Metrics for Migdal et al, Equation (64)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze1.0ms (0%)

Memory

1.0MiB live, 1.0MiB 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)

sample1.1s (14.3%)

Memory

57.9MiB live, 1 627.7MiB allocated

Samples

803.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 593.0ms

ival-mult: 222.0ms (37.4% of total)

ival-cos: 201.0ms (33.9% of total)

ival-sqrt: 65.0ms (11% of total)

ival-div: 56.0ms (9.4% of total)

ival-add: 34.0ms (5.7% of total)

ival-true: 6.0ms (1% of total)

exact: 6.0ms (1% of total)

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

Bogosity

explain137.0ms (1.8%)

Memory

-24.7MiB live, 217.9MiB 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 a1 a1))`
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 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))`
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	-	-	`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 a1 a1))`	*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

53.0ms

512×

valid

Compiler

Compiled 191 to 52 computations (72.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-cos: 12.0ms (35.8% of total)

ival-mult: 12.0ms (35.8% of total)

ival-div: 3.0ms (8.9% of total)

ival-sqrt: 3.0ms (8.9% of total)

ival-add: 2.0ms (6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess136.0ms (1.8%)

Memory

-0.3MiB live, 38.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	120
1	130	120
2	375	120
3	1021	120
4	2482	120
5	4852	120
6	5751	120
7	6539	120
8	6612	120
9	6628	120
10	6799	120
11	6917	120
12	6929	120
13	6929	120
14	6929	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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify4.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB 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

localize41.0ms (0.5%)

Memory

17.6MiB live, 58.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(cos.f64 th)
accuracy	0.19921875	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
accuracy	0.37965701494353055	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
accuracy	0.681972509768442	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

33.0ms

256×

valid

Compiler

Compiled 114 to 26 computations (77.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 8.0ms (33.5% of total)

ival-div: 7.0ms (29.3% of total)

ival-cos: 6.0ms (25.1% of total)

ival-sqrt: 2.0ms (8.4% of total)

ival-add: 1.0ms (4.2% of total)

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

exact: 0.0ms (0% of total)

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

series18.0ms (0.2%)

Memory

-11.7MiB live, 27.1MiB 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
4.0ms	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)))
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	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)))

simplify218.0ms (2.9%)

Memory

19.8MiB live, 245.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	111	576
1	343	562
2	1210	458
3	3908	429
0	8416	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)

rewrite201.0ms (2.6%)

Memory

-23.4MiB live, 237.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	44
0	20	38
1	58	38
2	411	38
3	7359	38
0	8465	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 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th)))
(fma.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (.f64 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th)))
(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 (*.f64 a1 (cos.f64 th)) (neg.f64 a1)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.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)) 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 (*.f64 (neg.f64 (cos.f64 th)) a2) a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.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)) 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 (neg.f64 (cos.f64 th)) a2) 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 (neg.f64 (cos.f64 th)) a2) 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 (.f64 (neg.f64 (cos.f64 th)) a2) a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 (neg.f64 a2) a2) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (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))))

eval44.0ms (0.6%)

Memory: 7.1MiB live, 83.7MiB allocated
Compiler: Compiled 11 519 to 1 067 computations (90.7% saved)

prune16.0ms (0.2%)

Memory

-5.5MiB live, 37.0MiB allocated

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	380	15	395
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	381	15	396

Accuracy

100.0%

Counts

396 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(fma.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 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (cos.f64 th)))
▶	99.6%	(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 (.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))))))
	99.3%	(+.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))))
	99.3%	(.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))
▶	99.2%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
▶	99.4%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
	47.4%	(.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)))))
▶	64.8%	#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 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (.f64 (*.f64 (cos.f64 th) a1) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	60.7%	#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))))
	99.5%	#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 678 to 450 computations (33.6% saved)

simplify13.0ms (0.2%)

Memory

-23.2MiB live, 16.0MiB 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	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
cost-diff	0	(/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1)))
cost-diff	1088	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1))))
cost-diff	0	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(*.f64 a1 a1)
cost-diff	0	(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff	0	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
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	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(cos.f64 th)
cost-diff	0	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	8064	(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)))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	240
0	53	243
1	86	225
2	149	225
3	257	219
4	444	219
5	550	219
6	550	219
0	550	219

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize84.0ms (1.1%)

Memory

15.3MiB live, 133.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 a1 a1)
accuracy	0.0	(cos.f64 th)
accuracy	0.08203125	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
accuracy	0.3929970051750885	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
accuracy	0.0	(cos.f64 th)
accuracy	0.2584762695368841	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
accuracy	0.29597668528734367	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1))))
accuracy	0.7746524954556098	(/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a2 a2 (*.f64 a1 a1)))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	(cos.f64 th)
accuracy	0.38356326494353055	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.681972509768442	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.1484375	(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
accuracy	0.375	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.4140625	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.386369573422424	#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	0.08203125	(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))
accuracy	0.12890625	(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
accuracy	0.375	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.681972509768442	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

58.0ms

256×

valid

Compiler

Compiled 479 to 66 computations (86.2% saved)

Precisions

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

ival-mult: 13.0ms (34.8% of total)

ival-div: 8.0ms (21.4% of total)

ival-cos: 6.0ms (16.1% of total)

ival-add: 4.0ms (10.7% of total)

ival-pow: 4.0ms (10.7% of total)

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

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

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

exact: 0.0ms (0% of total)

series37.0ms (0.5%)

Memory

18.2MiB live, 56.7MiB allocated

Counts

20 → 81

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	a2	@	0	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (* (/ a2 (sqrt 2)) a2) (cos th))) (/ (cos th) (sqrt 2)) (cos th) (sqrt 2) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a2 (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (/ (sqrt 2) (cos th)) (+ (* a2 a2) (* a1 a1)))) (/ (/ (sqrt 2) (cos th)) (+ (* a2 a2) (* a1 a1))) (/ (sqrt 2) (cos th)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (/ a2 (sqrt 2)) a2) (* (* (/ a2 (sqrt 2)) a2) (cos th)) (/ a1 (sqrt 2)) (* (/ a1 (sqrt 2)) a1))
5.0ms	a2	@	-inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (* (/ a2 (sqrt 2)) a2) (cos th))) (/ (cos th) (sqrt 2)) (cos th) (sqrt 2) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a2 (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (/ (sqrt 2) (cos th)) (+ (* a2 a2) (* a1 a1)))) (/ (/ (sqrt 2) (cos th)) (+ (* a2 a2) (* a1 a1))) (/ (sqrt 2) (cos th)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (/ a2 (sqrt 2)) a2) (* (* (/ a2 (sqrt 2)) a2) (cos th)) (/ a1 (sqrt 2)) (* (/ a1 (sqrt 2)) a1))
4.0ms	a2	@	inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (* (/ a2 (sqrt 2)) a2) (cos th))) (/ (cos th) (sqrt 2)) (cos th) (sqrt 2) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a2 (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (/ (sqrt 2) (cos th)) (+ (* a2 a2) (* a1 a1)))) (/ (/ (sqrt 2) (cos th)) (+ (* a2 a2) (* a1 a1))) (/ (sqrt 2) (cos th)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (/ a2 (sqrt 2)) a2) (* (* (/ a2 (sqrt 2)) a2) (cos th)) (/ a1 (sqrt 2)) (* (/ a1 (sqrt 2)) a1))
4.0ms	a1	@	0	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (* (/ a2 (sqrt 2)) a2) (cos th))) (/ (cos th) (sqrt 2)) (cos th) (sqrt 2) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a2 (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (/ (sqrt 2) (cos th)) (+ (* a2 a2) (* a1 a1)))) (/ (/ (sqrt 2) (cos th)) (+ (* a2 a2) (* a1 a1))) (/ (sqrt 2) (cos th)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (/ a2 (sqrt 2)) a2) (* (* (/ a2 (sqrt 2)) a2) (cos th)) (/ a1 (sqrt 2)) (* (/ a1 (sqrt 2)) a1))
4.0ms	a1	@	inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (* (/ a2 (sqrt 2)) a2) (cos th))) (/ (cos th) (sqrt 2)) (cos th) (sqrt 2) (+ (* (/ a2 (sqrt 2)) a2) (* (/ a1 (sqrt 2)) a1)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a2 (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (+ (* a2 a2) (* a1 a1)) (* a1 a1) (/ 1 (/ (/ (sqrt 2) (cos th)) (+ (* a2 a2) (* a1 a1)))) (/ (/ (sqrt 2) (cos th)) (+ (* a2 a2) (* a1 a1))) (/ (sqrt 2) (cos th)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (/ a2 (sqrt 2)) a2) (* (* (/ a2 (sqrt 2)) a2) (cos th)) (/ a1 (sqrt 2)) (* (/ a1 (sqrt 2)) a1))

simplify146.0ms (1.9%)

Memory

-5.0MiB live, 186.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	319	1872
1	1061	1751
2	4149	1727
0	8100	1605

Stop Event

1×	iter limit
1×	node limit

Counts

81 → 81

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

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

rewrite211.0ms (2.8%)

Memory

7.2MiB live, 325.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	177
0	53	185
1	178	157
2	1326	155
0	8286	155

Stop Event

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

Counts

20 → 2 106

Calls

Call 1

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

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

eval437.0ms (5.7%)

Memory: -114.2MiB live, 340.6MiB allocated
Compiler: Compiled 37 576 to 3 754 computations (90% saved)

prune44.0ms (0.6%)

Memory

-16.6MiB live, 114.6MiB allocated

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	1 347	25	1 372
Fresh	8	2	10
Picked	5	0	5
Done	0	0	0
Total	1 360	27	1 387

Accuracy

100.0%

Counts

1 387 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.7%	(fma.f64 (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
	72.7%	(pow.f64 (pow.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
	99.3%	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	99.0%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1))))
	55.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 a2 a2 (*.f64 a1 a1))))
	64.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1))))
▶	60.4%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	64.5%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	60.4%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (cos th) (sqrt 2)) (fma.f64 (*.f64 th (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	99.1%	(.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
	64.8%	#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)))
	64.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (.f64 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2 (.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
▶	64.4%	#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)))))
	59.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	52.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
	64.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
▶	32.2%	#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)))))
	57.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a1)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	64.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
▶	99.5%	#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)))))
	39.7%	#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 (fma.f64 (/.f64 a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 a2 a1) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))))
	64.7%	#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 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
	60.5%	#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 a2 a2 (.f64 a1 a1)))))
	99.4%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
	99.2%	#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)))
▶	64.6%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1))))
	27.5%	#s(approx (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (fma.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 th th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))))

Compiler

Compiled 1 582 to 1 012 computations (36% saved)

simplify86.0ms (1.1%)

Memory

2.1MiB live, 120.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
cost-diff	0	#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)))))
cost-diff	768	(/.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))))
cost-diff	1984	(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (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))) (/.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)))))
cost-diff	448	(/.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))))
cost-diff	1088	(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)))
cost-diff	1728	(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(/.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
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)) (/.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1)))
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 a2 a2 (.f64 a1 a1))))
cost-diff	0	(cos.f64 th)
cost-diff	0	(*.f64 (cos.f64 th) a2)
cost-diff	0	(.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	49	380
0	79	359
1	152	332
2	313	323
3	600	318
4	1185	314
5	3068	314
6	6261	314
0	8245	314

Stop Event

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

Calls

Call 1

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

localize119.0ms (1.6%)

Memory

38.9MiB live, 153.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	5.788481547023356	(fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
accuracy	7.360631318492769	(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)))
accuracy	21.365268199521317	(/.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))))
accuracy	22.386369573422424	#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)))))
accuracy	0.19768450517508848	(/.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))))
accuracy	0.24609375	(.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
accuracy	1.0	(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.386369573422424	#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)))))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.38356326494353055	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.681972509768442	(/.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	33.153232491978194	#s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))
accuracy	0.0	(*.f64 a1 a1)
accuracy	0.0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	0.3796570149435305	(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1)))
accuracy	22.386369573422424	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1))))
accuracy	0.08678108721462961	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.15234375	(*.f64 (cos.f64 th) a2)
accuracy	0.15853500976844204	(.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.375	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))

Samples

90.0ms

256×

valid

Compiler

Compiled 685 to 95 computations (86.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-mult: 29.0ms (46.7% of total)

ival-cos: 10.0ms (16.1% of total)

ival-div: 8.0ms (12.9% of total)

ival-add: 5.0ms (8.1% of total)

ival-pow: 4.0ms (6.4% of total)

ival-sqrt: 3.0ms (4.8% of total)

ival-neg: 2.0ms (3.2% of total)

exact: 1.0ms (1.6% of total)

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

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

series54.0ms (0.7%)

Memory

-20.7MiB live, 52.7MiB allocated

Counts

23 → 70

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
10.0ms	a1	@	0	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (sqrt 1/2) (+ (* a2 a2) (* a1 a1)) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (* a1 a1) (/ (cos th) (sqrt 2)) (* (neg (sqrt 2)) (sqrt 2)) (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (sqrt 2) a2) (/ (sqrt 2) (* a1 a1))) (/ (+ (* a2 (/ (sqrt 2) (* a1 a1))) (/ (sqrt 2) a2)) (* (/ (sqrt 2) a2) (/ (sqrt 2) (* a1 a1)))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* a2 (/ (sqrt 2) (* a1 a1))) (/ (sqrt 2) a2)) (/ a2 (sqrt 2)) (cos th) (sqrt 2) (* (neg (sqrt 2)) (* a1 a1)))
10.0ms	th	@	inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (sqrt 1/2) (+ (* a2 a2) (* a1 a1)) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (* a1 a1) (/ (cos th) (sqrt 2)) (* (neg (sqrt 2)) (sqrt 2)) (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (sqrt 2) a2) (/ (sqrt 2) (* a1 a1))) (/ (+ (* a2 (/ (sqrt 2) (* a1 a1))) (/ (sqrt 2) a2)) (* (/ (sqrt 2) a2) (/ (sqrt 2) (* a1 a1)))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* a2 (/ (sqrt 2) (* a1 a1))) (/ (sqrt 2) a2)) (/ a2 (sqrt 2)) (cos th) (sqrt 2) (* (neg (sqrt 2)) (* a1 a1)))
7.0ms	th	@	0	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (sqrt 1/2) (+ (* a2 a2) (* a1 a1)) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (* a1 a1) (/ (cos th) (sqrt 2)) (* (neg (sqrt 2)) (sqrt 2)) (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (sqrt 2) a2) (/ (sqrt 2) (* a1 a1))) (/ (+ (* a2 (/ (sqrt 2) (* a1 a1))) (/ (sqrt 2) a2)) (* (/ (sqrt 2) a2) (/ (sqrt 2) (* a1 a1)))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* a2 (/ (sqrt 2) (* a1 a1))) (/ (sqrt 2) a2)) (/ a2 (sqrt 2)) (cos th) (sqrt 2) (* (neg (sqrt 2)) (* a1 a1)))
5.0ms	a2	@	0	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (sqrt 1/2) (+ (* a2 a2) (* a1 a1)) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (* a1 a1) (/ (cos th) (sqrt 2)) (* (neg (sqrt 2)) (sqrt 2)) (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (sqrt 2) a2) (/ (sqrt 2) (* a1 a1))) (/ (+ (* a2 (/ (sqrt 2) (* a1 a1))) (/ (sqrt 2) a2)) (* (/ (sqrt 2) a2) (/ (sqrt 2) (* a1 a1)))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* a2 (/ (sqrt 2) (* a1 a1))) (/ (sqrt 2) a2)) (/ a2 (sqrt 2)) (cos th) (sqrt 2) (* (neg (sqrt 2)) (* a1 a1)))
5.0ms	a2	@	-inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (cos th) a2) (cos th) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (sqrt 1/2) (+ (* a2 a2) (* a1 a1)) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt 2))) (* a1 a1) (/ (cos th) (sqrt 2)) (* (neg (sqrt 2)) (sqrt 2)) (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (sqrt 2) a2) (/ (sqrt 2) (* a1 a1))) (/ (+ (* a2 (/ (sqrt 2) (* a1 a1))) (/ (sqrt 2) a2)) (* (/ (sqrt 2) a2) (/ (sqrt 2) (* a1 a1)))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* a2 (/ (sqrt 2) (* a1 a1))) (/ (sqrt 2) a2)) (/ a2 (sqrt 2)) (cos th) (sqrt 2) (* (neg (sqrt 2)) (* a1 a1)))

simplify173.0ms (2.3%)

Memory

7.3MiB live, 121.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	217	1207
1	709	1138
2	2545	1009
3	6979	991
0	8133	908

Stop Event

1×	iter limit
1×	node limit

Counts

70 → 69

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

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

rewrite202.0ms (2.6%)

Memory

19.1MiB live, 263.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	313
0	79	286
1	265	256
2	2009	232
0	8309	232

Stop Event

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

Counts

23 → 875

Calls

Call 1

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

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

eval150.0ms (2%)

Memory: 6.2MiB live, 200.0MiB allocated
Compiler: Compiled 39 780 to 3 357 computations (91.6% saved)

prune46.0ms (0.6%)

Memory

-3.1MiB live, 109.0MiB allocated

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	896	18	914
Fresh	11	11	22
Picked	4	1	5
Done	0	0	0
Total	911	30	941

Accuracy

100.0%

Counts

941 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.4%	(/.f64 (.f64 #s(approx (cos th) (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
	55.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 a2 a2 (*.f64 a1 a1))))
	64.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1))))
	64.5%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	60.4%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
	60.4%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (cos th) (sqrt 2)) (fma.f64 (*.f64 th (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	60.3%	(.f64 #s(approx (+ ( a2 a2) (* a1 a1)) (.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	64.8%	#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)))
	59.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
▶	52.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
	64.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	39.4%	#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 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a2))))
	32.2%	#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)) #s(literal 1 binary64)) (.f64 a2 (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))))
	64.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
	64.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (neg.f64 a2) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	99.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 2 binary64))))
	64.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
▶	64.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (.f64 (neg.f64 a2) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
	60.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.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 a2 a2 (.f64 a1 a1)))))
	99.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2))
▶	99.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 a2 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (*.f64 a2 (cos.f64 th)))))
	64.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
	14.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
▶	60.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
	99.4%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
	99.2%	#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)))
✓	64.6%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1))))
	64.4%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2))))
	64.7%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
▶	14.1%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))

Compiler

Compiled 1 972 to 1 226 computations (37.8% saved)

simplify130.0ms (1.7%)

Memory

9.5MiB live, 130.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
cost-diff	640	(fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	768	(/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))))
cost-diff	1984	(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))
cost-diff	0	#s(approx (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (.f64 (neg.f64 a2) (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (.f64 (neg.f64 a2) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	384	(/.f64 #s(approx (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (.f64 (neg.f64 a2) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	1728	(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
cost-diff	0	#s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) 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) (+ (* a2 a2) (* a1 a1))) (.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) (+ (* a2 a2) (* a1 a1))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
cost-diff	0	(pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))
cost-diff	0	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (.f64 a2 (cos.f64 th)))
cost-diff	0	(.f64 a2 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (*.f64 a2 (cos.f64 th))))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 a2 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (*.f64 a2 (cos.f64 th)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	460
0	98	436
1	186	406
2	372	397
3	671	397
4	1085	397
5	1940	397
6	3731	397
0	8305	384

Stop Event

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

Calls

Call 1

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

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

localize169.0ms (2.2%)

Memory

-32.1MiB live, 230.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.36628918528734367	(/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2))))
accuracy	0.8018748250539082	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2))
accuracy	8.476579023540152	(fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.386369573422424	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
accuracy	0.19768450517508848	(/.f64 #s(approx (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (.f64 (neg.f64 a2) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.47265625	(*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	1.0	(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.386369573422424	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (.f64 (neg.f64 a2) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.12890625	(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
accuracy	0.375	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy	3.8568455065794374	(.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
accuracy	25.168650470519275	#s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
accuracy	0.1484375	(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)
accuracy	0.44921875	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1)
accuracy	22.386369573422424	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
accuracy	53.38782017703549	#s(approx (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))
accuracy	0.08678108721462961	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 a2 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (*.f64 a2 (cos.f64 th)))))
accuracy	0.140625	(.f64 a2 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (*.f64 a2 (cos.f64 th))))
accuracy	0.15234375	(*.f64 a2 (cos.f64 th))
accuracy	0.453125	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (.f64 a2 (cos.f64 th)))

Samples

134.0ms

256×

valid

Compiler

Compiled 782 to 123 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 95.0ms

ival-mult: 37.0ms (38.8% of total)

ival-cos: 32.0ms (33.6% of total)

ival-pow: 8.0ms (8.4% of total)

ival-div: 7.0ms (7.3% of total)

ival-add: 5.0ms (5.2% of total)

ival-sqrt: 3.0ms (3.1% of total)

ival-neg: 2.0ms (2.1% of total)

exact: 1.0ms (1% of total)

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

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

series123.0ms (1.6%)

Memory

-16.8MiB live, 137.8MiB allocated

Counts

25 → 68

Calls

Call 1

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

Calls

9 calls:

Time	Variable		Point	Expression
62.0ms	a2	@	0	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* a2 (* (pow 4 -1/4) (* a2 (cos th)))) (* (pow 4 -1/4) (* a2 (cos th))) (pow 4 -1/4) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (+ (* (* th th) -1/2) 1) (* (neg (sqrt 2)) (sqrt 2)) (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (sqrt 2) (/ (sqrt 2) (* a2 a2))) (/ (+ (* (* a1 a1) (/ (sqrt 2) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (sqrt 2) (* a2 a2)))) (+ (* (* a1 a1) (/ (sqrt 2) (* a2 a2))) (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* a2 (cos th)) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* a2 (sqrt 2)) (/ (sqrt 2) (* a2 a2)))
13.0ms	a2	@	-inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* a2 (* (pow 4 -1/4) (* a2 (cos th)))) (* (pow 4 -1/4) (* a2 (cos th))) (pow 4 -1/4) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (+ (* (* th th) -1/2) 1) (* (neg (sqrt 2)) (sqrt 2)) (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (sqrt 2) (/ (sqrt 2) (* a2 a2))) (/ (+ (* (* a1 a1) (/ (sqrt 2) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (sqrt 2) (* a2 a2)))) (+ (* (* a1 a1) (/ (sqrt 2) (* a2 a2))) (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* a2 (cos th)) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* a2 (sqrt 2)) (/ (sqrt 2) (* a2 a2)))
11.0ms	a2	@	inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* a2 (* (pow 4 -1/4) (* a2 (cos th)))) (* (pow 4 -1/4) (* a2 (cos th))) (pow 4 -1/4) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (+ (* (* th th) -1/2) 1) (* (neg (sqrt 2)) (sqrt 2)) (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (sqrt 2) (/ (sqrt 2) (* a2 a2))) (/ (+ (* (* a1 a1) (/ (sqrt 2) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (sqrt 2) (* a2 a2)))) (+ (* (* a1 a1) (/ (sqrt 2) (* a2 a2))) (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* a2 (cos th)) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* a2 (sqrt 2)) (/ (sqrt 2) (* a2 a2)))
9.0ms	th	@	inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* a2 (* (pow 4 -1/4) (* a2 (cos th)))) (* (pow 4 -1/4) (* a2 (cos th))) (pow 4 -1/4) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (+ (* (* th th) -1/2) 1) (* (neg (sqrt 2)) (sqrt 2)) (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (sqrt 2) (/ (sqrt 2) (* a2 a2))) (/ (+ (* (* a1 a1) (/ (sqrt 2) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (sqrt 2) (* a2 a2)))) (+ (* (* a1 a1) (/ (sqrt 2) (* a2 a2))) (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* a2 (cos th)) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* a2 (sqrt 2)) (/ (sqrt 2) (* a2 a2)))
9.0ms	th	@	-inf	((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* a2 (* (pow 4 -1/4) (* a2 (cos th)))) (* (pow 4 -1/4) (* a2 (cos th))) (pow 4 -1/4) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (* (cos th) a2) (/ a2 (sqrt 2))) (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (+ (* (* th th) -1/2) 1) (* (neg (sqrt 2)) (sqrt 2)) (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (sqrt 2) (/ (sqrt 2) (* a2 a2))) (/ (+ (* (* a1 a1) (/ (sqrt 2) (* a2 a2))) (sqrt 2)) (* (sqrt 2) (/ (sqrt 2) (* a2 a2)))) (+ (* (* a1 a1) (/ (sqrt 2) (* a2 a2))) (sqrt 2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* a2 (cos th)) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* a2 (sqrt 2)) (/ (sqrt 2) (* a2 a2)))

simplify207.0ms (2.7%)

Memory

37.0MiB live, 186.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	202	1096
1	659	1036
2	2469	908
3	6218	898
4	7304	896
0	8057	827

Stop Event

1×	iter limit
1×	node limit

Counts

68 → 67

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

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

rewrite219.0ms (2.9%)

Memory

-2.4MiB live, 231.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	413
0	98	389
1	293	355
2	1848	355
0	8154	345

Stop Event

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

Counts

25 → 510

Calls

Call 1

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

Outputs
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) #s(literal -1 binary64)) (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 a2 a2) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 a2 (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 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a2 (cos.f64 th)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 a2 a2) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(.f64 (/.f64 (neg.f64 a2) #s(literal -1 binary64)) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)))
(.f64 (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) #s(literal -1 binary64)))
(.f64 (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 (cos.f64 th)) #s(literal -1 binary64)))
(.f64 (.f64 (*.f64 a2 (cos.f64 th)) a2) (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (/.f64 #s(literal 1 binary64) (pow.f64 a2 #s(literal -1 binary64))))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (/.f64 (neg.f64 a2) #s(literal -1 binary64)))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2)
(.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) (/.f64 (neg.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 (cos.f64 th) (pow.f64 a2 #s(literal -1 binary64))))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 (cos.f64 th)))
(.f64 (.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)) (/.f64 (.f64 a2 (cos.f64 th)) (pow.f64 a2 #s(literal -1 binary64))))
(.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)) (/.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)) (.f64 (*.f64 a2 (cos.f64 th)) 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 (pow.f64 a2 #s(literal -1 binary64))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)) (*.f64 a2 a2)))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2)) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 (neg.f64 a2) (.f64 a2 (cos.f64 th)))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 a2 (cos.f64 th)))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (neg.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 a2 a2))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 a2 a2))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(/.f64 (neg.f64 (.f64 (.f64 a2 (cos.f64 th)) (neg.f64 a2))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 a2 (cos.f64 th)) #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (neg.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th)))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 a2 (cos.f64 th)) a2))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 a2 (cos.f64 th))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (.f64 (neg.f64 a2) (.f64 a2 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 a2 (cos.f64 th))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 (.f64 (.f64 a2 (cos.f64 th)) (neg.f64 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 a2 (cos.f64 th)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 a2 a2) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 (neg.f64 (.f64 (.f64 a2 (cos.f64 th)) a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2))))
(/.f64 (*.f64 (neg.f64 a2) a2) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a2 (cos.f64 th)) a2)))
(/.f64 (*.f64 a2 (cos.f64 th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(*.f64 (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cos.f64 th) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (neg.f64 (cos.f64 th)) #s(literal -1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (*.f64 a2 (cos.f64 th)) (pow.f64 #s(literal 16 binary64) #s(literal -1/16 binary64))) (pow.f64 #s(literal 16 binary64) #s(literal -1/16 binary64)))
(*.f64 (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 #s(literal -1 binary64)))
(.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/16 binary64)) (.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/16 binary64)) (*.f64 a2 (cos.f64 th))))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(.f64 (.f64 a2 (cos.f64 th)) (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)))
(*.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)) (/.f64 a2 (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)) (.f64 a2 (cos.f64 th)))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) a2)
(*.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (cos.f64 th)) a2)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) a2)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
(/.f64 (neg.f64 (*.f64 a2 (cos.f64 th))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 (neg.f64 (cos.f64 th)) a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/16 binary64)) (pow.f64 #s(literal 16 binary64) #s(literal -1/16 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)))
(pow.f64 (exp.f64 #s(literal -1/4 binary64)) (log.f64 #s(literal 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 16 binary64) #s(literal -1/8 binary64))
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(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
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(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)))
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(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)
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(*.f64 a1 (sqrt.f64 #s(literal 1/2 binary64)))
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(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 th #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (.f64 a2 a2))) (neg.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
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(/.f64 (.f64 (.f64 a2 a2) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
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(/.f64 (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (fma.f64 (pow.f64 th #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal -1 binary64)))
(/.f64 (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal 1 binary64))) (fma.f64 (pow.f64 th #s(literal 4 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 th th) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
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(/.f64 (.f64 (.f64 a2 a2) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (pow.f64 th #s(literal 4 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 th th) #s(literal -1/2 binary64))))))
(/.f64 (.f64 (fma.f64 (pow.f64 th #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (.f64 a2 a2)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
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(fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 a1 (*.f64 a2 a2)) (/.f64 a1 (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 a1 #s(literal -1 binary64)) (/.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 a1 (neg.f64 a2)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a1) a2) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 a1 a2) (/.f64 (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a2) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 a1 a2) (/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a1) (neg.f64 a2)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 a1 a2) (/.f64 a1 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (.f64 a1 a1) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 (neg.f64 (.f64 a1 a1)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2) (/.f64 (*.f64 a1 a1) (neg.f64 a2)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (/.f64 a1 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 a2)))
(fma.f64 (pow.f64 a2 #s(literal -1 binary64)) (/.f64 (*.f64 a1 a1) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (pow.f64 a2 #s(literal -1 binary64)) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) a2) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (*.f64 a1 a1) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 a2)) (/.f64 (neg.f64 (*.f64 a1 a1)) a2) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 #s(literal -1 binary64) a2) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (neg.f64 a2)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) a1 (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a1) (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (pow.f64 a2 #s(literal -2 binary64)) (/.f64 (*.f64 a1 a1) (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (*.f64 a1 a1) a2) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 a2 #s(literal -2 binary64)) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (*.f64 (/.f64 a1 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 a1 a1) (.f64 (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 a1 (/.f64 a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (sqrt.f64 #s(literal 2 binary64)))
(-.f64 (/.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 a1 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 a2)))) (/.f64 (/.f64 (.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 2 binary64)) (pow.f64 a2 #s(literal 4 binary64))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 a1 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 a2)))))
(-.f64 (/.f64 (/.f64 (*.f64 (pow.f64 a1 #s(literal 4 binary64)) #s(literal 2 binary64)) (pow.f64 a2 #s(literal 4 binary64))) (fma.f64 (/.f64 a1 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 2 binary64) (fma.f64 (/.f64 a1 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (*.f64 (/.f64 a1 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 a1 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 a2 a2)) (fma.f64 (/.f64 a1 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a1 a2) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 #s(literal -1 binary64)))
(*.f64 (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 a2 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 a2 (pow.f64 #s(literal 16 binary64) #s(literal -1/16 binary64))) (pow.f64 #s(literal 16 binary64) #s(literal -1/16 binary64)))
(.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/16 binary64)) (.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/16 binary64)) a2))
(*.f64 #s(literal -1 binary64) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (neg.f64 a2) (pow.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)) (pow.f64 (pow.f64 a2 #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)) a2)
(*.f64 a2 (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (/.f64 (neg.f64 a2) #s(literal -1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 a2 #s(literal 1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 a2))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2)) #s(literal 2 binary64))
(/.f64 (/.f64 (neg.f64 a2) #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 a2 #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (neg.f64 a2)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (neg.f64 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a2 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 a2 a2) #s(literal -1 binary64)))
(*.f64 (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 a2 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 a2 #s(literal -1 binary64)) (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (neg.f64 a2) #s(literal -1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (neg.f64 a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 #s(literal -1 binary64)))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 a2 #s(literal -1 binary64))))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (neg.f64 a2) #s(literal -1 binary64)))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
(.f64 #s(literal 1 binary64) (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(*.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)) (/.f64 a2 (pow.f64 a2 #s(literal -1 binary64))))
(.f64 (.f64 a2 a2) (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 a2 (pow.f64 #s(literal 16 binary64) #s(literal -1/16 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 a2 #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) a2)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (*.f64 #s(literal 1 binary64) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (*.f64 a2 #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (neg.f64 (*.f64 (neg.f64 a2) a2)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 a2) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (*.f64 (neg.f64 a2) a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (-.f64 (*.f64 (log.f64 a2) #s(literal 2 binary64)) (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (fma.f64 (log.f64 a2) #s(literal 2 binary64) (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal -1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 a2) #s(literal 2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
(*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) a2) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) a2))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 a2 a2)))
(*.f64 (pow.f64 a2 #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 a2)) (/.f64 #s(literal -1 binary64) a2))
(*.f64 (/.f64 #s(literal -1 binary64) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 a2)))
(.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 a2) a2)))
(*.f64 (pow.f64 a2 #s(literal -2 binary64)) (pow.f64 (pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (pow.f64 a2 #s(literal -1 binary64)))
(.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 (neg.f64 a2) a2) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a2 #s(literal -2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (pow.f64 a2 #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (/.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 a2) a2)) #s(literal 3 binary64)) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 a2) a2)) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 a2) a2)) (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 a2) a2)) (+.f64 (pow.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal -2 binary64)) (.f64 (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 a2) a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 a2) a2))))))
(/.f64 (neg.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2)) (neg.f64 (neg.f64 a2)))
(/.f64 (neg.f64 (pow.f64 a2 #s(literal -1 binary64))) (neg.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (neg.f64 a2) a2))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (neg.f64 (*.f64 (neg.f64 a2) a2))))
(/.f64 (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) (neg.f64 (neg.f64 a2)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (.f64 (neg.f64 a2) a2)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (neg.f64 a2))) (pow.f64 a2 #s(literal 4 binary64)))
(/.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) a2) (neg.f64 a2))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 a2 a2))
(/.f64 (pow.f64 a2 #s(literal -1 binary64)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (*.f64 (neg.f64 a2) a2)))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (neg.f64 a2))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2)
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 a2) a2))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
(neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 a2) a2)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 a2) a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 a2) a2)))
(exp.f64 (-.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (log.f64 a2) #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) #s(literal -1 binary64)))

eval77.0ms (1%)

Memory: 10.3MiB live, 167.9MiB allocated
Compiler: Compiled 27 496 to 2 391 computations (91.3% saved)

prune47.0ms (0.6%)

Memory

2.1MiB live, 85.6MiB allocated

Pruning

33 alts after pruning (29 fresh and 4 done)

	Pruned	Kept	Total
New	591	11	602
Fresh	6	18	24
Picked	2	3	5
Done	0	1	1
Total	599	33	632

Accuracy

100.0%

Counts

632 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	55.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 a2 a2 (*.f64 a1 a1))))
	64.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt 2) (cos th)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1))))
	64.5%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	60.4%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
	60.4%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (cos th) (sqrt 2)) (fma.f64 (*.f64 th (/.f64 th (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	64.8%	#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)))
	53.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (sqrt.f64 #s(literal 2 binary64))) a2)))
	53.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
	64.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
	39.4%	#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 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a2))))
	32.2%	#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)) #s(literal 1 binary64)) (.f64 a2 (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))))
	64.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
	64.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (/.f64 #s(approx (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (neg.f64 a2))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	99.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 #s(literal 2 binary64))))
	64.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
✓	64.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (.f64 (neg.f64 a2) (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
	64.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) (* a2 a2))) (sqrt 2)) (.f64 (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) a2) a2) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
	64.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) (* a2 a2))) (sqrt 2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)))))
	99.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2))
✓	99.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 a2 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (*.f64 a2 (cos.f64 th)))))
	64.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
	14.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* (neg a2) a2) (sqrt 2)) (* (neg (sqrt 2)) (* a1 a1))) (* (neg (sqrt 2)) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
	60.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))
	60.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))) a2)))
	17.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) (.f64 #s(approx (+ ( (* th th) -1/2) 1) (.f64 (.f64 th th) #s(literal -1/2 binary64))) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
	20.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) #s(approx (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal -1/2 binary64)) th) th))))
	99.4%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
	99.2%	#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)))
✓	64.6%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a2 a2 (.f64 a1 a1))))
	64.4%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(approx (+ ( a2 a2) (* a1 a1)) (*.f64 a2 a2))))
	64.7%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
✓	14.1%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
	14.1%	#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 3 494 to 1 056 computations (69.8% saved)

regimes194.0ms (2.6%)

Memory

0.0MiB live, 224.8MiB allocated

Counts

70 → 1

Calls

Call 1

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

Outputs
(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)))

Calls

8 calls:

42.0ms	(cos.f64 th)
36.0ms	(*.f64 a2 a2)
24.0ms	th
20.0ms	a2
19.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes196.0ms (2.6%)

Memory

-2.2MiB live, 196.0MiB allocated

Counts

64 → 1

Calls

Call 1

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

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

Calls

8 calls:

55.0ms	(*.f64 a1 a1)
37.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
20.0ms	th
19.0ms	a2
18.0ms	a1

Results

Accuracy	Segments	Branch
99.5%	1	`a1`
99.5%	1	`a2`
99.5%	1	`th`
99.5%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
99.5%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.5%	1	`(cos.f64 th)`
99.5%	1	`(*.f64 a1 a1)`
99.5%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes157.0ms (2.1%)

Memory

28.8MiB live, 268.0MiB allocated

Counts

61 → 1

Calls

Call 1

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

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

Calls

8 calls:

26.0ms	(*.f64 a2 a2)
25.0ms	(cos.f64 th)
21.0ms	a2
20.0ms	a1
18.0ms	th

Results

Accuracy	Segments	Branch
99.5%	1	`a1`
99.5%	1	`a2`
99.5%	1	`th`
99.5%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
99.5%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.5%	1	`(cos.f64 th)`
99.5%	1	`(*.f64 a1 a1)`
99.5%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes171.0ms (2.3%)

Memory

-15.2MiB live, 221.4MiB allocated

Counts

50 → 1

Calls

Call 1

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

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

Calls

8 calls:

66.0ms	(*.f64 a1 a1)
20.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
15.0ms	th
14.0ms	a1
14.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Results

Accuracy	Segments	Branch
99.5%	1	`a1`
99.5%	1	`a2`
99.5%	1	`th`
99.5%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
99.5%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.5%	1	`(cos.f64 th)`
99.5%	1	`(*.f64 a1 a1)`
99.5%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes117.0ms (1.5%)

Memory

-19.0MiB live, 229.5MiB allocated

Counts

49 → 1

Calls

Call 1

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

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

Calls

8 calls:

19.0ms	(*.f64 a2 a2)
17.0ms	th
16.0ms	a2
14.0ms	(cos.f64 th)
13.0ms	a1

Results

Accuracy	Segments	Branch
99.4%	1	`a1`
99.4%	1	`a2`
99.4%	1	`th`
99.4%	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)))`
99.4%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
99.4%	1	`(cos.f64 th)`
99.4%	1	`(*.f64 a1 a1)`
99.4%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes102.0ms (1.3%)

Memory

8.3MiB live, 164.3MiB allocated

Counts

48 → 1

Calls

Call 1

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

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:

15.0ms	th
14.0ms	a1
12.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
12.0ms	a2
12.0ms	(*.f64 a1 a1)

Results

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

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes133.0ms (1.7%)

Memory

2.4MiB live, 159.2MiB allocated

Counts

47 → 2

Calls

Call 1

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

Outputs

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

#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)))

Calls

8 calls:

39.0ms	a1
20.0ms	th
13.0ms	(cos.f64 th)
12.0ms	a2
12.0ms	(*.f64 a1 a1)

Results

Accuracy	Segments	Branch
64.8%	1	`a1`
69.6%	3	`a2`
68.8%	3	`th`
77.9%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
77.8%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
77.8%	2	`(cos.f64 th)`
64.8%	1	`(*.f64 a1 a1)`
64.8%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes8.0ms (0.1%)

Memory

10.7MiB live, 10.7MiB allocated

Counts

27 → 2

Calls

Call 1

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

Outputs

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

#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)))

Calls

1 calls:

7.0ms

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

Results

Accuracy	Segments	Branch
77.9%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes31.0ms (0.4%)

Memory

-8.8MiB live, 27.3MiB allocated

Counts

21 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

18.0ms

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

6.0ms

(cos.f64 th)

5.0ms

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

Results

Accuracy	Segments	Branch
77.7%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
77.7%	2	`(cos.f64 th)`
77.7%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 26 to 23 computations (11.5% saved)

regimes40.0ms (0.5%)

Memory

11.2MiB live, 46.5MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

8 calls:

16.0ms	th
3.0ms	(*.f64 a2 a2)
3.0ms	a1
3.0ms	a2
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
64.7%	1	`a1`
64.7%	1	`(*.f64 a1 a1)`
64.7%	1	`(*.f64 a2 a2)`
64.7%	1	`th`
64.7%	1	`a2`
64.7%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
64.7%	1	`(cos.f64 th)`
64.7%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes37.0ms (0.5%)

Memory

-54.9MiB live, 25.5MiB 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) (+ (* a2 a2) (* a1 a1))) (*.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) (+ (* a2 a2) (* a1 a1))) (*.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) (+ (* a2 a2) (* a1 a1))) (.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 1/2 binary64)))))

Calls

8 calls:

27.0ms	th
1.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
1.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
1.0ms	a2
1.0ms	a1

Results

Accuracy	Segments	Branch
14.1%	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)))`
14.1%	1	`th`
14.1%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
14.1%	1	`(cos.f64 th)`
14.1%	1	`a1`
14.1%	1	`a2`
14.1%	1	`(*.f64 a1 a1)`
14.1%	1	`(*.f64 a2 a2)`

Compiler

Compiled 35 to 40 computations (-14.3% saved)

bsearch1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.381850536502465e-166	-8.125342568099107e-264

Compiler

Compiled 22 to 18 computations (18.2% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.381850536502465e-166	-8.125342568099107e-264

Compiler

Compiled 22 to 18 computations (18.2% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.381850536502465e-166	-8.125342568099107e-264

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify53.0ms (0.7%)

Memory

-1.3MiB live, 37.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	508
1	132	508
2	210	508
3	342	508
4	585	508
5	967	508
6	1033	508
7	1072	508
8	1082	508
9	1085	508
10	1090	508
11	1095	508
12	1097	508
13	1097	508
14	1225	508
15	1264	508

Stop Event

1×

saturated

Calls

Call 1

Inputs
(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)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 a2 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (*.f64 a2 (cos.f64 th)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (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)) (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 -4149515568880993/8299031137761985917024815727382322302024892464484873799991314659381305622825816292799414097894207588576395773222601578364790302150823550615773749668227927374122363606803019047370752 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) #s(approx (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal -1/2 binary64)) th) th)))) #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))))
(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 -4149515568880993/8299031137761985917024815727382322302024892464484873799991314659381305622825816292799414097894207588576395773222601578364790302150823550615773749668227927374122363606803019047370752 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) #s(approx (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal -1/2 binary64)) th) th)))) #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))))
(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 -4149515568880993/8299031137761985917024815727382322302024892464484873799991314659381305622825816292799414097894207588576395773222601578364790302150823550615773749668227927374122363606803019047370752 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) #s(approx (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal -1/2 binary64)) th) th)))) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (.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) (+ (* a2 a2) (* a1 a1))) (.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) (+ (* a2 a2) (* a1 a1))) (.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 1/2 binary64)))))

Outputs
(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)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 a2 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) (*.f64 a2 (cos.f64 th)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) a2))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (.f64 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (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)) (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 -4149515568880993/8299031137761985917024815727382322302024892464484873799991314659381305622825816292799414097894207588576395773222601578364790302150823550615773749668227927374122363606803019047370752 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) #s(approx (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal -1/2 binary64)) th) th)))) #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))))
(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 -4149515568880993/8299031137761985917024815727382322302024892464484873799991314659381305622825816292799414097894207588576395773222601578364790302150823550615773749668227927374122363606803019047370752 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) #s(approx (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal -1/2 binary64)) th) th)))) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #s(literal -1 binary64)) a2 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1))))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) #s(literal -4149515568880993/8299031137761985917024815727382322302024892464484873799991314659381305622825816292799414097894207588576395773222601578364790302150823550615773749668227927374122363606803019047370752 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) #s(approx (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal -1/2 binary64)) th) th)))) #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))))
(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 -4149515568880993/8299031137761985917024815727382322302024892464484873799991314659381305622825816292799414097894207588576395773222601578364790302150823550615773749668227927374122363606803019047370752 binary64)) #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (* (cos th) a2) (/ a2 (sqrt 2))) #s(approx (* (+ (* (* th th) -1/2) 1) (* (/ a2 (sqrt 2)) a2)) (.f64 (.f64 (.f64 (.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #s(literal -1/2 binary64)) th) th)))) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (sqrt 1/2) (+ (* a2 a2) (* a1 a1))) (.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) (+ (* a2 a2) (* a1 a1))) (.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) (+ (* a2 a2) (* a1 a1))) (.f64 (.f64 a1 a1) (sqrt.f64 #s(literal 1/2 binary64)))))

soundness1.5s (20.4%)

Memory

40.1MiB live, 1 107.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	177
0	53	185
1	178	157
2	1326	155
0	8286	155
0	49	313
0	79	286
1	265	256
2	2009	232
0	8309	232
0	111	576
1	343	562
2	1210	458
3	3908	429
0	8416	391
0	12	44
0	20	38
1	58	38
2	411	38
3	7359	38
0	8465	37
0	202	1096
1	659	1036
2	2469	908
3	6218	898
4	7304	896
0	8057	827
0	319	1872
1	1061	1751
2	4149	1727
0	8100	1605
0	217	1207
1	709	1138
2	2545	1009
3	6979	991
0	8133	908
0	66	413
0	98	389
1	293	355
2	1848	355
0	8154	345

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

Compiler

Compiled 1 019 to 414 computations (59.4% saved)

preprocess139.0ms (1.8%)

Memory: -15.2MiB live, 223.9MiB allocated
Remove: (abs th)
Compiler: Compiled 1 402 to 376 computations (73.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	34	240
0	53	243
1	86	225
2	149	225
3	257	219
4	444	219
5	550	219
6	550	219
0	550	219

Iter	Nodes	Cost
0	34	240
0	53	243
1	86	225
2	149	225
3	257	219
4	444	219
5	550	219
6	550	219
0	550	219

start0.0ms (0%)

analyze1.0ms (0%)

sample1.1s (14.3%)

explain137.0ms (1.8%)

preprocess136.0ms (1.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize41.0ms (0.5%)

series18.0ms (0.2%)

simplify218.0ms (2.9%)

rewrite201.0ms (2.6%)

eval44.0ms (0.6%)

prune16.0ms (0.2%)

simplify13.0ms (0.2%)

localize84.0ms (1.1%)

series37.0ms (0.5%)

simplify146.0ms (1.9%)

rewrite211.0ms (2.8%)

eval437.0ms (5.7%)

prune44.0ms (0.6%)

simplify86.0ms (1.1%)

localize119.0ms (1.6%)

series54.0ms (0.7%)

simplify173.0ms (2.3%)

rewrite202.0ms (2.6%)

eval150.0ms (2%)

prune46.0ms (0.6%)

simplify130.0ms (1.7%)

localize169.0ms (2.2%)

series123.0ms (1.6%)

simplify207.0ms (2.7%)

rewrite219.0ms (2.9%)

eval77.0ms (1%)

prune47.0ms (0.6%)

regimes194.0ms (2.6%)

regimes196.0ms (2.6%)

regimes157.0ms (2.1%)

regimes171.0ms (2.3%)

regimes117.0ms (1.5%)

regimes102.0ms (1.3%)

regimes133.0ms (1.7%)

regimes8.0ms (0.1%)

regimes31.0ms (0.4%)

regimes40.0ms (0.5%)

regimes37.0ms (0.5%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify53.0ms (0.7%)

soundness1.5s (20.4%)

preprocess139.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	34	240
0	53	243
1	86	225
2	149	225
3	257	219
4	444	219
5	550	219
6	550	219
0	550	219