Metrics for Migdal et al, Equation (64)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 21 to 14 computations (33.3% saved)

sample1.4s (11.6%)

Memory

12.8MiB live, 1 667.7MiB allocated

Samples

1.0s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 679.0ms

ival-mult: 312.0ms (46% of total)

ival-cos: 207.0ms (30.5% of total)

ival-sqrt: 55.0ms (8.1% of total)

ival-div: 46.0ms (6.8% of total)

ival-add: 45.0ms (6.6% of total)

ival-true: 5.0ms (0.7% of total)

exact: 5.0ms (0.7% of total)

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

Bogosity

explain145.0ms (1.2%)

Memory

4.9MiB live, 293.3MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

54.0ms

512×

valid

Compiler

Compiled 138 to 40 computations (71% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 14.0ms (39% of total)

ival-cos: 12.0ms (33.5% of total)

ival-sqrt: 4.0ms (11.2% of total)

ival-div: 3.0ms (8.4% of total)

ival-add: 2.0ms (5.6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess133.0ms (1.1%)

Memory

12.0MiB live, 50.6MiB allocated

Algorithm

1×	egg-herbie

Rules

1 520×	`times-frac`
1 254×	`distribute-lft-in`
1 236×	`distribute-rgt-in`
946×	`div-sub`
714×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	120
1	130	120
2	373	120
3	1018	120
4	2414	120
5	4784	120
6	5686	120
7	6500	120
8	6573	120
9	6589	120
10	6760	120
11	6878	120
12	6890	120
13	6890	120
14	6890	120
0	12	19
0	20	13
1	33	13
2	58	13
3	88	13
4	100	13
0	100	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 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))

Symmetry

(abs th)

(abs a2)

(abs a1)

(sort a1 a2)

Compiler

Compiled 22 to 12 computations (45.5% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Compiler

Compiled 22 to 12 computations (45.5% saved)

simplify15.0ms (0.1%)

Memory

-14.2MiB live, 27.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize39.0ms (0.3%)

Memory

-2.8MiB live, 72.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
accuracy	0.21875	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
accuracy	0.234375	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
accuracy	0.734375	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

26.0ms

256×

valid

Compiler

Compiled 58 to 14 computations (75.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 7.0ms (40.9% of total)

ival-cos: 6.0ms (35% of total)

ival-sqrt: 2.0ms (11.7% of total)

ival-div: 1.0ms (5.8% of total)

ival-add: 1.0ms (5.8% of total)

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.1%)

Memory

27.2MiB live, 27.3MiB allocated

Counts

5 → 108

Calls

Call 1

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

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

Calls

27 calls:

Time	Variable		Point	Expression
2.0ms	th	@	inf	(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
2.0ms	th	@	-inf	(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
2.0ms	th	@	-inf	(/ (cos th) (sqrt 2))
1.0ms	a1	@	0	(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
1.0ms	th	@	0	(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

simplify973.0ms (8.3%)

Memory

-68.9MiB live, 619.1MiB allocated

Algorithm

1×	egg-herbie

Rules

34 694×	`lower-fma.f64`
34 694×	`lower-fma.f32`
6 426×	`lower-*.f64`
6 426×	`lower-*.f32`
4 620×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	111	1498
1	343	1366
2	1205	1262
3	3898	1233
0	8422	1172

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

rewrite374.0ms (3.2%)

Memory

-5.2MiB live, 272.6MiB allocated

Rules

6 176×	`lower-fma.f64`
6 176×	`lower-fma.f32`
4 662×	`lower-*.f32`
4 654×	`lower-*.f64`
2 804×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

5 → 327

Calls

Call 1

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

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

eval116.0ms (1%)

Memory: 12.5MiB live, 87.3MiB allocated
Compiler: Compiled 14 708 to 1 014 computations (93.1% saved)

prune132.0ms (1.1%)

Memory

-12.4MiB live, 119.3MiB allocated

Pruning

15 alts after pruning (15 fresh and 0 done)

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

Accuracy

100.0%

Counts

491 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(fma.f64 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a2 (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	99.6%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	99.6%	(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
	18.5%	(/.f64 (.f64 (fma.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))))) (cos.f64 th)) (.f64 (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (sqrt.f64 #s(literal 2 binary64))))
	26.1%	(/.f64 (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (cos.f64 th)) (.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64))))
▶	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))))
	40.0%	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) #s(approx (* (/ (cos th) (sqrt 2)) (* a2 a2)) (fma.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 th th)) (fma.f64 th (.f64 th (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
	99.6%	(.f64 (fma.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (.f64 a1 a1)))) #s(literal 1/2 binary64))
	99.5%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
▶	99.6%	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
▶	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
▶	67.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
	99.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
	53.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a1 a1) (.f64 (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64)) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
	62.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))))

Compiler

Compiled 678 to 392 computations (42.2% saved)

simplify19.0ms (0.2%)

Memory

22.7MiB live, 22.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
cost-diff	1088	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
cost-diff	0	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))))
cost-diff	0	(*.f64 a2 a2)
cost-diff	0	(fma.f64 a1 a1 (*.f64 a2 a2))
cost-diff	0	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	1344	(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(cos.f64 th)
cost-diff	0	(*.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
cost-diff	8064	(fma.f64 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a2 (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))

Rules

378×	`times-frac`
284×	`lower-*.f32`
270×	`lower-*.f64`
170×	`associate-r`
158×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	262
0	56	268
1	103	244
2	193	244
3	363	235
4	557	235
5	712	235
6	833	235
7	856	235
0	856	235

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize185.0ms (1.6%)

Memory

-21.4MiB live, 175.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.08203125	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
accuracy	0.1171875	(/.f64 #s(literal 1 binary64) (cos.f64 th))
accuracy	0.23503876953688402	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0	(cos.f64 th)
accuracy	0.078125	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
accuracy	0.15234375	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))))
accuracy	0.5301695713026269	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.09375	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
accuracy	0.21160126953688405	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.00390625	(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.20769501953688405	(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.4140625	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	20.81076963029496	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.1484375	(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.20703125	(*.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.4140625	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.48046875	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))

Samples

96.0ms

256×

valid

Compiler

Compiled 263 to 34 computations (87.1% saved)

Precisions

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

ival-mult: 37.0ms (60.1% of total)

ival-div: 13.0ms (21.1% of total)

ival-cos: 6.0ms (9.8% of total)

ival-add: 4.0ms (6.5% of total)

ival-sqrt: 2.0ms (3.3% of total)

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

exact: 0.0ms (0% of total)

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

series55.0ms (0.5%)

Memory

12.3MiB live, 54.6MiB allocated

Counts

21 → 468

Calls

Call 1

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

Outputs
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (* (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))))>
#<alt (+ (* (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))))>
#<alt (+ (* (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))))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ a2 (sqrt 2))>
#<alt (+ (* -1/2 (/ (* a2 (pow th 2)) (sqrt 2))) (/ a2 (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ a2 (sqrt 2))) (* 1/24 (/ (* a2 (pow th 2)) (sqrt 2))))) (/ a2 (sqrt 2)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ a2 (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* a2 (pow th 2)) (sqrt 2))) (* 1/24 (/ a2 (sqrt 2))))))) (/ a2 (sqrt 2)))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt (/ (* a2 (cos th)) (sqrt 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow th 2)))>
#<alt (+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))>
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#<alt (/ (- (+ (* -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))>
#<alt (/ (sqrt 2) (* (pow a1 2) (cos th)))>
#<alt (/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a1 2))>
#<alt (/ (- (+ (/ (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))>
#<alt (/ (- (+ (* -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))>
#<alt (/ (sqrt 2) (* (pow a1 2) (cos th)))>
#<alt (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (sqrt 2) (* (pow a1 2) (cos th))))>
#<alt (+ (* (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))))>
#<alt (+ (* (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))))>
#<alt (/ (sqrt 2) (* (pow a2 2) (cos th)))>
#<alt (/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))>
#<alt (/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))>
#<alt (/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))>
#<alt (/ (sqrt 2) (* (pow a2 2) (cos th)))>
#<alt (/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))>
#<alt (/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))>
#<alt (/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (* -1/2 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (+ (pow a1 2) (pow a2 2)))>
#<alt (+ (* (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)))>
#<alt (+ (* (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)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (pow a2 2) (cos th))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (* (pow a1 2) (cos th))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (cos th))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (cos th))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (cos th))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (* (pow a1 2) (cos th))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (cos th))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))>
#<alt (* (pow a1 2) (cos th))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (cos th))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (* -1/2 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (+ (pow a1 2) (pow a2 2)))>
#<alt (+ (* (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)))>
#<alt (+ (* (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)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (* (cos th) (+ (pow a1 2) (pow a2 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))>
#<alt (+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (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))))>
#<alt (+ (* (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))))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt 1>
#<alt (+ 1 (* 1/2 (pow th 2)))>
#<alt (+ 1 (* (pow th 2) (+ 1/2 (* 5/24 (pow th 2)))))>
#<alt (+ 1 (* (pow th 2) (+ 1/2 (* (pow th 2) (+ 5/24 (* 61/720 (pow th 2)))))))>
#<alt (/ 1 (cos th))>
#<alt (/ 1 (cos th))>
#<alt (/ 1 (cos th))>
#<alt (/ 1 (cos th))>
#<alt (/ 1 (cos th))>
#<alt (/ 1 (cos th))>
#<alt (/ 1 (cos th))>
#<alt (/ 1 (cos th))>

Calls

117 calls:

Time	Variable		Point	Expression
29.0ms	a1	@	inf	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2))
1.0ms	th	@	0	(/ (sqrt 2) (* (cos th) (+ (* a1 a1) (* a2 a2))))
1.0ms	th	@	inf	(* (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (cos th))
1.0ms	a1	@	inf	(* (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (cos th))
1.0ms	th	@	-inf	(* (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2)) (cos th))

simplify389.0ms (3.3%)

Memory

-10.9MiB live, 548.0MiB allocated

Algorithm

1×	egg-herbie

Rules

14 190×	`lower-fma.f64`
14 190×	`lower-fma.f32`
6 000×	`lower-*.f64`
6 000×	`lower-*.f32`
4 580×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	272	7157
1	900	6537
2	3369	6203
0	8175	5832

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 468

Calls

Call 1

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

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

rewrite357.0ms (3.1%)

Memory

26.4MiB live, 784.1MiB allocated

Rules

5 572×	`lower-/.f32`
5 554×	`lower-/.f64`
4 526×	`lower-*.f32`
4 512×	`lower-*.f64`
3 744×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	193
0	56	199
1	213	165
2	1730	165
0	8743	165

Stop Event

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

Counts

21 → 2 790

Calls

Call 1

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

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

eval799.0ms (6.9%)

Memory: 16.2MiB live, 1 181.2MiB allocated
Compiler: Compiled 97 674 to 4 686 computations (95.2% saved)

prune800.0ms (6.9%)

Memory

3.3MiB live, 944.7MiB allocated

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	3 723	31	3 754
Fresh	9	1	10
Picked	5	0	5
Done	0	0	0
Total	3 737	32	3 769

Accuracy

100.0%

Counts

3 769 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.1%	(fma.f64 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a2 (.f64 #s(approx (cos th) #s(literal 1 binary64)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	99.6%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
▶	99.6%	(/.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
	99.5%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1))))
▶	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
	67.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (cos th) (+ (* a1 a1) (* a2 a2))) (fma.f64 a1 a1 (*.f64 a2 a2)))))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (cos th) (+ (* a1 a1) (* a2 a2))) (.f64 a2 (.f64 a2 (cos.f64 th))))))
	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (/.f64 #s(literal 1 binary64) (fma.f64 a2 a2 (.f64 a1 a1)))))
	57.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (cos th) (+ (* a1 a1) (* a2 a2)))) (.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
	99.5%	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
	99.6%	(.f64 (/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #s(literal 2 binary64)) (cos.f64 th))
	62.4%	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	99.5%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	62.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
	67.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (fma.f64 a1 a1 (*.f64 a2 a2))))
▶	62.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
	67.3%	#s(approx (/ 1 (/ (sqrt 2) (* (cos th) (+ (* a1 a1) (* a2 a2))))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
	99.5%	#s(approx (/ 1 (/ (sqrt 2) (* (cos th) (+ (* a1 a1) (* a2 a2))))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
	67.3%	#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 a1) (sqrt.f64 #s(literal 2 binary64)))))
	67.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	67.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 (neg.f64 a1) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) (.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 (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))))
	11.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a1 (.f64 a1 (.f64 a1 a1)))))))
	67.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))) #s(literal 2 binary64)))
	16.8%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64)) (/.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))))
	16.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
	99.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
▶	16.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64)))))
	57.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a1 a2)) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (-.f64 a1 a2))))
	67.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
▶	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 1 280 to 748 computations (41.6% saved)

simplify236.0ms (2%)

Memory

-28.9MiB live, 407.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64)))))
cost-diff	384	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64))
cost-diff	1088	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64))))
cost-diff	2432	(/.f64 (/.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64)))
cost-diff	0	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
cost-diff	0	(*.f64 a1 a1)
cost-diff	0	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff	0	(neg.f64 (fma.f64 a2 a2 (*.f64 a1 a1)))
cost-diff	320	(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
cost-diff	640	(/.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th))))

Rules

4 090×	`lower-*.f32`
4 072×	`lower-*.f64`
3 898×	`lower-/.f32`
3 878×	`lower-/.f64`
3 668×	`lower-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	468
0	88	454
1	167	444
2	427	436
3	1706	380
4	7065	380
0	8523	380

Stop Event

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

Calls

Call 1

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

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

localize154.0ms (1.3%)

Memory

35.7MiB live, 393.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.07206956875069717	#s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))
accuracy	0.078125	(.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))
accuracy	0.15234375	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
accuracy	0.5301695713026269	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))
accuracy	0.1640625	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64))))
accuracy	0.20769501953688405	(/.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	20.81076963029496	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64)))))
accuracy	46.023863942005555	(/.f64 (/.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64)))
accuracy	0.23503876953688402	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	2.2022963533861235	(.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
accuracy	24.654644086265783	#s(approx (/ (+ (* a1 a1) (* a2 a2)) (/ 1 (cos th))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.23113251953688405	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
accuracy	20.81076963029496	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	55.27902090372483	#s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0	(cos.f64 th)
accuracy	0.1171875	(/.f64 #s(literal 1 binary64) (cos.f64 th))
accuracy	0.15300751953688405	(/.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
accuracy	0.24285126953688402	(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))

Samples

92.0ms

256×

valid

Compiler

Compiled 386 to 46 computations (88.1% saved)

Precisions

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

ival-div: 21.0ms (36.2% of total)

ival-mult: 19.0ms (32.7% of total)

ival-add: 6.0ms (10.3% of total)

ival-cos: 6.0ms (10.3% of total)

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

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

ival-sub: 1.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series38.0ms (0.3%)

Memory

-21.2MiB live, 96.0MiB allocated

Counts

24 → 576

Calls

Call 1

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

Outputs
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))>
#<alt (+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (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))))>
#<alt (+ (* (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))))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (* -1 (sqrt 2))>
#<alt (+ (* -1 (sqrt 2)) (* -1/2 (* (pow th 2) (sqrt 2))))>
#<alt (+ (* -1 (sqrt 2)) (* (pow th 2) (+ (* -1/2 (sqrt 2)) (* (pow th 2) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))>
#<alt (+ (* -1 (sqrt 2)) (* (pow th 2) (+ (* -1/2 (sqrt 2)) (* (pow th 2) (+ (* -1/4 (sqrt 2)) (+ (* 1/24 (sqrt 2)) (* (pow th 2) (+ (* -1/720 (sqrt 2)) (+ (* 1/48 (sqrt 2)) (* 1/2 (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))))))))>
#<alt (* -1 (/ (sqrt 2) (cos th)))>
#<alt (* -1 (/ (sqrt 2) (cos th)))>
#<alt (* -1 (/ (sqrt 2) (cos th)))>
#<alt (* -1 (/ (sqrt 2) (cos th)))>
#<alt (* -1 (/ (sqrt 2) (cos th)))>
#<alt (* -1 (/ (sqrt 2) (cos th)))>
#<alt (* -1 (/ (sqrt 2) (cos th)))>
#<alt (* -1 (/ (sqrt 2) (cos th)))>
#<alt (* -1 (pow a1 2))>
#<alt (- (* -1 (pow a2 2)) (pow a1 2))>
#<alt (- (* -1 (pow a2 2)) (pow a1 2))>
#<alt (- (* -1 (pow a2 2)) (pow a1 2))>
#<alt (* -1 (pow a2 2))>
#<alt (* (pow a2 2) (- (* -1 (/ (pow a1 2) (pow a2 2))) 1))>
#<alt (* (pow a2 2) (- (* -1 (/ (pow a1 2) (pow a2 2))) 1))>
#<alt (* (pow a2 2) (- (* -1 (/ (pow a1 2) (pow a2 2))) 1))>
#<alt (* -1 (pow a2 2))>
#<alt (* (pow a2 2) (- (* -1 (/ (pow a1 2) (pow a2 2))) 1))>
#<alt (* (pow a2 2) (- (* -1 (/ (pow a1 2) (pow a2 2))) 1))>
#<alt (* (pow a2 2) (- (* -1 (/ (pow a1 2) (pow a2 2))) 1))>
#<alt (* -1 (pow a2 2))>
#<alt (- (* -1 (pow a1 2)) (pow a2 2))>
#<alt (- (* -1 (pow a1 2)) (pow a2 2))>
#<alt (- (* -1 (pow a1 2)) (pow a2 2))>
#<alt (* -1 (pow a1 2))>
#<alt (* (pow a1 2) (- (* -1 (/ (pow a2 2) (pow a1 2))) 1))>
#<alt (* (pow a1 2) (- (* -1 (/ (pow a2 2) (pow a1 2))) 1))>
#<alt (* (pow a1 2) (- (* -1 (/ (pow a2 2) (pow a1 2))) 1))>
#<alt (* -1 (pow a1 2))>
#<alt (* (pow a1 2) (- (* -1 (/ (pow a2 2) (pow a1 2))) 1))>
#<alt (* (pow a1 2) (- (* -1 (/ (pow a2 2) (pow a1 2))) 1))>
#<alt (* (pow a1 2) (- (* -1 (/ (pow a2 2) (pow a1 2))) 1))>
#<alt (pow a1 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (pow a2 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (* (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))))>
#<alt (+ (* (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))))>
#<alt (+ (* (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))))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
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#<alt (* (pow a2 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (pow a2 2)))))>
#<alt (* (pow a2 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (pow a2 2)))))>
#<alt (* (pow a2 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (pow a2 2)))))>
#<alt (* -1 (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (* -1 (/ (pow a2 2) (sqrt 2))) (* a1 (+ (* -1 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)))))>
#<alt (+ (* -1 (/ (pow a2 2) (sqrt 2))) (* a1 (+ (* -1 (/ a2 (sqrt 2))) (+ (/ a1 (sqrt 2)) (/ a2 (sqrt 2))))))>
#<alt (+ (* -1 (/ (pow a2 2) (sqrt 2))) (* a1 (+ (* -1 (/ a2 (sqrt 2))) (+ (/ a1 (sqrt 2)) (/ a2 (sqrt 2))))))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (* (pow a1 2) (+ (* -1 (/ a2 (* a1 (sqrt 2)))) (+ (/ 1 (sqrt 2)) (/ a2 (* a1 (sqrt 2))))))>
#<alt (* (pow a1 2) (+ (* -1 (/ a2 (* a1 (sqrt 2)))) (+ (* -1 (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))) (+ (/ 1 (sqrt 2)) (/ a2 (* a1 (sqrt 2)))))))>
#<alt (* (pow a1 2) (+ (* -1 (/ a2 (* a1 (sqrt 2)))) (+ (* -1 (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))) (+ (/ 1 (sqrt 2)) (/ a2 (* a1 (sqrt 2)))))))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (* (pow a1 2) (+ (* -1 (/ a2 (* a1 (sqrt 2)))) (+ (/ 1 (sqrt 2)) (/ a2 (* a1 (sqrt 2))))))>
#<alt (* (pow a1 2) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)))) (/ (pow a2 2) (* a1 (sqrt 2)))) a1)) (/ 1 (sqrt 2))))>
#<alt (* (pow a1 2) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)))) (/ (pow a2 2) (* a1 (sqrt 2)))) a1)) (/ 1 (sqrt 2))))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (+ (* a2 (+ (* -1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2)))) (/ (pow a1 2) (sqrt 2)))>
#<alt (+ (* a2 (+ (* -1 (/ a1 (sqrt 2))) (+ (* -1 (/ a2 (sqrt 2))) (/ a1 (sqrt 2))))) (/ (pow a1 2) (sqrt 2)))>
#<alt (+ (* a2 (+ (* -1 (/ a1 (sqrt 2))) (+ (* -1 (/ a2 (sqrt 2))) (/ a1 (sqrt 2))))) (/ (pow a1 2) (sqrt 2)))>
#<alt (* -1 (/ (pow a2 2) (sqrt 2)))>
#<alt (* (pow a2 2) (- (+ (* -1 (/ a1 (* a2 (sqrt 2)))) (/ a1 (* a2 (sqrt 2)))) (/ 1 (sqrt 2))))>
#<alt (* (pow a2 2) (- (+ (* -1 (/ a1 (* a2 (sqrt 2)))) (+ (/ a1 (* a2 (sqrt 2))) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (/ 1 (sqrt 2))))>
#<alt (* (pow a2 2) (- (+ (* -1 (/ a1 (* a2 (sqrt 2)))) (+ (/ a1 (* a2 (sqrt 2))) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (/ 1 (sqrt 2))))>
#<alt (* -1 (/ (pow a2 2) (sqrt 2)))>
#<alt (* (pow a2 2) (- (* -1 (/ (+ (* -1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2))) a2)) (/ 1 (sqrt 2))))>
#<alt (* (pow a2 2) (- (* -1 (/ (+ (* -1 (/ a1 (sqrt 2))) (+ (* -1 (/ (pow a1 2) (* a2 (sqrt 2)))) (/ a1 (sqrt 2)))) a2)) (/ 1 (sqrt 2))))>
#<alt (* (pow a2 2) (- (* -1 (/ (+ (* -1 (/ a1 (sqrt 2))) (+ (* -1 (/ (pow a1 2) (* a2 (sqrt 2)))) (/ a1 (sqrt 2)))) a2)) (/ 1 (sqrt 2))))>
#<alt (pow a2 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>

Calls

144 calls:

Time	Variable		Point	Expression
6.0ms	a1	@	-inf	(/ (* (+ a1 a2) (- a1 a2)) (sqrt 2))
3.0ms	th	@	inf	(* (+ (* (* th th) -1/2) 1) (+ (* a1 a1) (* a2 a2)))
1.0ms	a2	@	inf	(/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))
1.0ms	th	@	-inf	(* (neg (sqrt 2)) (/ 1 (cos th)))
1.0ms	th	@	inf	(* (neg (sqrt 2)) (/ 1 (cos th)))

simplify243.0ms (2.1%)

Memory

15.6MiB live, 399.0MiB allocated

Algorithm

1×	egg-herbie

Rules

8 388×	`lower-fma.f64`
8 388×	`lower-fma.f32`
5 356×	`lower-*.f64`
5 356×	`lower-*.f32`
3 036×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	571	9397
1	1928	8594
2	7282	8515
0	8428	7992

Stop Event

1×	iter limit
1×	node limit

Counts

576 → 576

Calls

Call 1

Inputs
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(+ (* -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))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(* -1 (sqrt 2))
(+ (* -1 (sqrt 2)) (* -1/2 (* (pow th 2) (sqrt 2))))
(+ (* -1 (sqrt 2)) (* (pow th 2) (+ (* -1/2 (sqrt 2)) (* (pow th 2) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))
(+ (* -1 (sqrt 2)) (* (pow th 2) (+ (* -1/2 (sqrt 2)) (* (pow th 2) (+ (* -1/4 (sqrt 2)) (+ (* 1/24 (sqrt 2)) (* (pow th 2) (+ (* -1/720 (sqrt 2)) (+ (* 1/48 (sqrt 2)) (* 1/2 (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))))))))
(* -1 (/ (sqrt 2) (cos th)))
(* -1 (/ (sqrt 2) (cos th)))
(* -1 (/ (sqrt 2) (cos th)))
(* -1 (/ (sqrt 2) (cos th)))
(* -1 (/ (sqrt 2) (cos th)))
(* -1 (/ (sqrt 2) (cos th)))
(* -1 (/ (sqrt 2) (cos th)))
(* -1 (/ (sqrt 2) (cos th)))
(* -1 (pow a1 2))
(- (* -1 (pow a2 2)) (pow a1 2))
(- (* -1 (pow a2 2)) (pow a1 2))
(- (* -1 (pow a2 2)) (pow a1 2))
(* -1 (pow a2 2))
(* (pow a2 2) (- (* -1 (/ (pow a1 2) (pow a2 2))) 1))
(* (pow a2 2) (- (* -1 (/ (pow a1 2) (pow a2 2))) 1))
(* (pow a2 2) (- (* -1 (/ (pow a1 2) (pow a2 2))) 1))
(* -1 (pow a2 2))
(* (pow a2 2) (- (* -1 (/ (pow a1 2) (pow a2 2))) 1))
(* (pow a2 2) (- (* -1 (/ (pow a1 2) (pow a2 2))) 1))
(* (pow a2 2) (- (* -1 (/ (pow a1 2) (pow a2 2))) 1))
(* -1 (pow a2 2))
(- (* -1 (pow a1 2)) (pow a2 2))
(- (* -1 (pow a1 2)) (pow a2 2))
(- (* -1 (pow a1 2)) (pow a2 2))
(* -1 (pow a1 2))
(* (pow a1 2) (- (* -1 (/ (pow a2 2) (pow a1 2))) 1))
(* (pow a1 2) (- (* -1 (/ (pow a2 2) (pow a1 2))) 1))
(* (pow a1 2) (- (* -1 (/ (pow a2 2) (pow a1 2))) 1))
(* -1 (pow a1 2))
(* (pow a1 2) (- (* -1 (/ (pow a2 2) (pow a1 2))) 1))
(* (pow a1 2) (- (* -1 (/ (pow a2 2) (pow a1 2))) 1))
(* (pow a1 2) (- (* -1 (/ (pow a2 2) (pow a1 2))) 1))
(pow a1 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(pow a2 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(+ (/ (pow a1 2) (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) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(/ (pow a1 2) (sqrt 2))
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (+ (pow 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))))
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
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(/ (sqrt 2) (+ (pow a1 2) (pow a2 2)))
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(/ (sqrt 2) (* (cos th) (+ (pow a1 2) (pow a2 2))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
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(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(/ (sqrt 2) (* (pow 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))
(/ (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))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(+ (* (pow a2 2) (- (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 6) (cos th))) (/ (sqrt 2) (* (pow a1 4) (cos th))))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(+ (* (pow a2 2) (- (* (pow a2 2) (- (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a1 6) (cos th)))))) (/ (sqrt 2) (* (pow a1 4) (cos th))))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(+ (pow 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)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (pow a2 2) (cos th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (cos th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
1
(+ 1 (* 1/2 (pow th 2)))
(+ 1 (* (pow th 2) (+ 1/2 (* 5/24 (pow th 2)))))
(+ 1 (* (pow th 2) (+ 1/2 (* (pow th 2) (+ 5/24 (* 61/720 (pow th 2)))))))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
(/ 1 (cos th))
1
(+ 1 (* -1/2 (pow th 2)))
(+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))
(+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(+ (pow a1 2) (pow a2 2))
(+ (* -1/2 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (+ (pow a1 2) (pow a2 2)))
(+ (* -1/2 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (+ (pow a1 2) (pow a2 2)))
(+ (* -1/2 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (+ (pow a1 2) (pow a2 2)))
(* -1/2 (* (pow th 2) (+ (pow a1 2) (pow a2 2))))
(* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (+ (/ (pow a1 2) (pow th 2)) (/ (pow a2 2) (pow th 2)))))
(* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (+ (/ (pow a1 2) (pow th 2)) (/ (pow a2 2) (pow th 2)))))
(* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (+ (/ (pow a1 2) (pow th 2)) (/ (pow a2 2) (pow th 2)))))
(* -1/2 (* (pow th 2) (+ (pow a1 2) (pow a2 2))))
(* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (+ (/ (pow a1 2) (pow th 2)) (/ (pow a2 2) (pow th 2)))))
(* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (+ (/ (pow a1 2) (pow th 2)) (/ (pow a2 2) (pow th 2)))))
(* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (+ (/ (pow a1 2) (pow th 2)) (/ (pow a2 2) (pow th 2)))))
(* (pow a2 2) (+ 1 (* -1/2 (pow th 2))))
(+ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (* (pow a2 2) (+ 1 (* -1/2 (pow th 2)))))
(+ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (* (pow a2 2) (+ 1 (* -1/2 (pow th 2)))))
(+ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (* (pow a2 2) (+ 1 (* -1/2 (pow th 2)))))
(* (pow a1 2) (+ 1 (* -1/2 (pow th 2))))
(* (pow a1 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a2 2) (+ 1 (* -1/2 (pow th 2)))) (pow a1 2)))))
(* (pow a1 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a2 2) (+ 1 (* -1/2 (pow th 2)))) (pow a1 2)))))
(* (pow a1 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a2 2) (+ 1 (* -1/2 (pow th 2)))) (pow a1 2)))))
(* (pow a1 2) (+ 1 (* -1/2 (pow th 2))))
(* (pow a1 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a2 2) (+ 1 (* -1/2 (pow th 2)))) (pow a1 2)))))
(* (pow a1 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a2 2) (+ 1 (* -1/2 (pow th 2)))) (pow a1 2)))))
(* (pow a1 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a2 2) (+ 1 (* -1/2 (pow th 2)))) (pow a1 2)))))
(* (pow a1 2) (+ 1 (* -1/2 (pow th 2))))
(+ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (* (pow a2 2) (+ 1 (* -1/2 (pow th 2)))))
(+ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (* (pow a2 2) (+ 1 (* -1/2 (pow th 2)))))
(+ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (* (pow a2 2) (+ 1 (* -1/2 (pow th 2)))))
(* (pow a2 2) (+ 1 (* -1/2 (pow th 2))))
(* (pow a2 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (pow a2 2)))))
(* (pow a2 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (pow a2 2)))))
(* (pow a2 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (pow a2 2)))))
(* (pow a2 2) (+ 1 (* -1/2 (pow th 2))))
(* (pow a2 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (pow a2 2)))))
(* (pow a2 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (pow a2 2)))))
(* (pow a2 2) (+ 1 (+ (* -1/2 (pow th 2)) (/ (* (pow a1 2) (+ 1 (* -1/2 (pow th 2)))) (pow a2 2)))))
(* -1 (/ (pow a2 2) (sqrt 2)))
(+ (* -1 (/ (pow a2 2) (sqrt 2))) (* a1 (+ (* -1 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)))))
(+ (* -1 (/ (pow a2 2) (sqrt 2))) (* a1 (+ (* -1 (/ a2 (sqrt 2))) (+ (/ a1 (sqrt 2)) (/ a2 (sqrt 2))))))
(+ (* -1 (/ (pow a2 2) (sqrt 2))) (* a1 (+ (* -1 (/ a2 (sqrt 2))) (+ (/ a1 (sqrt 2)) (/ a2 (sqrt 2))))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (* -1 (/ a2 (* a1 (sqrt 2)))) (+ (/ 1 (sqrt 2)) (/ a2 (* a1 (sqrt 2))))))
(* (pow a1 2) (+ (* -1 (/ a2 (* a1 (sqrt 2)))) (+ (* -1 (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))) (+ (/ 1 (sqrt 2)) (/ a2 (* a1 (sqrt 2)))))))
(* (pow a1 2) (+ (* -1 (/ a2 (* a1 (sqrt 2)))) (+ (* -1 (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))) (+ (/ 1 (sqrt 2)) (/ a2 (* a1 (sqrt 2)))))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (* -1 (/ a2 (* a1 (sqrt 2)))) (+ (/ 1 (sqrt 2)) (/ a2 (* a1 (sqrt 2))))))
(* (pow a1 2) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)))) (/ (pow a2 2) (* a1 (sqrt 2)))) a1)) (/ 1 (sqrt 2))))
(* (pow a1 2) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)))) (/ (pow a2 2) (* a1 (sqrt 2)))) a1)) (/ 1 (sqrt 2))))
(/ (pow a1 2) (sqrt 2))
(+ (* a2 (+ (* -1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2)))) (/ (pow a1 2) (sqrt 2)))
(+ (* a2 (+ (* -1 (/ a1 (sqrt 2))) (+ (* -1 (/ a2 (sqrt 2))) (/ a1 (sqrt 2))))) (/ (pow a1 2) (sqrt 2)))
(+ (* a2 (+ (* -1 (/ a1 (sqrt 2))) (+ (* -1 (/ a2 (sqrt 2))) (/ a1 (sqrt 2))))) (/ (pow a1 2) (sqrt 2)))
(* -1 (/ (pow a2 2) (sqrt 2)))
(* (pow a2 2) (- (+ (* -1 (/ a1 (* a2 (sqrt 2)))) (/ a1 (* a2 (sqrt 2)))) (/ 1 (sqrt 2))))
(* (pow a2 2) (- (+ (* -1 (/ a1 (* a2 (sqrt 2)))) (+ (/ a1 (* a2 (sqrt 2))) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (/ 1 (sqrt 2))))
(* (pow a2 2) (- (+ (* -1 (/ a1 (* a2 (sqrt 2)))) (+ (/ a1 (* a2 (sqrt 2))) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (/ 1 (sqrt 2))))
(* -1 (/ (pow a2 2) (sqrt 2)))
(* (pow a2 2) (- (* -1 (/ (+ (* -1 (/ a1 (sqrt 2))) (/ a1 (sqrt 2))) a2)) (/ 1 (sqrt 2))))
(* (pow a2 2) (- (* -1 (/ (+ (* -1 (/ a1 (sqrt 2))) (+ (* -1 (/ (pow a1 2) (* a2 (sqrt 2)))) (/ a1 (sqrt 2)))) a2)) (/ 1 (sqrt 2))))
(* (pow a2 2) (- (* -1 (/ (+ (* -1 (/ a1 (sqrt 2))) (+ (* -1 (/ (pow a1 2) (* a2 (sqrt 2)))) (/ a1 (sqrt 2)))) a2)) (/ 1 (sqrt 2))))
(pow a2 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))

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

rewrite284.0ms (2.4%)

Memory

7.2MiB live, 488.9MiB allocated

Rules

5 908×	`lower-*.f32`
5 890×	`lower-*.f64`
4 044×	`lower-/.f32`
4 024×	`lower-/.f64`
3 794×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	374
0	88	340
1	326	283
2	2824	279
0	8587	279

Stop Event

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

Counts

24 → 1 110

Calls

Call 1

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

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

eval254.0ms (2.2%)

Memory: -12.0MiB live, 466.7MiB allocated
Compiler: Compiled 49 944 to 3 972 computations (92% saved)

prune255.0ms (2.2%)

Memory

-17.1MiB live, 557.0MiB allocated

Pruning

42 alts after pruning (40 fresh and 2 done)

	Pruned	Kept	Total
New	1 852	24	1 876
Fresh	11	16	27
Picked	3	2	5
Done	0	0	0
Total	1 866	42	1 908

Accuracy

100.0%

Counts

1 908 → 42

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.1%	(fma.f64 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a2 (.f64 #s(approx (cos th) #s(literal 1 binary64)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
▶	99.6%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	99.5%	(/.f64 (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
	62.4%	(/.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) #s(approx (cos th) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))))
	57.5%	(/.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))) #s(approx ( (neg (sqrt 2)) (/ 1 (cos th))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 th (.f64 th #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
	99.5%	(/.f64 (neg.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (.f64 a2 a2))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
	99.5%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1))))
✓	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
▶	67.2%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (cos th) #s(literal 1 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (cos th) (+ (* a1 a1) (* a2 a2))) (.f64 a2 (.f64 a2 (cos.f64 th))))))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (/.f64 #s(literal 1 binary64) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
	99.6%	(.f64 (/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #s(literal 2 binary64)) (cos.f64 th))
▶	99.4%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))
	99.5%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	62.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
	67.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) (fma.f64 a1 a1 (*.f64 a2 a2))))
	62.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) #s(approx (* (+ (* (* th th) -1/2) 1) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 a2 a2) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))))
	14.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) #s(approx (* (+ (* (* th th) -1/2) 1) (+ (* a1 a1) (* a2 a2))) (.f64 a1 (.f64 a1 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
	99.5%	#s(approx (/ 1 (/ (sqrt 2) (* (cos th) (+ (* a1 a1) (* a2 a2))))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
	67.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	67.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 (neg.f64 a1) a1) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) (.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 (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))))
	11.9%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 a1 (.f64 a1 (.f64 a1 a1)))))))
	15.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (fma.f64 a1 (.f64 a1 a1) (.f64 a2 (.f64 a2 a2))) (-.f64 a1 a2)) (.f64 (fma.f64 a2 (-.f64 a2 a1) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64)))))
	16.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a1 a2)) (.f64 (.f64 (+.f64 a2 a1) (-.f64 a1 a2)) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
	16.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (.f64 (.f64 a1 a1) (neg.f64 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (neg.f64 (.f64 a2 a2)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))))
	10.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64)))))
▶	57.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a1 a2)) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (-.f64 a1 a2))))
	16.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (.f64 (.f64 (+.f64 a2 a1) (-.f64 a1 a2)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(literal 1/2 binary64))) (.f64 (+.f64 a2 a1) (-.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))))
	16.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 a2 a1) (-.f64 a1 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (+.f64 a2 a1) (-.f64 a1 a2)) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(literal 1/2 binary64))))))
	67.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (*.f64 a2 #s(literal 1/2 binary64))))))
▶	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
	67.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
	67.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
✓	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))
	38.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (.f64 a1 a1) (fma.f64 a2 (/.f64 a2 (.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
	67.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))

Compiler

Compiled 1 682 to 992 computations (41% saved)

simplify156.0ms (1.3%)

Memory

21.0MiB live, 334.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
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	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a1 a2)) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (-.f64 a1 a2))))
cost-diff	384	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a1 a2))
cost-diff	1344	(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a1 a2)) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (-.f64 a1 a2)))
cost-diff	1408	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (-.f64 a1 a2))
cost-diff	0	(.f64 #s(approx (cos th) #s(literal 1 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (cos th) #s(literal 1 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (cos th) #s(literal 1 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
cost-diff	0	(.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
cost-diff	0	(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
cost-diff	0	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
cost-diff	0	(*.f64 a1 a1)
cost-diff	0	(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff	384	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))

Rules

5 146×	`lower-*.f32`
5 126×	`lower-*.f64`
3 920×	`lower-fma.f32`
3 918×	`lower-fma.f64`
3 338×	`lower-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	421
0	77	401
1	134	401
2	343	361
3	1653	319
0	8676	319

Stop Event

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

Calls

Call 1

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

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

localize127.0ms (1.1%)

Memory

-10.6MiB live, 229.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 th)
accuracy	0.07206956875069717	#s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))
accuracy	0.23046875	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))
accuracy	0.734375	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	4.154026414981054	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (-.f64 a1 a2))
accuracy	10.004492766612405	(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a1 a2)) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (-.f64 a1 a2)))
accuracy	20.81076963029496	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a1 a2)) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (-.f64 a1 a2))))
accuracy	0.078125	(.f64 #s(approx (cos th) #s(literal 1 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))
accuracy	0.15234375	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (cos th) #s(literal 1 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
accuracy	0.5301695713026269	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (cos th) #s(literal 1 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))))
accuracy	29.55413606906455	#s(approx (cos th) #s(literal 1 binary64))
accuracy	0.1484375	(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
accuracy	0.45703125	(.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
accuracy	20.81076963029496	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
accuracy	55.27902090372483	#s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(cos.f64 th)
accuracy	0.15300751953688405	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
accuracy	0.23046875	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))

Samples

71.0ms

256×

valid

Compiler

Compiled 322 to 39 computations (87.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-mult: 19.0ms (38.8% of total)

ival-div: 16.0ms (32.7% of total)

ival-cos: 6.0ms (12.3% of total)

ival-add: 4.0ms (8.2% of total)

ival-sqrt: 2.0ms (4.1% of total)

ival-sub: 1.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.1%)

Memory

30.5MiB live, 30.5MiB allocated

Counts

22 → 480

Calls

Call 1

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

Outputs
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))>
#<alt (+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (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))))>
#<alt (+ (* (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))))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (pow a1 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (pow a2 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (pow a1 2)>
#<alt (sqrt 2)>
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#<alt (* (pow a2 3) (+ 1 (+ (/ a1 a2) (+ (/ (pow a1 2) (pow a2 2)) (/ (pow a1 3) (pow a2 3))))))>
#<alt (pow a2 3)>
#<alt (* -1 (* (pow a2 3) (- (* -1 (/ a1 a2)) 1)))>
#<alt (* -1 (* (pow a2 3) (- (* -1 (/ (+ a1 (/ (pow a1 2) a2)) a2)) 1)))>
#<alt (* -1 (* (pow a2 3) (- (* -1 (/ (+ a1 (* -1 (/ (+ (* -1 (/ (pow a1 3) a2)) (* -1 (pow a1 2))) a2))) a2)) 1)))>
#<alt (pow a2 3)>
#<alt (+ (* a1 (pow a2 2)) (pow a2 3))>
#<alt (+ (* a1 (+ (* a1 a2) (pow a2 2))) (pow a2 3))>
#<alt (+ (* a1 (+ (* a1 (+ a1 a2)) (pow a2 2))) (pow a2 3))>
#<alt (pow a1 3)>
#<alt (* (pow a1 3) (+ 1 (/ a2 a1)))>
#<alt (* (pow a1 3) (+ 1 (+ (/ a2 a1) (/ (pow a2 2) (pow a1 2)))))>
#<alt (* (pow a1 3) (+ 1 (+ (/ a2 a1) (+ (/ (pow a2 2) (pow a1 2)) (/ (pow a2 3) (pow a1 3))))))>
#<alt (pow a1 3)>
#<alt (* -1 (* (pow a1 3) (- (* -1 (/ a2 a1)) 1)))>
#<alt (* -1 (* (pow a1 3) (- (* -1 (/ (+ a2 (/ (pow a2 2) a1)) a1)) 1)))>
#<alt (* -1 (* (pow a1 3) (- (* -1 (/ (+ a2 (* -1 (/ (+ (* -1 (/ (pow a2 3) a1)) (* -1 (pow a2 2))) a1))) a1)) 1)))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (pow a1 2) (sqrt 2))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (pow a2 2) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ 1 (* a2 (sqrt 2)))>
#<alt (+ (* -1 (/ a1 (* (pow a2 2) (sqrt 2)))) (/ 1 (* a2 (sqrt 2))))>
#<alt (+ (* a1 (- (/ a1 (* (pow a2 3) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2))))) (/ 1 (* a2 (sqrt 2))))>
#<alt (+ (* a1 (- (* a1 (+ (* -1 (/ a1 (* (pow a2 4) (sqrt 2)))) (/ 1 (* (pow a2 3) (sqrt 2))))) (/ 1 (* (pow a2 2) (sqrt 2))))) (/ 1 (* a2 (sqrt 2))))>
#<alt (/ 1 (* a1 (sqrt 2)))>
#<alt (/ (+ (* -1 (/ a2 (* a1 (sqrt 2)))) (/ 1 (sqrt 2))) a1)>
#<alt (/ (- (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))) (/ a2 (* a1 (sqrt 2)))) a1)>
#<alt (/ (- (+ (* -1 (/ (pow a2 3) (* (pow a1 3) (sqrt 2)))) (/ 1 (sqrt 2))) (+ (* -1 (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))) (/ a2 (* a1 (sqrt 2))))) a1)>
#<alt (/ 1 (* a1 (sqrt 2)))>
#<alt (* -1 (/ (- (/ a2 (* a1 (sqrt 2))) (/ 1 (sqrt 2))) a1))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow a2 2) (* a1 (sqrt 2))) (/ a2 (sqrt 2))) a1)) (/ 1 (sqrt 2))) a1))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow a2 3) (* a1 (sqrt 2))) (/ (pow a2 2) (sqrt 2))) a1)) (/ a2 (sqrt 2))) a1)) (/ 1 (sqrt 2))) a1))>
#<alt (/ 1 (* a1 (sqrt 2)))>
#<alt (+ (* -1 (/ a2 (* (pow a1 2) (sqrt 2)))) (/ 1 (* a1 (sqrt 2))))>
#<alt (+ (* a2 (- (/ a2 (* (pow a1 3) (sqrt 2))) (/ 1 (* (pow a1 2) (sqrt 2))))) (/ 1 (* a1 (sqrt 2))))>
#<alt (+ (* a2 (- (* a2 (+ (* -1 (/ a2 (* (pow a1 4) (sqrt 2)))) (/ 1 (* (pow a1 3) (sqrt 2))))) (/ 1 (* (pow a1 2) (sqrt 2))))) (/ 1 (* a1 (sqrt 2))))>
#<alt (/ 1 (* a2 (sqrt 2)))>
#<alt (/ (+ (* -1 (/ a1 (* a2 (sqrt 2)))) (/ 1 (sqrt 2))) a2)>
#<alt (/ (- (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))) (/ a1 (* a2 (sqrt 2)))) a2)>
#<alt (/ (- (+ (* -1 (/ (pow a1 3) (* (pow a2 3) (sqrt 2)))) (/ 1 (sqrt 2))) (+ (* -1 (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))) (/ a1 (* a2 (sqrt 2))))) a2)>
#<alt (/ 1 (* a2 (sqrt 2)))>
#<alt (* -1 (/ (- (/ a1 (* a2 (sqrt 2))) (/ 1 (sqrt 2))) a2))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow a1 2) (* a2 (sqrt 2))) (/ a1 (sqrt 2))) a2)) (/ 1 (sqrt 2))) a2))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow a1 3) (* a2 (sqrt 2))) (/ (pow a1 2) (sqrt 2))) a2)) (/ a1 (sqrt 2))) a2)) (/ 1 (sqrt 2))) a2))>
#<alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))>
#<alt (+ (* (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))))>
#<alt (+ (* (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))))>
#<alt (+ (* (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))))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))>
#<alt (+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))>
#<alt (+ (* (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))))>
#<alt (+ (* (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))))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))>
#<alt (/ (* (pow a1 2) (cos th)) (sqrt 2))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ (* (pow a2 2) (cos th)) (sqrt 2))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))>
#<alt (/ 1 (sqrt 2))>
#<alt (+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2)))>
#<alt (+ (* (pow th 2) (- (* 1/24 (/ (pow th 2) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))>
#<alt (+ (* (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)))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt (/ (cos th) (sqrt 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow th 2)))>
#<alt (+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))>
#<alt (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow th 2)))>
#<alt (+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))>
#<alt (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (cos th)>
#<alt (pow a2 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))>
#<alt (pow a1 2)>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (+ (pow a1 2) (pow a2 2))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>
#<alt (* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))>

Calls

120 calls:

Time	Variable		Point	Expression
0.0ms	a1	@	inf	(* a1 (* a1 (* (sqrt 2) 1/2)))
0.0ms	a2	@	inf	(/ (/ 1 (sqrt 2)) (+ a1 a2))
0.0ms	a1	@	0	(/ (/ 1 (sqrt 2)) (+ a1 a2))
0.0ms	a2	@	0	(/ (/ 1 (sqrt 2)) (+ a1 a2))
0.0ms	a1	@	inf	(/ (/ 1 (sqrt 2)) (+ a1 a2))

simplify234.0ms (2%)

Memory

-21.1MiB live, 371.3MiB allocated

Algorithm

1×	egg-herbie

Rules

7 936×	`lower-fma.f64`
7 936×	`lower-fma.f32`
6 396×	`lower-*.f64`
6 396×	`lower-*.f32`
2 338×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	485	7609
1	1573	6960
2	5485	6900
0	8111	6499

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 480

Calls

Call 1

Inputs
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(+ (* -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))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(pow a1 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(pow a2 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(sqrt 2)
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(+ (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 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(/ (sqrt 2) (cos th))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
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(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
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(* 1/2 (* (pow a2 2) (sqrt 2)))
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(* 1/2 (* (pow a1 2) (sqrt 2)))
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(* 1/2 (* (pow a1 2) (sqrt 2)))
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(* 1/2 (* (pow a1 2) (sqrt 2)))
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(* 1/2 (* (pow a2 2) (sqrt 2)))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* 1/2 (* (pow a2 2) (sqrt 2)))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 2) (+ (* 1/2 (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* 1/2 (* (pow a1 2) (sqrt 2)))
(* 1/2 (* a1 (sqrt 2)))
(* 1/2 (* a1 (sqrt 2)))
(* 1/2 (* a1 (sqrt 2)))
(* 1/2 (* a1 (sqrt 2)))
(* 1/2 (* a1 (sqrt 2)))
(* 1/2 (* a1 (sqrt 2)))
(* 1/2 (* a1 (sqrt 2)))
(* 1/2 (* a1 (sqrt 2)))
(* 1/2 (* a1 (sqrt 2)))
(* 1/2 (* a1 (sqrt 2)))
(* 1/2 (* a1 (sqrt 2)))
(* 1/2 (* a1 (sqrt 2)))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (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) (* (cos th) (+ (pow a1 2) (pow a2 2))))
(/ (sqrt 2) (* (cos th) (+ (pow a1 2) (pow a2 2))))
(/ (sqrt 2) (* (cos th) (+ (pow a1 2) (pow a2 2))))
(/ (sqrt 2) (* (cos th) (+ (pow a1 2) (pow a2 2))))
(/ (sqrt 2) (* (cos th) (+ (pow a1 2) (pow a2 2))))
(/ (sqrt 2) (* (cos th) (+ (pow a1 2) (pow a2 2))))
(/ (sqrt 2) (* (cos th) (+ (pow a1 2) (pow a2 2))))
(/ (sqrt 2) (* (cos th) (+ (pow a1 2) (pow a2 2))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(/ (sqrt 2) (* (pow 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))
(/ (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))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(+ (* (pow a2 2) (- (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 6) (cos th))) (/ (sqrt 2) (* (pow a1 4) (cos th))))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(+ (* (pow a2 2) (- (* (pow a2 2) (- (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a1 6) (cos th)))))) (/ (sqrt 2) (* (pow a1 4) (cos th))))) (/ (sqrt 2) (* (pow a1 2) (cos th))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(+ (pow 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)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(* (pow a2 2) (cos th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (cos th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(pow a1 3)
(+ (* (pow a1 2) a2) (pow a1 3))
(+ (* a2 (+ (* a1 a2) (pow a1 2))) (pow a1 3))
(+ (* a2 (+ (* a2 (+ a1 a2)) (pow a1 2))) (pow a1 3))
(pow a2 3)
(* (pow a2 3) (+ 1 (/ a1 a2)))
(* (pow a2 3) (+ 1 (+ (/ a1 a2) (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 3) (+ 1 (+ (/ a1 a2) (+ (/ (pow a1 2) (pow a2 2)) (/ (pow a1 3) (pow a2 3))))))
(pow a2 3)
(* -1 (* (pow a2 3) (- (* -1 (/ a1 a2)) 1)))
(* -1 (* (pow a2 3) (- (* -1 (/ (+ a1 (/ (pow a1 2) a2)) a2)) 1)))
(* -1 (* (pow a2 3) (- (* -1 (/ (+ a1 (* -1 (/ (+ (* -1 (/ (pow a1 3) a2)) (* -1 (pow a1 2))) a2))) a2)) 1)))
(pow a2 3)
(+ (* a1 (pow a2 2)) (pow a2 3))
(+ (* a1 (+ (* a1 a2) (pow a2 2))) (pow a2 3))
(+ (* a1 (+ (* a1 (+ a1 a2)) (pow a2 2))) (pow a2 3))
(pow a1 3)
(* (pow a1 3) (+ 1 (/ a2 a1)))
(* (pow a1 3) (+ 1 (+ (/ a2 a1) (/ (pow a2 2) (pow a1 2)))))
(* (pow a1 3) (+ 1 (+ (/ a2 a1) (+ (/ (pow a2 2) (pow a1 2)) (/ (pow a2 3) (pow a1 3))))))
(pow a1 3)
(* -1 (* (pow a1 3) (- (* -1 (/ a2 a1)) 1)))
(* -1 (* (pow a1 3) (- (* -1 (/ (+ a2 (/ (pow a2 2) a1)) a1)) 1)))
(* -1 (* (pow a1 3) (- (* -1 (/ (+ a2 (* -1 (/ (+ (* -1 (/ (pow a2 3) a1)) (* -1 (pow a2 2))) a1))) a1)) 1)))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ 1 (* a2 (sqrt 2)))
(+ (* -1 (/ a1 (* (pow a2 2) (sqrt 2)))) (/ 1 (* a2 (sqrt 2))))
(+ (* a1 (- (/ a1 (* (pow a2 3) (sqrt 2))) (/ 1 (* (pow a2 2) (sqrt 2))))) (/ 1 (* a2 (sqrt 2))))
(+ (* a1 (- (* a1 (+ (* -1 (/ a1 (* (pow a2 4) (sqrt 2)))) (/ 1 (* (pow a2 3) (sqrt 2))))) (/ 1 (* (pow a2 2) (sqrt 2))))) (/ 1 (* a2 (sqrt 2))))
(/ 1 (* a1 (sqrt 2)))
(/ (+ (* -1 (/ a2 (* a1 (sqrt 2)))) (/ 1 (sqrt 2))) a1)
(/ (- (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))) (/ a2 (* a1 (sqrt 2)))) a1)
(/ (- (+ (* -1 (/ (pow a2 3) (* (pow a1 3) (sqrt 2)))) (/ 1 (sqrt 2))) (+ (* -1 (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))) (/ a2 (* a1 (sqrt 2))))) a1)
(/ 1 (* a1 (sqrt 2)))
(* -1 (/ (- (/ a2 (* a1 (sqrt 2))) (/ 1 (sqrt 2))) a1))
(* -1 (/ (- (* -1 (/ (- (/ (pow a2 2) (* a1 (sqrt 2))) (/ a2 (sqrt 2))) a1)) (/ 1 (sqrt 2))) a1))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow a2 3) (* a1 (sqrt 2))) (/ (pow a2 2) (sqrt 2))) a1)) (/ a2 (sqrt 2))) a1)) (/ 1 (sqrt 2))) a1))
(/ 1 (* a1 (sqrt 2)))
(+ (* -1 (/ a2 (* (pow a1 2) (sqrt 2)))) (/ 1 (* a1 (sqrt 2))))
(+ (* a2 (- (/ a2 (* (pow a1 3) (sqrt 2))) (/ 1 (* (pow a1 2) (sqrt 2))))) (/ 1 (* a1 (sqrt 2))))
(+ (* a2 (- (* a2 (+ (* -1 (/ a2 (* (pow a1 4) (sqrt 2)))) (/ 1 (* (pow a1 3) (sqrt 2))))) (/ 1 (* (pow a1 2) (sqrt 2))))) (/ 1 (* a1 (sqrt 2))))
(/ 1 (* a2 (sqrt 2)))
(/ (+ (* -1 (/ a1 (* a2 (sqrt 2)))) (/ 1 (sqrt 2))) a2)
(/ (- (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))) (/ a1 (* a2 (sqrt 2)))) a2)
(/ (- (+ (* -1 (/ (pow a1 3) (* (pow a2 3) (sqrt 2)))) (/ 1 (sqrt 2))) (+ (* -1 (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))) (/ a1 (* a2 (sqrt 2))))) a2)
(/ 1 (* a2 (sqrt 2)))
(* -1 (/ (- (/ a1 (* a2 (sqrt 2))) (/ 1 (sqrt 2))) a2))
(* -1 (/ (- (* -1 (/ (- (/ (pow a1 2) (* a2 (sqrt 2))) (/ a1 (sqrt 2))) a2)) (/ 1 (sqrt 2))) a2))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow a1 3) (* a2 (sqrt 2))) (/ (pow a1 2) (sqrt 2))) a2)) (/ a1 (sqrt 2))) a2)) (/ 1 (sqrt 2))) a2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (+ (pow 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))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ 1 (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) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (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)))
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
1
(+ 1 (* -1/2 (pow th 2)))
(+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))
(+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(cos th)
(pow a2 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(pow a1 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))

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

rewrite259.0ms (2.2%)

Memory

14.8MiB live, 446.0MiB allocated

Rules

6 180×	`lower-/.f32`
6 164×	`lower-/.f64`
3 222×	`lower-*.f32`
3 202×	`lower-*.f64`
2 824×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	337
0	77	318
1	258	238
2	2232	238
0	8250	238

Stop Event

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

Counts

22 → 800

Calls

Call 1

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

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

eval190.0ms (1.6%)

Memory: 9.5MiB live, 405.0MiB allocated
Compiler: Compiled 36 706 to 2 742 computations (92.5% saved)

prune200.0ms (1.7%)

Memory

-6.5MiB live, 389.2MiB allocated

Pruning

53 alts after pruning (48 fresh and 5 done)

	Pruned	Kept	Total
New	1 449	21	1 470
Fresh	8	27	35
Picked	2	3	5
Done	0	2	2
Total	1 459	53	1 512

Accuracy

100.0%

Counts

1 512 → 53

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.1%	(fma.f64 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a2 (.f64 #s(approx (cos th) #s(literal 1 binary64)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
	57.5%	(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(approx (/ (sqrt 2) (cos th)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	99.5%	(/.f64 (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
	99.5%	(/.f64 (neg.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (.f64 a2 a2))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
	99.5%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 a2 (*.f64 a1 a1))))
	99.5%	(/.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
✓	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
✓	67.2%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (cos th) #s(literal 1 binary64)) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (cos th) (+ (* a1 a1) (* a2 a2))) (.f64 a2 (.f64 a2 (cos.f64 th))))))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (/.f64 #s(literal 1 binary64) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
	67.2%	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(approx (cos th) #s(literal 1 binary64)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))) (sqrt.f64 #s(literal 2 binary64))))
	99.6%	(.f64 (/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) #s(literal 2 binary64)) (cos.f64 th))
✓	99.4%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))
	99.5%	(.f64 (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
	62.2%	(.f64 (/.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 (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))
	67.2%	(.f64 (/.f64 #s(approx (cos th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)))
	62.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(approx (+ ( a1 a1) (* a2 a2)) (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
	62.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) #s(approx (* (+ (* (* th th) -1/2) 1) (+ (* a1 a1) (* a2 a2))) (.f64 (.f64 a2 a2) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))))))
	14.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(approx (/ (+ ( a1 a1) (* a2 a2)) (/ 1 (cos th))) #s(approx (* (+ (* (* th th) -1/2) 1) (+ (* a1 a1) (* a2 a2))) (.f64 a1 (.f64 a1 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
	99.4%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))
	99.5%	#s(approx (/ 1 (/ (sqrt 2) (* (cos th) (+ (* a1 a1) (* a2 a2))))) (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64))))
	67.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 a2 (/.f64 #s(literal 1 binary64) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	59.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1))) (-.f64 a1 a2)) (-.f64 a1 a2)))
	15.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (fma.f64 a1 (.f64 a1 a1) (.f64 a2 (.f64 a2 a2))) (-.f64 a1 a2)) (.f64 (fma.f64 a2 (-.f64 a2 a1) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64)))))
	16.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (+.f64 a2 a1) (-.f64 a1 a2)) (.f64 (.f64 (+.f64 a2 a1) (-.f64 a1 a2)) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
	16.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (.f64 (.f64 a1 a1) (neg.f64 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (neg.f64 (.f64 a2 a2)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))))
	16.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (.f64 (+.f64 a2 a1) (-.f64 a1 a2))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (-.f64 a1 a2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (+.f64 a2 a1)))))))
	10.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) #s(literal 2 binary64)))))
	59.4%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (+.f64 a2 a1))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a2 a1)))))
	67.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 a2 a1) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a2 a1))))))
	16.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a1 a2)) (/.f64 (.f64 (/.f64 (.f64 (-.f64 a1 a2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (+.f64 a2 a1))) (.f64 (+.f64 a2 a1) (-.f64 a1 a2))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (-.f64 a1 a2))))
	57.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a1 a2)) (/.f64 (.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (-.f64 a1 a2))))
	33.0%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a1 a2)) #s(approx (/ ( (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) (- a1 a2)) (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 a2 (/.f64 (fma.f64 a2 (/.f64 (.f64 a2 a2) a1) (.f64 a2 a2)) a1)) a1)) (.f64 a1 (*.f64 a1 (neg.f64 a1)))))))
	59.5%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 a1 a2)) #s(approx (/ ( (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) (- a1 a2)) (.f64 a2 (.f64 a2 a2)))))
	18.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1))) (-.f64 a1 a2)) (.f64 (fma.f64 a2 (+.f64 a2 a1) (.f64 a1 a1)) (-.f64 a1 a2))) (fma.f64 a2 (+.f64 a2 a1) (*.f64 a1 a1))))
	16.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 (.f64 (.f64 (+.f64 a2 a1) (-.f64 a1 a2)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) #s(literal 1/2 binary64))) (.f64 (+.f64 a2 a1) (-.f64 a1 a2))) (sqrt.f64 #s(literal 2 binary64))))
	59.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (+.f64 a2 a1)) (+.f64 a2 a1))))
	15.6%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 (.f64 a1 a1) (.f64 a2 (.f64 a2 a2)))) (fma.f64 a2 (-.f64 a2 a1) (.f64 a1 a1))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (-.f64 a1 a2))))
	12.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (.f64 #s(approx (/ (/ 1 (sqrt 2)) (+ a1 a2)) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 a2 (.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (-.f64 a1 a2))))
	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 (.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))))
	67.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 (.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #s(literal 1/2 binary64))))
	67.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (*.f64 a2 #s(literal 1/2 binary64))))))
✓	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
	67.3%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
	67.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
✓	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))))
	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 a1 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a1))))
	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)))
	11.7%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))))
	67.2%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
	61.1%	#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (* (/ (/ 1 (sqrt 2)) (+ a1 a2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) (- a1 a2))) (.f64 a2 (.f64 a2 (fma.f64 a1 (/.f64 a1 (.f64 a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))))

Compiler

Compiled 2 879 to 957 computations (66.8% saved)

regimes211.0ms (1.8%)

Memory

7.4MiB live, 244.3MiB allocated

Counts

92 → 1

Calls

Call 1

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

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

Calls

8 calls:

29.0ms	(+.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)))
28.0ms	a1
27.0ms	a2
27.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
25.0ms	(cos.f64 th)

Results

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

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes201.0ms (1.7%)

Memory

4.3MiB live, 283.1MiB allocated

Counts

90 → 1

Calls

Call 1

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

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

Calls

8 calls:

27.0ms	(cos.f64 th)
26.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
26.0ms	(*.f64 a2 a2)
25.0ms	a2
25.0ms	a1

Results

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

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes172.0ms (1.5%)

Memory

-0.3MiB live, 227.8MiB allocated

Counts

77 → 1

Calls

Call 1

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

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

Calls

8 calls:

23.0ms	a2
22.0ms	th
21.0ms	(+.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)))
21.0ms	(cos.f64 th)
20.0ms	(*.f64 a2 a2)

Results

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

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes161.0ms (1.4%)

Memory

19.1MiB live, 223.1MiB allocated

Counts

66 → 1

Calls

Call 1

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

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

Calls

8 calls:

25.0ms	(*.f64 a1 a1)
21.0ms	(cos.f64 th)
20.0ms	(+.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)))
20.0ms	a1
20.0ms	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 59 to 40 computations (32.2% saved)

regimes134.0ms (1.2%)

Memory

1.3MiB live, 195.8MiB allocated

Counts

60 → 2

Calls

Call 1

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

Outputs

(*.f64 (/.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 (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))

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

Calls

8 calls:

18.0ms	th
17.0ms	a1
17.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
17.0ms	(cos.f64 th)
16.0ms	(*.f64 a2 a2)

Results

Accuracy	Segments	Branch
67.3%	1	`a1`
67.3%	1	`a2`
67.3%	1	`th`
78.8%	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)))`
78.0%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
78.0%	2	`(cos.f64 th)`
67.3%	1	`(*.f64 a1 a1)`
67.3%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes29.0ms (0.2%)

Memory

14.0MiB live, 49.1MiB allocated

Counts

15 → 1

Calls

Call 1

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

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

Calls

5 calls:

8.0ms	(cos.f64 th)
5.0ms	a2
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
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)))
5.0ms	(*.f64 a2 a2)

Results

Accuracy	Segments	Branch
67.3%	1	`a2`
67.3%	1	`(*.f64 a2 a2)`
67.3%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
67.3%	1	`(cos.f64 th)`
67.3%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 45 to 30 computations (33.3% saved)

regimes65.0ms (0.6%)

Memory

-16.8MiB live, 62.8MiB allocated

Counts

12 → 1

Calls

Call 1

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

Outputs

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

Calls

8 calls:

32.0ms	th
8.0ms	a2
4.0ms	a1
4.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
4.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Results

Accuracy	Segments	Branch
67.3%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
67.3%	1	`th`
67.3%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
67.3%	1	`(cos.f64 th)`
67.3%	1	`a1`
67.3%	1	`(*.f64 a1 a1)`
67.3%	1	`a2`
67.3%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes49.0ms (0.4%)

Memory

7.7MiB live, 45.7MiB allocated

Counts

9 → 1

Calls

Call 1

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

Outputs

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

Calls

8 calls:

25.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
4.0ms	th
3.0ms	a1
3.0ms	a2
3.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Results

Accuracy	Segments	Branch
67.2%	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)))`
67.2%	1	`th`
67.2%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
67.2%	1	`(cos.f64 th)`
67.2%	1	`a1`
67.2%	1	`a2`
67.2%	1	`(*.f64 a1 a1)`
67.2%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes27.0ms (0.2%)

Memory

7.4MiB live, 45.6MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs

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

Calls

8 calls:

6.0ms	a1
3.0ms	th
3.0ms	a2
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
3.0ms	(cos.f64 th)

Results

Accuracy	Segments	Branch
67.2%	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)))`
67.2%	1	`th`
67.2%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
67.2%	1	`(cos.f64 th)`
67.2%	1	`a1`
67.2%	1	`(*.f64 a1 a1)`
67.2%	1	`a2`
67.2%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes40.0ms (0.3%)

Memory

-7.2MiB live, 30.7MiB allocated

Counts

4 → 1

Calls

Call 1

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

Calls

8 calls:

25.0ms	(cos.f64 th)
2.0ms	a2
2.0ms	th
2.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
2.0ms	a1

Results

Accuracy	Segments	Branch
67.2%	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)))`
67.2%	1	`th`
67.2%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
67.2%	1	`(cos.f64 th)`
67.2%	1	`a1`
67.2%	1	`(*.f64 a1 a1)`
67.2%	1	`a2`
67.2%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes21.0ms (0.2%)

Memory

-18.5MiB live, 30.3MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

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

Outputs

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

Calls

8 calls:

9.0ms	th
2.0ms	a1
2.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
2.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
2.0ms	a2

Results

Accuracy	Segments	Branch
67.2%	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)))`
67.2%	1	`th`
67.2%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
67.2%	1	`(cos.f64 th)`
67.2%	1	`a1`
67.2%	1	`a2`
67.2%	1	`(*.f64 a1 a1)`
67.2%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes11.0ms (0.1%)

Memory

23.3MiB live, 23.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs

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

Calls

8 calls:

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

Results

Accuracy	Segments	Branch
11.7%	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)))`
11.7%	1	`th`
11.7%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
11.7%	1	`(cos.f64 th)`
11.7%	1	`a1`
11.7%	1	`a2`
11.7%	1	`(*.f64 a2 a2)`
11.7%	1	`(*.f64 a1 a1)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-4.54709373272074e-120	-4.4357075134972517e-131

Compiler

Compiled 25 to 18 computations (28% saved)

simplify50.0ms (0.4%)

Memory

-19.2MiB live, 55.8MiB allocated

Algorithm

1×	egg-herbie

Rules

480×	`distribute-lft-neg-in_binary64`
242×	`cancel-sign-sub_binary64`
240×	`neg-mul-1_binary64`
234×	`neg-sub0_binary64`
210×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	93	490
1	127	490
2	145	488
3	177	488
4	229	488
5	327	488
6	491	488
7	756	488
8	1000	488
9	1213	488
10	1346	488
11	1388	488
12	1394	488

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a2 (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) #s(literal -5814709794364855/1453677448591213781098647615776009068707282721374636120562980398361278576226795846652382101427527131121525043212532355867069203257229312 binary64)) (.f64 (/.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 (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2))) #s(approx (/ 1 (/ (sqrt 2) ( (cos th) (+ (* a1 a1) (* a2 a2))))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ 1 (/ (sqrt 2) (* (cos th) (+ (* a1 a1) (* a2 a2))))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.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 (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 (.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (*.f64 a2 #s(literal 1/2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))

Outputs
(fma.f64 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a2 (.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 th))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) #s(literal -5814709794364855/1453677448591213781098647615776009068707282721374636120562980398361278576226795846652382101427527131121525043212532355867069203257229312 binary64)) (.f64 (/.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 (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2))) #s(approx (/ 1 (/ (sqrt 2) ( (cos th) (+ (* a1 a1) (* a2 a2))))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 (+.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) #s(literal -5814709794364855/1453677448591213781098647615776009068707282721374636120562980398361278576226795846652382101427527131121525043212532355867069203257229312 binary64)) (.f64 (/.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 (+ (* a1 a1) (* a2 a2)) (.f64 a2 a2))) #s(approx (/ 1 (/ (sqrt 2) ( (cos th) (+ (* a1 a1) (* a2 a2))))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ 1 (/ (sqrt 2) (* (cos th) (+ (* a1 a1) (* a2 a2))))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* a1 (/ a1 (sqrt 2))) (/ (* a2 a2) (sqrt 2))) (*.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 (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 (.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 #s(literal 1/2 binary64) (.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 (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 (*.f64 a2 #s(literal 1/2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ 1 (/ (/ (* (+ a1 a2) (- a1 a2)) (sqrt 2)) (/ (* (+ (* a2 a2) (* a1 a1)) (* (+ a1 a2) (- a1 a2))) 2))) (.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))

soundness1.8s (15%)

Memory

1.1MiB live, 1 342.3MiB allocated

Rules

34 694×	`lower-fma.f64`
34 694×	`lower-fma.f32`
14 190×	`lower-fma.f64`
14 190×	`lower-fma.f32`
8 388×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	374
0	88	340
1	326	283
2	2824	279
0	8587	279
0	272	7157
1	900	6537
2	3369	6203
0	8175	5832
0	12	44
0	20	38
1	58	38
2	411	38
3	7331	38
0	8434	37
0	35	193
0	56	199
1	213	165
2	1730	165
0	8743	165
0	571	9397
1	1928	8594
2	7282	8515
0	8428	7992
0	485	7609
1	1573	6960
2	5485	6900
0	8111	6499
0	111	1498
1	343	1366
2	1205	1262
3	3898	1233
0	8422	1172

Stop Event

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

Compiler

Compiled 676 to 331 computations (51% saved)

preprocess193.0ms (1.7%)

Memory: 14.3MiB live, 210.1MiB allocated
Remove: (abs th)
Compiler: Compiled 1 860 to 964 computations (48.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	35	262
0	56	268
1	103	244
2	193	244
3	363	235
4	557	235
5	712	235
6	833	235
7	856	235
0	856	235

Iter	Nodes	Cost
0	35	262
0	56	268
1	103	244
2	193	244
3	363	235
4	557	235
5	712	235
6	833	235
7	856	235
0	856	235

start0.0ms (0%)

analyze0.0ms (0%)

sample1.4s (11.6%)

explain145.0ms (1.2%)

preprocess133.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify15.0ms (0.1%)

localize39.0ms (0.3%)

series14.0ms (0.1%)

simplify973.0ms (8.3%)

rewrite374.0ms (3.2%)

eval116.0ms (1%)

prune132.0ms (1.1%)

simplify19.0ms (0.2%)

localize185.0ms (1.6%)

series55.0ms (0.5%)

simplify389.0ms (3.3%)

rewrite357.0ms (3.1%)

eval799.0ms (6.9%)

prune800.0ms (6.9%)

simplify236.0ms (2%)

localize154.0ms (1.3%)

series38.0ms (0.3%)

simplify243.0ms (2.1%)

rewrite284.0ms (2.4%)

eval254.0ms (2.2%)

prune255.0ms (2.2%)

simplify156.0ms (1.3%)

localize127.0ms (1.1%)

series15.0ms (0.1%)

simplify234.0ms (2%)

rewrite259.0ms (2.2%)

eval190.0ms (1.6%)

prune200.0ms (1.7%)

regimes211.0ms (1.8%)

regimes201.0ms (1.7%)

regimes172.0ms (1.5%)

regimes161.0ms (1.4%)

regimes134.0ms (1.2%)

regimes29.0ms (0.2%)

regimes65.0ms (0.6%)

regimes49.0ms (0.4%)

regimes27.0ms (0.2%)

regimes40.0ms (0.3%)

regimes21.0ms (0.2%)

regimes11.0ms (0.1%)

bsearch1.0ms (0%)

simplify50.0ms (0.4%)

soundness1.8s (15%)

preprocess193.0ms (1.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	35	262
0	56	268
1	103	244
2	193	244
3	363	235
4	557	235
5	712	235
6	833	235
7	856	235
0	856	235