.0ms (0.7%)

Memory

-17.7MiB live, 182.2MiB allocated

Pruning

38 alts after pruning (31 fresh and 7 done)

	Pruned	Kept	Total
New	885	11	896
Fresh	4	20	24
Picked	1	4	5
Done	0	3	3
Total	890	38	928

Accuracy

100.0%

Counts

928 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.9%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (*.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 1/2 binary64))))
	98.9%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
	98.8%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 a2 (cos.f64 th))) a2))
✓	98.9%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
	60.5%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) (.f64 th th) #s(literal 1 binary64)))) (*.f64 a2 a2)))
	62.2%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(approx (cos th) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (.f64 a2 a2)))
	99.6%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 a2 a2)))
	99.6%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (cos.f64 th) (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))))
	98.9%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 (cos.f64 th) #s(approx (+ ( (* (sqrt 1/2) a2) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))))
	66.4%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) (.f64 #s(approx ( (sqrt 1/2) (cos th)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 a2 a2)))
	66.4%	#s(approx (+ (* (pow 2 -1/2) (* (* a2 (cos th)) a2)) (* (* (/ a1 (sqrt 2)) a1) (cos th))) #s(approx (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 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 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))))
	66.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 a2) #s(literal 1 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)))
	66.8%	#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 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (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))))
✓	98.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 (cos.f64 th)) 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 (.f64 a2 #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) (sqrt.f64 #s(literal 2 binary64))))
	60.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 #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) (sqrt.f64 #s(literal 2 binary64))))
✓	61.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))) a2) (sqrt.f64 #s(literal 2 binary64))))
	62.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 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 (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 (cos th)) a2) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	66.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.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)))
	66.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))) #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 (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 a2 (/.f64 (.f64 #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) 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 (/ (* (* a2 (cos th)) a2) (sqrt 2)) (*.f64 (/.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 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))

Compiler

Compiled 1 553 to 709 computations (54.3% saved)

regimes164.0ms (1.7%)

Memory

-21.5MiB live, 381.4MiB allocated

Counts

66 → 1

Calls

Call 1

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

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

Calls

8 calls:

33.0ms	(*.f64 a1 a1)
19.0ms	a1
18.0ms	a2
18.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
18.0ms	th

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes130.0ms (1.3%)

Memory

23.9MiB live, 344.5MiB allocated

Counts

58 → 1

Calls

Call 1

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

Outputs

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

Calls

8 calls:

19.0ms	a1
17.0ms	th
16.0ms	a2
16.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
15.0ms	(*.f64 a2 a2)

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes118.0ms (1.2%)

Memory

4.2MiB live, 323.5MiB allocated

Counts

53 → 1

Calls

Call 1

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

Outputs

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

Calls

8 calls:

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

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes116.0ms (1.2%)

Memory

5.6MiB live, 326.0MiB allocated

Counts

52 → 1

Calls

Call 1

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

Calls

8 calls:

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

regimes102.0ms (1.1%)

Memory

-3.9MiB live, 273.3MiB allocated

Counts

45 → 1

Calls

Call 1

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

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

regimes101.0ms (1.1%)

Memory

9.1MiB live, 289.2MiB allocated

Counts

44 → 1

Calls

Call 1

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

Outputs

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

Calls

8 calls:

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

regimes93.0ms (1%)

Memory

-5.4MiB live, 275.9MiB allocated

Counts

39 → 2

Calls

Call 1

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

Outputs

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

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

Calls

8 calls:

12.0ms	a2
12.0ms	(cos.f64 th)
11.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
11.0ms	a1
11.0ms	(+.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
66.8%	1	`a1`
68.8%	2	`a2`
66.8%	1	`th`
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)

regimes8.0ms (0.1%)

Memory

-16.4MiB live, 22.9MiB allocated

Counts

22 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

7.0ms

(+.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)

regimes7.0ms (0.1%)

Memory

18.4MiB live, 18.4MiB allocated

Counts

19 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

5.0ms

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

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)

regimes7.0ms (0.1%)

Memory

-20.3MiB live, 18.9MiB allocated

Counts

16 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

6.0ms

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

Results

Accuracy	Segments	Branch
80.2%	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)

regimes26.0ms (0.3%)

Memory

-3.5MiB live, 78.1MiB allocated

Counts

8 → 1

Calls

Call 1

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

Calls

8 calls:

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

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes15.0ms (0.2%)

Memory

9.7MiB live, 49.2MiB allocated

Accuracy

Total -32.6b remaining (-151.8%)

Threshold costs -32.6b (-151.8%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

8 calls:

2.0ms	a1
2.0ms	th
2.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
2.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
2.0ms	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	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
66.4%	1	`(cos.f64 th)`
66.4%	1	`a1`
66.4%	1	`th`
66.4%	1	`(*.f64 a1 a1)`
66.4%	1	`a2`
66.4%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

bsearch1.0ms (0%)

Memory

2.1MiB live, 2.1MiB 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

1.5MiB 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

1.6MiB live, 1.7MiB 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)

simplify31.0ms (0.3%)

Memory

-18.3MiB live, 100.0MiB allocated

Algorithm

1×	egg-herbie

Rules

36×	`-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	87	644
1	109	644

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.6s (16.6%)

Memory

4.1MiB live, 1 363.1MiB allocated

Rules

34 694×	`lower-fma.f64`
34 694×	`lower-fma.f32`
21 500×	`lower-fma.f64`
21 500×	`lower-fma.f32`
20 208×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	198	7413
1	647	6553
2	2216	6128
3	4641	5958
4	7520	5938
0	8274	5103
0	38	214
0	61	185
1	202	185
2	1483	185
0	8317	163
0	57	367
0	87	341
1	283	334
2	2057	326
0	8507	302
0	228	7180
1	747	6698
2	2750	6072
3	6537	5881
0	8409	5142
0	12	44
0	20	38
1	58	38
2	411	38
3	7331	38
0	8434	34
0	228	6156
1	724	5619
2	2557	5202
3	5549	5048
0	8146	4342
0	111	1498
1	343	1366
2	1206	1262
3	3900	1233
0	8428	1068

Stop Event

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

Compiler

Compiled 848 to 417 computations (50.8% saved)

preprocess219.0ms (2.3%)

Memory

24.0MiB live, 456.7MiB allocated

Remove

(abs a1)

(abs th)

Compiler

Compiled 1 922 to 1 012 computations (47.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.6s (16.3%)

explain236.0ms (2.5%)

preprocess135.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize57.0ms (0.6%)

series27.0ms (0.3%)

simplify329.0ms (3.4%)

rewrite177.0ms (1.8%)

eval60.0ms (0.6%)

prune78.0ms (0.8%)

simplify9.0ms (0.1%)

localize142.0ms (1.5%)

series50.0ms (0.5%)

simplify283.0ms (2.9%)

rewrite230.0ms (2.4%)

eval299.0ms (3.1%)

prune59.0ms (0.6%)

simplify268.0ms (2.8%)

localize168.0ms (1.7%)

series71.0ms (0.7%)

simplify299.0ms (3.1%)

rewrite264.0ms (2.7%)

eval288.0ms (3%)

prune127.0ms (1.3%)

simplify292.0ms (3%)

localize165.0ms (1.7%)

series105.0ms (1.1%)

simplify327.0ms (3.4%)

rewrite592.0ms (6.1%)

eval110.0ms (1.1%)

prune66.0ms (0.7%)

regimes164.0ms (1.7%)

regimes130.0ms (1.3%)

regimes118.0ms (1.2%)

regimes116.0ms (1.2%)

regimes102.0ms (1.1%)

regimes101.0ms (1.1%)

regimes93.0ms (1%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes7.0ms (0.1%)

regimes26.0ms (0.3%)

regimes15.0ms (0.2%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify31.0ms (0.3%)

soundness1.6s (16.6%)

preprocess219.0ms (2.3%)

end0.0ms (0%)

Profiling