Metrics for Migdal et al, Equation (64)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

sample1.4s (17.8%)

Memory

12.4MiB live, 1 909.8MiB allocated

Samples

997.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 712.0ms

ival-mult: 297.0ms (41.7% of total)

ival-cos: 244.0ms (34.2% of total)

ival-sqrt: 69.0ms (9.7% of total)

ival-div: 53.0ms (7.4% of total)

ival-add: 34.0ms (4.8% of total)

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

exact: 6.0ms (0.8% of total)

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

Bogosity

explain242.0ms (3%)

Memory

-20.9MiB live, 512.7MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`*.f64`	`(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))`	*no**	1	0

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	255

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

57.0ms

512×

valid

Compiler

Compiled 247 to 81 computations (67.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-cos: 15.0ms (40.5% of total)

ival-mult: 12.0ms (32.4% of total)

ival-sqrt: 4.0ms (10.8% of total)

ival-div: 3.0ms (8.1% of total)

ival-add: 2.0ms (5.4% of total)

ival-true: 1.0ms (2.7% of total)

exact: 0.0ms (0% of total)

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

preprocess135.0ms (1.7%)

Memory

1.0MiB live, 39.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Symmetry

(abs th)

(abs a2)

(abs a1)

(sort a1 a2)

Compiler

Compiled 19 to 12 computations (36.8% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB 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
▶	99.3%	(+.f64 (.f64 (/.f64 (cos.f64 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)

simplify4.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize43.0ms (0.5%)

Memory

-8.7MiB live, 70.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 th)
accuracy	0.23113251953688405	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
accuracy	0.392991128216253	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
accuracy	0.6796875	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

28.0ms

256×

valid

Compiler

Compiled 114 to 26 computations (77.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-cos: 6.0ms (32.5% of total)

ival-mult: 5.0ms (27.1% of total)

ival-sqrt: 4.0ms (21.7% of total)

ival-div: 2.0ms (10.8% of total)

ival-add: 1.0ms (5.4% of total)

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

exact: 0.0ms (0% of total)

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

series17.0ms (0.2%)

Memory

17.9MiB live, 17.9MiB allocated

Counts

5 → 27

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

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	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	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)))
1.0ms	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)))

simplify231.0ms (2.9%)

Memory

-9.0MiB live, 211.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	111	576
1	343	562
2	1204	458
3	3899	429
0	8437	391

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 27

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

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

rewrite192.0ms (2.4%)

Memory

-0.4MiB live, 204.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	44
0	20	38
1	58	38
2	411	38
3	7331	38
0	8434	37

Stop Event

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

Counts

5 → 327

Calls

Call 1

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

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

eval55.0ms (0.7%)

Memory: 1.5MiB live, 85.3MiB allocated
Compiler: Compiled 11 519 to 1 066 computations (90.7% saved)

prune18.0ms (0.2%)

Memory

-2.5MiB live, 36.2MiB allocated

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	379	16	395
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	380	16	396

Accuracy

100.0%

Counts

396 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.2%	(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)))
	99.3%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	99.3%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	99.0%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1))))
▶	99.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))))
	99.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))))
	99.6%	(+.f64 (.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 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64))
	99.3%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
▶	99.3%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
▶	99.3%	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
▶	64.2%	#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)))
	58.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (.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))))
	62.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (.f64 (*.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	63.3%	#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 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))))
	99.0%	#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)))))

Compiler

Compiled 688 to 478 computations (30.5% saved)

simplify41.0ms (0.5%)

Memory

3.8MiB live, 41.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	267
0	61	261
1	108	249
2	197	249
3	405	249
4	875	240
5	1220	240
6	1351	240
7	1460	240
8	1546	240
9	1594	240
10	1615	240
0	1615	240

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize107.0ms (1.3%)

Memory

-9.4MiB live, 147.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 a1 a1)
accuracy	0	(cos.f64 th)
accuracy	0.18654252930532603	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
accuracy	0.30905104959584007	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
accuracy	0	(cos.f64 th)
accuracy	0.30591061063659675	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))))
accuracy	0.30905104959584007	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
accuracy	0.9630928539494988	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.21941376953688405	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.30638985867936896	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
accuracy	0.125	(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))
accuracy	0.4296875	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.48046875	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.76629696919684	#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)))
accuracy	0.140625	(fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.16015625	(.f64 (.f64 a1 (cos.f64 th)) (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.3828125	(*.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.43359375	(*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))

Samples

76.0ms

256×

valid

Compiler

Compiled 536 to 77 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-mult: 27.0ms (49% of total)

ival-div: 9.0ms (16.3% of total)

ival-cos: 6.0ms (10.9% of total)

ival-add: 4.0ms (7.3% of total)

ival-sqrt: 4.0ms (7.3% of total)

ival-pow: 4.0ms (7.3% of total)

exact: 1.0ms (1.8% of total)

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

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

series47.0ms (0.6%)

Memory

26.4MiB live, 111.6MiB allocated

Counts

21 → 98

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
9.0ms	a2	@	0	((+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (* (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) 1/2) (* a2 (cos th)) (cos th) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a2 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* a2 (sqrt 2)) (* a1 (sqrt 2)) (* (* a1 (cos th)) (* a1 (sqrt 2))) (/ a1 (sqrt 2)))
5.0ms	a1	@	0	((+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (* (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) 1/2) (* a2 (cos th)) (cos th) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a2 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* a2 (sqrt 2)) (* a1 (sqrt 2)) (* (* a1 (cos th)) (* a1 (sqrt 2))) (/ a1 (sqrt 2)))
5.0ms	a1	@	inf	((+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (* (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) 1/2) (* a2 (cos th)) (cos th) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a2 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* a2 (sqrt 2)) (* a1 (sqrt 2)) (* (* a1 (cos th)) (* a1 (sqrt 2))) (/ a1 (sqrt 2)))
5.0ms	a2	@	inf	((+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (* (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) 1/2) (* a2 (cos th)) (cos th) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a2 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* a2 (sqrt 2)) (* a1 (sqrt 2)) (* (* a1 (cos th)) (* a1 (sqrt 2))) (/ a1 (sqrt 2)))
5.0ms	a2	@	-inf	((+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) (* (+ (* (* a2 (cos th)) (* a2 (sqrt 2))) (* (* a1 (cos th)) (* a1 (sqrt 2)))) 1/2) (* a2 (cos th)) (cos th) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a2 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* a2 (sqrt 2)) (* a1 (sqrt 2)) (* (* a1 (cos th)) (* a1 (sqrt 2))) (/ a1 (sqrt 2)))

simplify163.0ms (2%)

Memory

-15.2MiB live, 180.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	362	2263
1	1250	2147
2	5012	2124
0	8735	1969

Stop Event

1×	iter limit
1×	node limit

Counts

98 → 97

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

Outputs
(* (pow a2 2) (* (cos th) (sqrt 2)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 #s(literal 1/2 binary64) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(+ (* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2)))) (* 1/2 (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (fma.f64 a1 a1 (.f64 a2 a2)))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(pow a2 2)
(*.f64 a2 a2)
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(pow a1 2)
(*.f64 a1 a1)
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (.f64 (neg.f64 a1) a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 4 binary64)) (cos.f64 th))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2)))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (-.f64 (.f64 (/.f64 (.f64 a1 a1) (cos.f64 th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a2 #s(literal 6 binary64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 4 binary64)) (cos.f64 th)))) (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2)))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (neg.f64 a1) a1) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a2 #s(literal 8 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 6 binary64)) (cos.f64 th)))) (.f64 a1 a1) (/.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) (cos.f64 th))) (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2)))
(* (pow a2 2) (cos th))
(.f64 (.f64 (cos.f64 th) a2) a2)
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))
(* a1 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) a1)
(* (pow a1 2) (* (cos th) (sqrt 2)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (.f64 a1 a1))) (.f64 a1 a1))
(* 1/2 (* (pow a1 2) (* (cos th) (sqrt 2))))
(.f64 (.f64 #s(literal 1/2 binary64) (.f64 a1 a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(* (pow a1 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a2 2) (* (cos th) (sqrt 2))) (pow a1 2)))))
(.f64 (.f64 #s(literal 1/2 binary64) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (*.f64 a1 a1))))
(/ (pow a1 2) (sqrt 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 (fma.f64 (/.f64 a2 (.f64 a1 a1)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(.f64 (.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (.f64 a1 a1))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a1) a1))
(/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a1 2))
(/.f64 (fma.f64 (.f64 (neg.f64 a2) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a1) a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (.f64 a1 a1))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (pow a1 2))
(/.f64 (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (-.f64 (/.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (*.f64 (/.f64 a2 a1) (/.f64 a2 a1))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) a1) a1)
(/ (- (+ (* -1 (/ (* (pow a2 6) (sqrt 2)) (* (pow a1 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th))))) (pow a1 2))
(/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (-.f64 (/.f64 (pow.f64 a2 #s(literal 4 binary64)) (pow.f64 a1 #s(literal 4 binary64))) (.f64 (/.f64 a2 a1) (/.f64 a2 a1))) (fma.f64 (neg.f64 (pow.f64 a2 #s(literal 6 binary64))) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a1 #s(literal 6 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (.f64 a1 a1))
(* (pow a1 2) (cos th))
(.f64 (.f64 (cos.f64 th) a1) a1)
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(.f64 (fma.f64 (/.f64 (.f64 a2 a2) a1) (/.f64 (cos.f64 th) a1) (cos.f64 th)) (*.f64 a1 a1))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a1 a1))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a2 a2)) (.f64 a1 a1))) (.f64 a1 a1))
(* a2 (cos th))
(*.f64 (cos.f64 th) a2)
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(fma.f64 (.f64 (neg.f64 a2) a2) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a1 #s(literal 4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 th) a1) a1)))
(+ (* (pow a2 2) (- (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 6) (cos th))) (/ (sqrt 2) (* (pow a1 4) (cos th))))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(fma.f64 (-.f64 (.f64 (/.f64 (.f64 a2 a2) (cos.f64 th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a1 #s(literal 6 binary64)))) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a1 #s(literal 4 binary64)))) (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 th) a1) a1)))
(+ (* (pow a2 2) (- (* (pow a2 2) (- (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a1 6) (cos th)))))) (/ (sqrt 2) (* (pow a1 4) (cos th))))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (neg.f64 a2) a2) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a1 #s(literal 8 binary64))) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (pow.f64 a1 #s(literal 6 binary64)))) (.f64 a2 a2) (/.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 a1 #s(literal 4 binary64))) (cos.f64 th))) (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 th) a1) a1)))
(* a2 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
(* (pow a2 2) (+ (* (cos th) (sqrt 2)) (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 a1 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (.f64 a2 a2))) (.f64 a2 a2))
(* (pow a2 2) (+ (* 1/2 (* (cos th) (sqrt 2))) (* 1/2 (/ (* (pow a1 2) (* (cos th) (sqrt 2))) (pow a2 2)))))
(.f64 (.f64 #s(literal 1/2 binary64) (.f64 a2 a2)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 a1 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (*.f64 a2 a2))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 (fma.f64 (/.f64 a1 (.f64 a2 a2)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (.f64 a2 a2))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/.f64 (fma.f64 (.f64 (neg.f64 a1) a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 th) a2) a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (.f64 a2 a2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/.f64 (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (-.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64))) (*.f64 (/.f64 a1 a2) (/.f64 a1 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) a2) a2)
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (-.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64))) (.f64 (/.f64 a1 a2) (/.f64 a1 a2))) (fma.f64 (neg.f64 (pow.f64 a1 #s(literal 6 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal 6 binary64)) (cos.f64 th))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(.f64 (fma.f64 (/.f64 (.f64 a1 a1) a2) (/.f64 (cos.f64 th) a2) (cos.f64 th)) (*.f64 a2 a2))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (.f64 a1 a1)) (.f64 a2 a2))) (.f64 a2 a2))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* (pow a1 2) (sqrt 2)) (+ (* (pow a2 2) (sqrt 2)) (* (pow th 2) (+ (* -1/2 (* (pow a1 2) (sqrt 2))) (* -1/2 (* (pow a2 2) (sqrt 2)))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 th th)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (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))))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 th th)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 th th) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (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)))))))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (.f64 #s(literal -1/720 binary64) (.f64 th th)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 th th))) (.f64 th th) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (* 1/2 (* (pow th 2) (+ (* -1/2 (* (pow a1 2) (sqrt 2))) (* -1/2 (* (pow a2 2) (sqrt 2)))))) (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 th th)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(+ (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* (pow th 2) (+ (* 1/2 (* (pow th 2) (+ (* 1/24 (* (pow a1 2) (sqrt 2))) (* 1/24 (* (pow a2 2) (sqrt 2)))))) (* 1/2 (+ (* -1/2 (* (pow a1 2) (sqrt 2))) (* -1/2 (* (pow a2 2) (sqrt 2))))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/48 binary64) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 th th) (.f64 #s(literal -1/4 binary64) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 th th) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(+ (* 1/2 (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))) (* (pow th 2) (+ (* 1/2 (+ (* -1/2 (* (pow a1 2) (sqrt 2))) (* -1/2 (* (pow a2 2) (sqrt 2))))) (* (pow th 2) (+ (* 1/2 (* (pow th 2) (+ (* -1/720 (* (pow a1 2) (sqrt 2))) (* -1/720 (* (pow a2 2) (sqrt 2)))))) (* 1/2 (+ (* 1/24 (* (pow a1 2) (sqrt 2))) (* 1/24 (* (pow a2 2) (sqrt 2))))))))))
(fma.f64 (fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (fma.f64 (.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (.f64 #s(literal -1/720 binary64) (.f64 th th)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal -1/4 binary64) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 th th) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2))))
a2
(+ a2 (* -1/2 (* a2 (pow th 2))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 th th)) a2 a2)
(+ a2 (* (pow th 2) (+ (* -1/2 a2) (* 1/24 (* a2 (pow th 2))))))
(fma.f64 (fma.f64 (.f64 (.f64 th th) a2) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) a2)) (.f64 th th) a2)
(+ a2 (* (pow th 2) (+ (* -1/2 a2) (* (pow th 2) (+ (* -1/720 (* a2 (pow th 2))) (* 1/24 a2))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 th th) a2) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) a2)) th) th (.f64 #s(literal -1/2 binary64) a2)) (.f64 th th) a2)
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 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) (.f64 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 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))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 th th)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 th th)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal -1/2 binary64) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))) (.f64 th th) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow 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 (fma.f64 (fma.f64 (.f64 #s(literal -1/720 binary64) (.f64 th th)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/24 binary64) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))) (.f64 th th) (.f64 #s(literal -1/2 binary64) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))) (.f64 th th) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 th th) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) th) th) (/.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (.f64 th th) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) th) th) (/.f64 #s(literal -1/720 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal 2 binary64))))) (.f64 th th) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (.f64 th th) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (* 1/2 (/ (* (pow th 2) (sqrt 2)) (+ (pow a1 2) (pow a2 2)))) (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))
(fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))
(+ (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))))) (* -1/2 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))))) (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))
(fma.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 th th)) #s(literal 5/24 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))) (.f64 th th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
(+ (* (pow th 2) (- (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/720 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (+ (* 1/48 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/2 (+ (* -1/4 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))))))))) (+ (* -1/4 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))))) (* -1/2 (/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))))) (/ (sqrt 2) (+ (pow a1 2) (pow a2 2))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 5/24 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 (.f64 (neg.f64 th) th) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) #s(literal 7/360 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) #s(literal -5/48 binary64))))) (.f64 th th) (/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))) (.f64 th th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
(+ (* -1/2 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (+ (pow a1 2) (pow a2 2)))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (* 1/24 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))))) (+ (pow a1 2) (pow a2 2)))
(fma.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64))) (.f64 th th) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (* (pow th 2) (+ (* -1/720 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (+ (pow a1 2) (pow a2 2))))))) (+ (pow a1 2) (pow a2 2)))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (pow.f64 th #s(literal 4 binary64)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)))))
(* (sqrt 1/2) (+ (pow a1 2) (pow a2 2)))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* -1/2 (* (pow th 2) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))))) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))
(+ (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))) (* (pow th 2) (+ (* -1/2 (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (* (pow th 2) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))))))))
(fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64))) (.f64 th th) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
(+ (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))) (* (pow th 2) (+ (* -1/2 (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2)))) (* (pow th 2) (+ (* -1/720 (* (pow th 2) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))))) (* 1/24 (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2)))))))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 (pow.f64 th #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)))))
(* (pow a1 2) (sqrt 2))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1)
(+ (* -1/2 (* (pow a1 2) (* (pow th 2) (sqrt 2)))) (* (pow a1 2) (sqrt 2)))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 a1 a1)) (.f64 th th)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))
(+ (* (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)))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 a1 a1)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) th) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) (.f64 th th) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))
(+ (* (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))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (.f64 (fma.f64 (.f64 #s(literal -1/720 binary64) (.f64 a1 a1)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) th) (.f64 (.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) (.f64 th th))) (.f64 th th) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1))
(* 1/2 (+ (* (pow a1 2) (* (cos th) (sqrt 2))) (* (pow a2 2) (* (cos th) (sqrt 2)))))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (fma.f64 a1 a1 (.f64 a2 a2)))
(cos th)
(cos.f64 th)
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(/ (sqrt 2) (* (cos th) (+ (pow a1 2) (pow a2 2))))
(/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) (cos.f64 th))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
(* (cos th) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))))
(.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))

rewrite274.0ms (3.4%)

Memory

21.5MiB live, 263.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	196
0	61	213
1	200	174
2	1369	166
0	8145	166

Stop Event

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

Counts

21 → 2 246

Calls

Call 1

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

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

eval232.0ms (2.9%)

Memory: -10.6MiB live, 174.2MiB allocated
Compiler: Compiled 40 138 to 3 643 computations (90.9% saved)

prune71.0ms (0.9%)

Memory

-3.1MiB live, 75.5MiB allocated

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	1 206	22	1 228
Fresh	8	3	11
Picked	5	0	5
Done	0	0	0
Total	1 219	25	1 244

Accuracy

100.0%

Counts

1 244 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	63.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))))
	98.7%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (.f64 (.f64 (cos.f64 th) a2) a2))))
	57.1%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))))
	64.2%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
	62.6%	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)) (.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
	58.9%	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 th th) #s(literal -1/2 binary64)) (.f64 th th) #s(literal 1 binary64))))
▶	63.4%	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))
	98.7%	(.f64 (/.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	64.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
	64.1%	#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)))))
	49.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
	64.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	32.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
	64.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	63.3%	#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 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))))
	99.0%	#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)))))
	98.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))))
▶	32.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (fma.f64 (/.f64 a2 (.f64 a1 a1)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))))
	63.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
	17.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	63.4%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))))
▶	99.3%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
▶	98.7%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
▶	64.3%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))

Compiler

Compiled 1 552 to 984 computations (36.6% saved)

simplify160.0ms (2%)

Memory

9.0MiB live, 95.0MiB 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 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
cost-diff	0	#s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (fma.f64 (/.f64 a2 (.f64 a1 a1)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1)))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (fma.f64 (/.f64 a2 (.f64 a1 a1)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))))
cost-diff	640	(fma.f64 (/.f64 a2 (*.f64 a1 a1)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	2048	(.f64 (fma.f64 (/.f64 a2 (.f64 a1 a1)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
cost-diff	0	(*.f64 a1 a1)
cost-diff	0	(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff	0	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))
cost-diff	0	(fma.f64 a1 a1 (*.f64 a2 a2))
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
cost-diff	0	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))
cost-diff	0	(fma.f64 a1 a1 (*.f64 a2 a2))
cost-diff	0	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
cost-diff	0	(.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	358
0	78	342
1	140	342
2	238	342
3	429	342
4	710	336
5	1530	324
6	2592	316
7	3148	316
8	3702	316
9	4189	316
10	4472	316
11	4814	316
12	5223	316
13	5749	316
14	7719	316
0	8183	315

Stop Event

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

Calls

Call 1

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

localize148.0ms (1.8%)

Memory

21.8MiB live, 97.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 th)
accuracy	0.265625	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))
accuracy	0.392991128216253	(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
accuracy	0.4123831389308211	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
accuracy	6.48375131013747	(fma.f64 (/.f64 a2 (*.f64 a1 a1)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
accuracy	6.487656666211707	(/.f64 a2 (*.f64 a1 a1))
accuracy	21.865769526638612	(.f64 (fma.f64 (/.f64 a2 (.f64 a1 a1)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
accuracy	22.76629696919684	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (fma.f64 (/.f64 a2 (.f64 a1 a1)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.21941376953688405	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.30638985867936896	(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))
accuracy	32.66473950873784	#s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))
accuracy	0	(*.f64 a2 a2)
accuracy	0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	0.20835878907376806	(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
accuracy	22.76629696919684	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))
accuracy	0	(cos.f64 th)
accuracy	0	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	0.18654252930532603	(.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	0.30905104959584007	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))

Samples

121.0ms

256×

valid

Compiler

Compiled 636 to 96 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-mult: 71.0ms (70.9% of total)

ival-div: 9.0ms (9% of total)

ival-add: 6.0ms (6% of total)

ival-cos: 6.0ms (6% of total)

ival-pow: 4.0ms (4% of total)

ival-sqrt: 3.0ms (3% of total)

exact: 1.0ms (1% of total)

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

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

series64.0ms (0.8%)

Memory

-2.8MiB live, 39.1MiB allocated

Counts

23 → 66

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
32.0ms	a1	@	0	((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 1/2)) (* (+ (* a1 a1) (* a2 a2)) (cos th)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (sqrt 1/2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (* (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (* a1 a1)) (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (cos th) (* a2 a2) (cos th) (sqrt 2) (/ a2 (* a1 a1)))
11.0ms	a2	@	inf	((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 1/2)) (* (+ (* a1 a1) (* a2 a2)) (cos th)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (sqrt 1/2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (* (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (* a1 a1)) (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (cos th) (* a2 a2) (cos th) (sqrt 2) (/ a2 (* a1 a1)))
4.0ms	a2	@	0	((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 1/2)) (* (+ (* a1 a1) (* a2 a2)) (cos th)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (sqrt 1/2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (* (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (* a1 a1)) (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (cos th) (* a2 a2) (cos th) (sqrt 2) (/ a2 (* a1 a1)))
4.0ms	a2	@	-inf	((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 1/2)) (* (+ (* a1 a1) (* a2 a2)) (cos th)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (sqrt 1/2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (* (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (* a1 a1)) (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (cos th) (* a2 a2) (cos th) (sqrt 2) (/ a2 (* a1 a1)))
3.0ms	a1	@	inf	((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 1/2)) (* (+ (* a1 a1) (* a2 a2)) (cos th)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (sqrt 1/2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (* (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (* a1 a1)) (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (cos th) (* a2 a2) (cos th) (sqrt 2) (/ a2 (* a1 a1)))

simplify280.0ms (3.5%)

Memory

-0.7MiB live, 152.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	194	1164
1	649	1073
2	2426	951
3	6474	934
4	7953	934
0	8226	846

Stop Event

1×	iter limit
1×	node limit

Counts

66 → 66

Calls

Call 1

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

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

rewrite210.0ms (2.6%)

Memory

-11.9MiB live, 145.1MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	298
0	78	291
1	257	276
2	2028	276
0	8211	276

Stop Event

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

Counts

23 → 780

Calls

Call 1

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

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

eval155.0ms (1.9%)

Memory: 19.5MiB live, 131.3MiB allocated
Compiler: Compiled 41 702 to 4 050 computations (90.3% saved)

prune75.0ms (0.9%)

Memory

2.4MiB live, 88.2MiB allocated

Pruning

36 alts after pruning (33 fresh and 3 done)

	Pruned	Kept	Total
New	891	20	911
Fresh	7	13	20
Picked	2	3	5
Done	0	0	0
Total	900	36	936

Accuracy

100.0%

Counts

936 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	63.4%	(/.f64 (.f64 #s(approx (cos th) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
	98.7%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (.f64 (.f64 (cos.f64 th) a2) a2))))
	57.1%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))))
	64.2%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
	63.3%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	98.7%	(.f64 (/.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	63.0%	(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (.f64 (/.f64 a2 (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))))
	16.2%	(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
	64.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
	64.1%	#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)))))
	49.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
	64.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	64.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	99.0%	#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)))))
	32.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 a1 a1) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))))
	42.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 #s(literal 1 binary64))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))))
▶	32.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 a2 (.f64 a1 a1)) a2) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 a1 a1))))
	17.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))))
	41.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (.f64 (/.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a1) (/.f64 a2 a1))) (.f64 a1 a1))))
▶	33.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 a2 (.f64 a1 a1)) a2 #s(literal 1 binary64)))) (*.f64 a1 a1))))
	63.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
	17.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
✓	99.3%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
	98.7%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)))
	99.1%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 1/2 binary64))))
	99.0%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (cos.f64 th) a2)) a2))
✓	98.7%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
	62.4%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(approx (cos th) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)) (.f64 th th) #s(literal -1/2 binary64)) (.f64 th th) #s(literal 1 binary64)))) (.f64 a2 a2)))
	58.7%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 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)))
▶	63.1%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 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)))
✓	64.3%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))
	64.0%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))
	63.1%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2))))
	64.0%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
▶	17.4%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))

Compiler

Compiled 2 427 to 1 527 computations (37.1% saved)

simplify91.0ms (1.1%)

Memory

-0.5MiB live, 75.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	256	(neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
cost-diff	320	(/.f64 (fma.f64 (.f64 (/.f64 a2 (.f64 a1 a1)) a2) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
cost-diff	640	(fma.f64 (.f64 (/.f64 a2 (.f64 a1 a1)) a2) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	1600	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 a2 (.f64 a1 a1)) a2 #s(literal 1 binary64)))) (*.f64 a1 a1))
cost-diff	0	#s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 a2 (.f64 a1 a1)) a2 #s(literal 1 binary64)))) (*.f64 a1 a1)))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 a2 (.f64 a1 a1)) a2 #s(literal 1 binary64)))) (*.f64 a1 a1))))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 a2 (.f64 a1 a1)) a2 #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(.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))))
cost-diff	0	(.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))
cost-diff	0	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 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)))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1)
cost-diff	0	(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)
cost-diff	0	#s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))
cost-diff	0	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
cost-diff	0	(*.f64 a1 a1)
cost-diff	0	(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff	0	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
cost-diff	0	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	597
0	101	550
1	194	522
2	474	506
3	1784	500
4	4632	500
5	7658	500
0	8035	496

Stop Event

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

Calls

Call 1

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

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

localize141.0ms (1.8%)

Memory

-1.8MiB live, 195.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	6.456057068038484	(.f64 (/.f64 a2 (.f64 a1 a1)) a2)
accuracy	6.487656666211707	(/.f64 a2 (*.f64 a1 a1))
accuracy	21.865769526638612	(.f64 (/.f64 (fma.f64 (.f64 (/.f64 a2 (.f64 a1 a1)) a2) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 a1 a1))
accuracy	22.76629696919684	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 a2 (.f64 a1 a1)) a2) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 a1 a1))))
accuracy	6.456057068038484	(fma.f64 (/.f64 a2 (*.f64 a1 a1)) a2 #s(literal 1 binary64))
accuracy	6.487656666211707	(/.f64 a2 (*.f64 a1 a1))
accuracy	21.865769526638612	(.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 a2 (.f64 a1 a1)) a2 #s(literal 1 binary64)))) (*.f64 a1 a1))
accuracy	22.76629696919684	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 a2 (.f64 a1 a1)) a2 #s(literal 1 binary64)))) (*.f64 a1 a1))))
accuracy	0.265625	(.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))))
accuracy	0.392991128216253	(.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))
accuracy	0.4123831389308211	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 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)))
accuracy	32.66473950873784	#s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	0.109375	(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)
accuracy	0.3828125	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1)
accuracy	22.76629696919684	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
accuracy	52.05551783875991	#s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.22332001953688402	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.30905104959584007	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))

Samples

106.0ms

256×

valid

Compiler

Compiled 968 to 122 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 76.0ms

ival-mult: 36.0ms (47.6% of total)

ival-add: 12.0ms (15.9% of total)

ival-div: 10.0ms (13.2% of total)

ival-cos: 8.0ms (10.6% of total)

ival-pow: 4.0ms (5.3% of total)

ival-sqrt: 3.0ms (4% of total)

ival-neg: 2.0ms (2.6% of total)

exact: 1.0ms (1.3% of total)

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

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

series37.0ms (0.5%)

Memory

-17.7MiB live, 59.2MiB allocated

Counts

28 → 76

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
7.0ms	a1	@	inf	((/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (sqrt 1/2) (* (/ 1 (sqrt 2)) (+ (* (/ a2 (* a1 a1)) a2) 1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (* (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (* a1 a1)) (* (sqrt 2) (neg (neg (sqrt 2)))) (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (/ (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (* (sqrt 2) (neg (neg (sqrt 2))))) (neg (neg (sqrt 2))) (cos th) (sqrt 2) (cos th) (/ a2 (* a1 a1)) (+ (* (/ a2 (* a1 a1)) a2) 1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (* (sqrt 2) (neg (neg (sqrt 2))))) (* a1 a1)) (* (/ a2 (* a1 a1)) a2))
5.0ms	a2	@	inf	((/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (sqrt 1/2) (* (/ 1 (sqrt 2)) (+ (* (/ a2 (* a1 a1)) a2) 1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (* (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (* a1 a1)) (* (sqrt 2) (neg (neg (sqrt 2)))) (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (/ (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (* (sqrt 2) (neg (neg (sqrt 2))))) (neg (neg (sqrt 2))) (cos th) (sqrt 2) (cos th) (/ a2 (* a1 a1)) (+ (* (/ a2 (* a1 a1)) a2) 1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (* (sqrt 2) (neg (neg (sqrt 2))))) (* a1 a1)) (* (/ a2 (* a1 a1)) a2))
5.0ms	a1	@	0	((/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (sqrt 1/2) (* (/ 1 (sqrt 2)) (+ (* (/ a2 (* a1 a1)) a2) 1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (* (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (* a1 a1)) (* (sqrt 2) (neg (neg (sqrt 2)))) (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (/ (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (* (sqrt 2) (neg (neg (sqrt 2))))) (neg (neg (sqrt 2))) (cos th) (sqrt 2) (cos th) (/ a2 (* a1 a1)) (+ (* (/ a2 (* a1 a1)) a2) 1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (* (sqrt 2) (neg (neg (sqrt 2))))) (* a1 a1)) (* (/ a2 (* a1 a1)) a2))
4.0ms	a2	@	0	((/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (sqrt 1/2) (* (/ 1 (sqrt 2)) (+ (* (/ a2 (* a1 a1)) a2) 1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (* (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (* a1 a1)) (* (sqrt 2) (neg (neg (sqrt 2)))) (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (/ (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (* (sqrt 2) (neg (neg (sqrt 2))))) (neg (neg (sqrt 2))) (cos th) (sqrt 2) (cos th) (/ a2 (* a1 a1)) (+ (* (/ a2 (* a1 a1)) a2) 1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (* (sqrt 2) (neg (neg (sqrt 2))))) (* a1 a1)) (* (/ a2 (* a1 a1)) a2))
4.0ms	a2	@	-inf	((/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (* (sqrt 1/2) (cos th)) (sqrt 1/2) (* (/ 1 (sqrt 2)) (+ (* (/ a2 (* a1 a1)) a2) 1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (* (+ (* (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (* a1 a1)) (* (sqrt 2) (neg (neg (sqrt 2)))) (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (/ (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (* (sqrt 2) (neg (neg (sqrt 2))))) (neg (neg (sqrt 2))) (cos th) (sqrt 2) (cos th) (/ a2 (* a1 a1)) (+ (* (/ a2 (* a1 a1)) a2) 1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (+ (* (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (* (sqrt 2) (neg (neg (sqrt 2))))) (* a1 a1)) (* (/ a2 (* a1 a1)) a2))

simplify226.0ms (2.8%)

Memory

4.2MiB live, 279.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	208	1280
1	682	1189
2	2514	1067
3	6774	1040
0	8474	946

Stop Event

1×	iter limit
1×	node limit

Counts

76 → 76

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

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

rewrite203.0ms (2.5%)

Memory

17.8MiB live, 333.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	474
0	101	435
1	338	383
2	2714	369
0	8079	369

Stop Event

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

Counts

28 → 1 169

Calls

Call 1

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

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

eval130.0ms (1.6%)

Memory: 31.7MiB live, 263.7MiB allocated
Compiler: Compiled 53 873 to 5 010 computations (90.7% saved)

prune100.0ms (1.2%)

Memory

-6.8MiB live, 158.0MiB allocated

Pruning

40 alts after pruning (34 fresh and 6 done)

	Pruned	Kept	Total
New	983	16	999
Fresh	10	18	28
Picked	2	3	5
Done	0	3	3
Total	995	40	1 035

Accuracy

100.0%

Counts

1 035 → 40

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	63.4%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	99.0%	(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (.f64 (.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 2 binary64)))
	57.1%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (.f64 (.f64 th th) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))))
	63.3%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	63.0%	(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (.f64 (/.f64 a2 (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))))
	16.2%	(.f64 #s(approx (/ (+ ( a2 a2) (* a1 a1)) (sqrt 2)) (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
	64.3%	#s(approx (/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	99.0%	#s(approx (/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
	64.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
	64.1%	#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)))))
	49.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2)))))
	64.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	42.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 #s(literal 1 binary64))) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))))
	42.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 (/.f64 a2 a1) a2) a1) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))) (.f64 a1 a1))))
	32.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 a2 (.f64 a1 a1)) a2) (/.f64 #s(literal -2 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 a1 a1))))
	41.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (/.f64 #s(approx (+ ( (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a1) (/.f64 a2 a1))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))) (.f64 a1 a1))))
	32.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (/.f64 #s(approx (+ ( (* (/ a2 (* a1 a1)) a2) (neg (neg (sqrt 2)))) (sqrt 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (/.f64 a2 (.f64 a1 a1)) a2 #s(literal 1 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))) (.f64 a1 a1))))
	63.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
	17.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
	64.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))))
	17.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))))
	41.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (.f64 (/.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a1) (/.f64 a2 a1))) (.f64 a1 a1))))
	42.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)))) (.f64 a1 a1))))
	33.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 a1 a1) a2)) a2 #s(literal 1 binary64)))) (*.f64 a1 a1))))
	26.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (.f64 #s(approx (+ ( (/ a2 (* a1 a1)) (/ a2 (sqrt 2))) (/ 1 (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( (/ a2 (* a1 a1)) a2) 1) (.f64 (/.f64 a2 (.f64 a1 a1)) a2)))) (*.f64 a1 a1))))
✓	99.3%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
	98.7%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (cos.f64 th)))
	63.1%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) #s(approx (cos th) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
	99.1%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 1/2 binary64))))
	99.0%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (cos.f64 th) a2)) a2))
✓	98.7%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
	62.4%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(approx (cos th) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 th th) #s(literal 1/24 binary64)) (.f64 th th) #s(literal -1/2 binary64)) (.f64 th th) #s(literal 1 binary64)))) (.f64 a2 a2)))
	58.7%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 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)))
✓	63.1%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 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)))
✓	64.3%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))
	64.0%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))
	64.0%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
✓	17.4%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
	17.4%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 4 135 to 1 281 computations (69% saved)

regimes236.0ms (2.9%)

Memory

-8.5MiB live, 314.0MiB allocated

Counts

75 → 1

Calls

Call 1

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

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

Calls

8 calls:

52.0ms	(*.f64 a1 a1)
44.0ms	(*.f64 a2 a2)
34.0ms	a1
22.0ms	a2
21.0ms	th

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes283.0ms (3.5%)

Memory

-31.1MiB live, 331.0MiB allocated

Counts

71 → 1

Calls

Call 1

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

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

Calls

8 calls:

62.0ms	(+.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)))
45.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
41.0ms	(*.f64 a2 a2)
36.0ms	a1
29.0ms	th

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes185.0ms (2.3%)

Memory

27.5MiB live, 260.1MiB allocated

Counts

65 → 1

Calls

Call 1

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

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

Calls

8 calls:

46.0ms	(cos.f64 th)
24.0ms	(+.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)))
23.0ms	th
19.0ms	a2
19.0ms	a1

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes164.0ms (2%)

Memory

-43.8MiB live, 230.4MiB allocated

Counts

55 → 1

Calls

Call 1

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

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

Calls

8 calls:

30.0ms	(*.f64 a2 a2)
27.0ms	a1
25.0ms	(cos.f64 th)
18.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
18.0ms	th

Results

Accuracy	Segments	Branch
99.1%	1	`a1`
99.1%	1	`a2`
99.1%	1	`th`
99.1%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
99.1%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.1%	1	`(cos.f64 th)`
99.1%	1	`(*.f64 a1 a1)`
99.1%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes162.0ms (2%)

Memory

21.8MiB live, 219.8MiB allocated

Counts

53 → 1

Calls

Call 1

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

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

Calls

8 calls:

57.0ms	th
16.0ms	a2
16.0ms	(cos.f64 th)
15.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
14.0ms	a1

Results

Accuracy	Segments	Branch
99.0%	1	`a1`
99.0%	1	`a2`
99.0%	1	`th`
99.0%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
99.0%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.0%	1	`(cos.f64 th)`
99.0%	1	`(*.f64 a1 a1)`
99.0%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes119.0ms (1.5%)

Memory

0.1MiB live, 194.9MiB allocated

Counts

52 → 1

Calls

Call 1

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

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

Calls

8 calls:

17.0ms	a1
15.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
14.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
14.0ms	(*.f64 a2 a2)
14.0ms	a2

Results

Accuracy	Segments	Branch
98.7%	1	`a1`
98.7%	1	`th`
98.7%	1	`(*.f64 a1 a1)`
98.7%	1	`a2`
98.7%	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)))`
98.7%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
98.7%	1	`(cos.f64 th)`
98.7%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes152.0ms (1.9%)

Memory

1.6MiB live, 192.8MiB allocated

Counts

51 → 2

Calls

Call 1

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

Outputs

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

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

Calls

8 calls:

35.0ms	a1
25.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
17.0ms	(+.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)))
15.0ms	(*.f64 a1 a1)
15.0ms	(*.f64 a2 a2)

Results

Accuracy	Segments	Branch
78.1%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
68.7%	3	`th`
76.4%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
76.4%	2	`(cos.f64 th)`
68.4%	3	`a1`
68.3%	2	`a2`
67.7%	3	`(*.f64 a1 a1)`
68.3%	2	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes53.0ms (0.7%)

Memory

1.3MiB live, 50.5MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

8 calls:

24.0ms	a2
4.0ms	a1
4.0ms	th
4.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
4.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Results

Accuracy	Segments	Branch
64.3%	1	`(*.f64 a1 a1)`
64.3%	1	`a1`
64.3%	1	`th`
64.3%	1	`(*.f64 a2 a2)`
64.3%	1	`a2`
64.3%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
64.3%	1	`(cos.f64 th)`
64.3%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes32.0ms (0.4%)

Memory

-15.3MiB live, 22.8MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

8 calls:

17.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
2.0ms	a1
2.0ms	a2
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)))

Results

Accuracy	Segments	Branch
64.0%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
64.0%	1	`a1`
64.0%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
64.0%	1	`(cos.f64 th)`
64.0%	1	`(*.f64 a1 a1)`
64.0%	1	`th`
64.0%	1	`a2`
64.0%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes15.0ms (0.2%)

Memory

26.3MiB live, 26.3MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

8 calls:

2.0ms	a1
2.0ms	th
2.0ms	a2
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)))

Results

Accuracy	Segments	Branch
64.0%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
64.0%	1	`a1`
64.0%	1	`(*.f64 a1 a1)`
64.0%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
64.0%	1	`(cos.f64 th)`
64.0%	1	`th`
64.0%	1	`a2`
64.0%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes23.0ms (0.3%)

Memory

-7.2MiB live, 29.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

8 calls:

12.0ms	a2
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	th
2.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
2.0ms	a1

Results

Accuracy	Segments	Branch
17.4%	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)))`
17.4%	1	`a1`
17.4%	1	`(*.f64 a1 a1)`
17.4%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
17.4%	1	`(cos.f64 th)`
17.4%	1	`th`
17.4%	1	`a2`
17.4%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.396188023618093e-274	-2.533718237735085e-284

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify33.0ms (0.4%)

Memory

-27.5MiB live, 55.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	332
1	98	332

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (cos.f64 th) a2)) a2))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 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 -152270531428125/304541062856249971261043199621099634714882089299843985214622076787904646586450815702050470808812820600790778632231520880733099058287596688955562103009770419360352428123639782183462176734064176511024987296225574339802674935168589842054573862983405175400866837597008673346307143437247315968 binary64)) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 1/2 binary64)))))

Outputs
(.f64 (fma.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 a1 (cos.f64 th)) (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 (cos.f64 th) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 (cos.f64 th)))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (cos.f64 th) a2)) a2))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 #s(literal 1/2 binary64))) a2))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 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 -152270531428125/304541062856249971261043199621099634714882089299843985214622076787904646586450815702050470808812820600790778632231520880733099058287596688955562103009770419360352428123639782183462176734064176511024987296225574339802674935168589842054573862983405175400866837597008673346307143437247315968 binary64)) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))) #s(literal -152270531428125/304541062856249971261043199621099634714882089299843985214622076787904646586450815702050470808812820600790778632231520880733099058287596688955562103009770419360352428123639782183462176734064176511024987296225574339802674935168589842054573862983405175400866837597008673346307143437247315968 binary64)) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (* (sqrt 1/2) (cos th)) (* a2 a2)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a1 a1) (* a2 a2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 a1 a1))))

soundness1.1s (14.1%)

Memory

25.6MiB live, 817.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	474
0	101	435
1	338	383
2	2714	369
0	8079	369
0	362	2263
1	1250	2147
2	5012	2124
0	8735	1969
0	12	44
0	20	38
1	58	38
2	411	38
3	7331	38
0	8434	37
0	194	1164
1	649	1073
2	2426	951
3	6474	934
4	7953	934
0	8226	846
0	51	298
0	78	291
1	257	276
2	2028	276
0	8211	276

Stop Event

1×	fuel
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×	node limit
1×	iter limit

Compiler

Compiled 875 to 429 computations (51% saved)

preprocess144.0ms (1.8%)

Memory

-2.8MiB live, 189.2MiB allocated

Remove

(sort a1 a2)

(abs a1)

(abs a2)

(abs th)

Compiler

Compiled 1 662 to 844 computations (49.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.4s (17.8%)

explain242.0ms (3%)

preprocess135.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize43.0ms (0.5%)

series17.0ms (0.2%)

simplify231.0ms (2.9%)

rewrite192.0ms (2.4%)

eval55.0ms (0.7%)

prune18.0ms (0.2%)

simplify41.0ms (0.5%)

localize107.0ms (1.3%)

series47.0ms (0.6%)

simplify163.0ms (2%)

rewrite274.0ms (3.4%)

eval232.0ms (2.9%)

prune71.0ms (0.9%)

simplify160.0ms (2%)

localize148.0ms (1.8%)

series64.0ms (0.8%)

simplify280.0ms (3.5%)

rewrite210.0ms (2.6%)

eval155.0ms (1.9%)

prune75.0ms (0.9%)

simplify91.0ms (1.1%)

localize141.0ms (1.8%)

series37.0ms (0.5%)

simplify226.0ms (2.8%)

rewrite203.0ms (2.5%)

eval130.0ms (1.6%)

prune100.0ms (1.2%)

regimes236.0ms (2.9%)

regimes283.0ms (3.5%)

regimes185.0ms (2.3%)

regimes164.0ms (2%)

regimes162.0ms (2%)

regimes119.0ms (1.5%)

regimes152.0ms (1.9%)

regimes53.0ms (0.7%)

regimes32.0ms (0.4%)

regimes15.0ms (0.2%)

regimes23.0ms (0.3%)

bsearch1.0ms (0%)

simplify33.0ms (0.4%)

soundness1.1s (14.1%)

preprocess144.0ms (1.8%)

end0.0ms (0%)

Profiling