Metrics for Migdal et al, Equation (64)

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 21 to 14 computations (33.3% saved)

sample1.6s (14.2%)

Memory

27.1MiB live, 1 730.1MiB allocated

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 820.0ms

ival-cos: 275.0ms (33.5% of total)

ival-mult: 225.0ms (27.4% of total)

ival-add: 105.0ms (12.8% of total)

ival-sqrt: 103.0ms (12.6% of total)

ival-div: 97.0ms (11.8% of total)

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

exact: 6.0ms (0.7% of total)

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

Bogosity

preprocess136.0ms (1.2%)

Memory

8.1MiB live, 47.1MiB 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)

explain216.0ms (1.9%)

Memory

15.2MiB live, 256.3MiB 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 160 to 52 computations (67.5% saved)

Precisions

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

ival-cos: 12.0ms (35.7% of total)

ival-mult: 11.0ms (32.7% of total)

ival-sqrt: 4.0ms (11.9% of total)

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

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

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(+.f64 (.f64 (/.f64 (cos.f64 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)

simplify11.0ms (0.1%)

Memory

-25.3MiB live, 12.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	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 (.f64 a1 (.f64 (cos.f64 th) 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 a2 (.f64 (cos.f64 th) a2)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 a2 a2)
a2

localize45.0ms (0.4%)

Memory

-14.3MiB live, 74.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 th)
✓	accuracy	99.7%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
✓	accuracy	99.7%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1))
✓	accuracy	98.9%	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))

Samples

27.0ms

256×

valid

Compiler

Compiled 58 to 14 computations (75.9% saved)

Precisions

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

ival-cos: 6.0ms (37.8% of total)

ival-mult: 5.0ms (31.5% of total)

ival-div: 2.0ms (12.6% of total)

ival-sqrt: 2.0ms (12.6% of total)

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

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB 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))
2.0ms	th	@	-inf	(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
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)))

rewrite341.0ms (3.1%)

Memory

27.5MiB live, 451.9MiB allocated

Algorithm

1×	batch-egg-rewrite

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)))))
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(/.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))))

simplify688.0ms (6.2%)

Memory

-12.1MiB live, 1 230.9MiB 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 (.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 (.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 (.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 (.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 (.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) (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 (.f64 a1 (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))
(/.f64 (.f64 a1 (.f64 a1 (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))
(/.f64 (.f64 a1 (.f64 a1 (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))
(/.f64 (.f64 a1 (.f64 a1 (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))
(/.f64 (.f64 a1 (.f64 a1 (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))
(/.f64 (.f64 a1 (.f64 a1 (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))
(/.f64 (.f64 a1 (.f64 a1 (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))
(/.f64 (.f64 a1 (.f64 a1 (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))
(/.f64 (.f64 a1 (.f64 a1 (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))
(/.f64 (.f64 a1 (.f64 a1 (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)))
(/ 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)))

eval55.0ms (0.5%)

Memory: 16.8MiB live, 171.2MiB allocated
Compiler: Compiled 14 576 to 1 018 computations (93% saved)

prune75.0ms (0.7%)

Memory

-12.6MiB live, 195.6MiB allocated

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	472	18	490
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	473	18	491

Accuracy

100.0%

Counts

491 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.4%	(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
▶	99.7%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	99.6%	(/.f64 (/.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)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
▶	99.7%	(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
	14.5%	(/.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))))) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 a1 (.f64 a1 (.f64 a1 a1)) (.f64 (.f64 a2 a2) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))))
▶	14.6%	(/.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))))
	21.3%	(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
	21.3%	(/.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))))
	99.3%	(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	52.5%	(/.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)))
	99.2%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
	99.2%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))))
	39.9%	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (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))
	65.4%	(.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)))))
▶	99.7%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
	99.7%	(.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 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))

Compiler

Compiled 872 to 488 computations (44% saved)

simplify289.0ms (2.6%)

Memory

7.1MiB live, 559.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 (.f64 a1 a1) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (*.f64 a2 a2)))))
✓	cost-diff	0	(.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))
✓	cost-diff	0	(/.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))))
✓	cost-diff	128	(-.f64 (.f64 a2 a2) (.f64 a1 a1))
✓	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	1088	(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
✓	cost-diff	0	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
✓	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)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
✓	cost-diff	0	(*.f64 a2 a2)
✓	cost-diff	0	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	cost-diff	384	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))

Rules

9 660×	`lower-fma.f32`
9 652×	`lower-fma.f64`
3 874×	`lower-*.f32`
3 852×	`lower-*.f64`
2 052×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	343
0	61	302
1	116	267
2	214	267
3	471	267
4	1586	267
5	4361	267
6	7308	267
0	8190	264

Stop Event

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

Calls

Call 1

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

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

localize127.0ms (1.1%)

Memory

23.3MiB live, 339.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 a1 (.f64 a1 a1))
✓	accuracy	99.9%	(.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)))
✓	accuracy	94.1%	(-.f64 (.f64 a2 a2) (.f64 a1 a1))
✓	accuracy	23.1%	(/.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))))
✓	accuracy	100.0%	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	accuracy	99.9%	(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (cos.f64 th))
✓	accuracy	99.7%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(cos.f64 th)
✓	accuracy	100.0%	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	accuracy	99.7%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	98.9%	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(*.f64 a2 a2)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.7%	(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.4%	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(cos.f64 th)
✓	accuracy	100.0%	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	accuracy	99.7%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
✓	accuracy	99.7%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))

Samples

70.0ms

256×

valid

Compiler

Compiled 359 to 36 computations (90% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-mult: 18.0ms (39.3% of total)

ival-div: 13.0ms (28.4% of total)

ival-cos: 8.0ms (17.5% of total)

ival-add: 4.0ms (8.7% of total)

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

ival-sub: 1.0ms (2.2% of total)

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

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

exact: 0.0ms (0% of total)

series41.0ms (0.4%)

Memory

-25.9MiB live, 94.6MiB allocated

Counts

20 → 420

Calls

Call 1

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

Outputs
#<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)>
#<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))))>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (pow a2 2)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))>
#<alt (+ (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)))))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<alt (/ (sqrt 2) (cos th))>
#<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 (/ a1 (sqrt 2))>
#<alt (/ a1 (sqrt 2))>
#<alt (/ a1 (sqrt 2))>
#<alt (/ a1 (sqrt 2))>
#<alt (/ a1 (sqrt 2))>
#<alt (/ a1 (sqrt 2))>
#<alt (/ a1 (sqrt 2))>
#<alt (/ a1 (sqrt 2))>
#<alt (/ a1 (sqrt 2))>
#<alt (/ a1 (sqrt 2))>
#<alt (/ a1 (sqrt 2))>
#<alt (/ a1 (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 (/ (* (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 (/ 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 (/ (* (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) (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 (pow a1 2))>
#<alt (- (pow a2 2) (pow a1 2))>
#<alt (- (pow a2 2) (pow a1 2))>
#<alt (- (pow a2 2) (pow a1 2))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))>
#<alt (* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))>
#<alt (* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))>
#<alt (pow a2 2)>
#<alt (* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))>
#<alt (* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))>
#<alt (* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))>
#<alt (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) (- (/ (pow a2 2) (pow a1 2)) 1))>
#<alt (* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))>
#<alt (* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))>
#<alt (* -1 (pow a1 2))>
#<alt (* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))>
#<alt (* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))>
#<alt (* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))>
#<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) (- (* -1 (* (pow a1 2) (+ (* -1 (/ (cos th) (* (pow a2 2) (sqrt 2)))) (/ (cos th) (* (pow a2 2) (sqrt 2)))))) (* -1 (/ (cos th) (sqrt 2))))) (/ (* (pow a2 2) (cos th)) (sqrt 2)))>
#<alt (+ (* (pow a1 2) (- (* (pow a1 2) (- (* (pow a1 2) (- (/ (cos th) (* (pow a2 4) (sqrt 2))) (+ (* -1 (/ (cos th) (* (pow a2 4) (sqrt 2)))) (* 2 (/ (cos th) (* (pow a2 4) (sqrt 2))))))) (+ (* -1 (/ (cos th) (* (pow a2 2) (sqrt 2)))) (/ (cos th) (* (pow a2 2) (sqrt 2)))))) (* -1 (/ (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) (- (+ (* -1 (/ (+ (* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2))) (/ (* (pow a2 4) (cos th)) (sqrt 2))) (pow a1 4))) (/ (cos th) (sqrt 2))) (* -1 (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))))>
#<alt (* (pow a1 2) (- (+ (* -1 (/ (* (pow a2 2) (+ (* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2))) (/ (* (pow a2 4) (cos th)) (sqrt 2)))) (pow a1 6))) (/ (cos th) (sqrt 2))) (+ (* -1 (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))) (+ (* -1 (/ (* (pow a2 4) (cos th)) (* (pow a1 4) (sqrt 2)))) (/ (* (pow a2 4) (cos th)) (* (pow a1 4) (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) (- (+ (* -1 (/ (+ (* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2))) (/ (* (pow a2 4) (cos th)) (sqrt 2))) (pow a1 4))) (/ (cos th) (sqrt 2))) (* -1 (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))))>
#<alt (* (pow a1 2) (- (+ (* -1 (/ (* (pow a2 2) (+ (* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2))) (/ (* (pow a2 4) (cos th)) (sqrt 2)))) (pow a1 6))) (/ (cos th) (sqrt 2))) (+ (* -1 (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))) (+ (* -1 (/ (* (pow a2 4) (cos th)) (* (pow a1 4) (sqrt 2)))) (/ (* (pow a2 4) (cos th)) (* (pow a1 4) (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 a2 2) (- (* -1 (* (pow a2 2) (+ (* -1 (/ (cos th) (* (pow a1 2) (sqrt 2)))) (/ (cos th) (* (pow a1 2) (sqrt 2)))))) (* -1 (/ (cos th) (sqrt 2))))) (/ (* (pow a1 2) (cos th)) (sqrt 2)))>
#<alt (+ (* (pow a2 2) (- (* (pow a2 2) (- (* (pow a2 2) (- (/ (cos th) (* (pow a1 4) (sqrt 2))) (+ (* -1 (/ (cos th) (* (pow a1 4) (sqrt 2)))) (* 2 (/ (cos th) (* (pow a1 4) (sqrt 2))))))) (+ (* -1 (/ (cos th) (* (pow a1 2) (sqrt 2)))) (/ (cos th) (* (pow a1 2) (sqrt 2)))))) (* -1 (/ (cos th) (sqrt 2))))) (/ (* (pow a1 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) (- (+ (* -1 (/ (+ (* -1 (/ (* (pow a1 4) (cos th)) (sqrt 2))) (/ (* (pow a1 4) (cos th)) (sqrt 2))) (pow a2 4))) (/ (cos th) (sqrt 2))) (* -1 (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))))>
#<alt (* (pow a2 2) (- (+ (* -1 (/ (* (pow a1 2) (+ (* -1 (/ (* (pow a1 4) (cos th)) (sqrt 2))) (/ (* (pow a1 4) (cos th)) (sqrt 2)))) (pow a2 6))) (/ (cos th) (sqrt 2))) (+ (* -1 (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))) (+ (* -1 (/ (* (pow a1 4) (cos th)) (* (pow a2 4) (sqrt 2)))) (/ (* (pow a1 4) (cos th)) (* (pow a2 4) (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) (- (+ (* -1 (/ (+ (* -1 (/ (* (pow a1 4) (cos th)) (sqrt 2))) (/ (* (pow a1 4) (cos th)) (sqrt 2))) (pow a2 4))) (/ (cos th) (sqrt 2))) (* -1 (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))))>
#<alt (* (pow a2 2) (- (+ (* -1 (/ (* (pow a1 2) (+ (* -1 (/ (* (pow a1 4) (cos th)) (sqrt 2))) (/ (* (pow a1 4) (cos th)) (sqrt 2)))) (pow a2 6))) (/ (cos th) (sqrt 2))) (+ (* -1 (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))) (+ (* -1 (/ (* (pow a1 4) (cos th)) (* (pow a2 4) (sqrt 2)))) (/ (* (pow a1 4) (cos th)) (* (pow a2 4) (sqrt 2)))))))>
#<alt (/ (+ (pow a1 6) (pow a2 6)) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))>
#<alt (+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))) (+ (/ (pow a1 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4)))) (/ (pow a2 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 6) (pow a2 6)) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))) (+ (/ (pow a1 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4)))) (/ (pow a2 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 6) (pow a2 6)) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))) (* 1/24 (/ (+ (pow a1 6) (pow a2 6)) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))))) (+ (/ (pow a1 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4)))) (/ (pow a2 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))>
#<alt (/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))>
#<alt (/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))>
#<alt (/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))>
#<alt (/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))>
#<alt (/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))>
#<alt (/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))>
#<alt (/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))>
#<alt (/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))>
#<alt (* (pow a2 6) (cos th))>
#<alt (+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))>
#<alt (+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))>
#<alt (+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))>
#<alt (* (pow a1 6) (cos th))>
#<alt (* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))>
#<alt (* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))>
#<alt (* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))>
#<alt (* (pow a1 6) (cos th))>
#<alt (* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))>
#<alt (* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))>
#<alt (* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))>
#<alt (* (pow a1 6) (cos th))>
#<alt (+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))>
#<alt (+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))>
#<alt (+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))>
#<alt (* (pow a2 6) (cos th))>
#<alt (* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))>
#<alt (* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))>
#<alt (* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))>
#<alt (* (pow a2 6) (cos th))>
#<alt (* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))>
#<alt (* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))>
#<alt (* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))>
#<alt (+ (pow a1 6) (pow a2 6))>
#<alt (+ (* -1/2 (* (pow th 2) (+ (pow a1 6) (pow a2 6)))) (+ (pow a1 6) (pow a2 6)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 6) (pow a2 6))) (* 1/24 (* (pow th 2) (+ (pow a1 6) (pow a2 6)))))) (+ (pow a1 6) (pow a2 6)))>
#<alt (+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 6) (pow a2 6))) (* (pow th 2) (+ (* -1/720 (* (pow th 2) (+ (pow a1 6) (pow a2 6)))) (* 1/24 (+ (pow a1 6) (pow a2 6))))))) (+ (pow a1 6) (pow a2 6)))>
#<alt (* (cos th) (+ (pow a1 6) (pow a2 6)))>
#<alt (* (cos th) (+ (pow a1 6) (pow a2 6)))>
#<alt (* (cos th) (+ (pow a1 6) (pow a2 6)))>
#<alt (* (cos th) (+ (pow a1 6) (pow a2 6)))>
#<alt (* (cos th) (+ (pow a1 6) (pow a2 6)))>
#<alt (* (cos th) (+ (pow a1 6) (pow a2 6)))>
#<alt (* (cos th) (+ (pow a1 6) (pow a2 6)))>
#<alt (* (cos th) (+ (pow a1 6) (pow a2 6)))>
#<alt (pow a2 6)>
#<alt (+ (pow a1 6) (pow a2 6))>
#<alt (+ (pow a1 6) (pow a2 6))>
#<alt (+ (pow a1 6) (pow a2 6))>
#<alt (pow a1 6)>
#<alt (* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))>
#<alt (* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))>
#<alt (* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))>
#<alt (pow a1 6)>
#<alt (* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))>
#<alt (* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))>
#<alt (* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))>
#<alt (pow a1 6)>
#<alt (+ (pow a1 6) (pow a2 6))>
#<alt (+ (pow a1 6) (pow a2 6))>
#<alt (+ (pow a1 6) (pow a2 6))>
#<alt (pow a2 6)>
#<alt (* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))>
#<alt (* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))>
#<alt (* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))>
#<alt (pow a2 6)>
#<alt (* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))>
#<alt (* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))>
#<alt (* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))>
#<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) (+ 1/2 (* 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))>
#<alt (* (pow a2 4) (sqrt 2))>
#<alt (+ (* -1 (* (pow a1 2) (* (pow a2 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))>
#<alt (+ (* (pow a1 2) (+ (* -1 (* (pow a2 2) (sqrt 2))) (* (pow a1 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))>
#<alt (+ (* (pow a1 2) (+ (* -1 (* (pow a2 2) (sqrt 2))) (* (pow a1 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))>
#<alt (* (pow a1 4) (sqrt 2))>
#<alt (* (pow a1 4) (+ (sqrt 2) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))>
#<alt (* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))>
#<alt (* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))>
#<alt (* (pow a1 4) (sqrt 2))>
#<alt (* (pow a1 4) (+ (sqrt 2) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))>
#<alt (* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))>
#<alt (* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))>
#<alt (* (pow a1 4) (sqrt 2))>
#<alt (+ (* -1 (* (pow a1 2) (* (pow a2 2) (sqrt 2)))) (* (pow a1 4) (sqrt 2)))>
#<alt (+ (* (pow a1 4) (sqrt 2)) (* (pow a2 2) (+ (* -1 (* (pow a1 2) (sqrt 2))) (* (pow a2 2) (sqrt 2)))))>
#<alt (+ (* (pow a1 4) (sqrt 2)) (* (pow a2 2) (+ (* -1 (* (pow a1 2) (sqrt 2))) (* (pow a2 2) (sqrt 2)))))>
#<alt (* (pow a2 4) (sqrt 2))>
#<alt (* (pow a2 4) (+ (sqrt 2) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))>
#<alt (* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))>
#<alt (* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))>
#<alt (* (pow a2 4) (sqrt 2))>
#<alt (* (pow a2 4) (+ (sqrt 2) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))>
#<alt (* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))>
#<alt (* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))>
#<alt (pow a1 3)>
#<alt (pow a1 3)>
#<alt (pow a1 3)>
#<alt (pow a1 3)>
#<alt (pow a1 3)>
#<alt (pow a1 3)>
#<alt (pow a1 3)>
#<alt (pow a1 3)>
#<alt (pow a1 3)>
#<alt (pow a1 3)>
#<alt (pow a1 3)>
#<alt (pow a1 3)>

Calls

105 calls:

Time	Variable		Point	Expression
3.0ms	a2	@	0	(- (* a2 a2) (* a1 a1))
3.0ms	th	@	inf	(/ (* (+ (* (* a1 a1) (* a1 (* a1 (* a1 a1)))) (* (* a2 a2) (* a2 (* a2 (* a2 a2))))) (cos th)) (* (+ (* a1 (* a1 (* a1 a1))) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2)))
2.0ms	a2	@	0	(/ (* (+ (* (* a1 a1) (* a1 (* a1 (* a1 a1)))) (* (* a2 a2) (* a2 (* a2 (* a2 a2))))) (cos th)) (* (+ (* a1 (* a1 (* a1 a1))) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2)))
1.0ms	a1	@	0	(/ (* (+ (* (* a1 a1) (* a1 (* a1 (* a1 a1)))) (* (* a2 a2) (* a2 (* a2 (* a2 a2))))) (cos th)) (* (+ (* a1 (* a1 (* a1 a1))) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2)))
1.0ms	th	@	0	(/ (* (+ (* (* a1 a1) (* a1 (* a1 (* a1 a1)))) (* (* a2 a2) (* a2 (* a2 (* a2 a2))))) (cos th)) (* (+ (* a1 (* a1 (* a1 a1))) (* (* a2 a2) (- (* a2 a2) (* a1 a1)))) (sqrt 2)))

rewrite384.0ms (3.4%)

Memory

-5.8MiB live, 813.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 992×	`lower-fma.f32`
4 984×	`lower-fma.f64`
4 790×	`lower-/.f32`
4 772×	`lower-/.f64`
4 698×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	223
0	61	168
1	227	149
2	1672	149
0	8273	149

Stop Event

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

Counts

20 → 1 500

Calls

Call 1

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

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

simplify413.0ms (3.7%)

Memory

16.5MiB live, 850.5MiB allocated

Algorithm

1×	egg-herbie

Rules

16 070×	`lower-fma.f64`
16 070×	`lower-fma.f32`
5 204×	`lower-*.f64`
5 204×	`lower-*.f32`
4 758×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	315	5987
1	1062	5586
2	4014	5381
0	8415	5106

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow 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)
(+ (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))))
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(+ (sqrt 2) (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(+ (sqrt 2) (* (pow th 2) (- (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/720 (sqrt 2)) (+ (* 1/48 (sqrt 2)) (* 1/2 (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(/ (sqrt 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 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)))))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (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))
(/ (* (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))))
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(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ 1 (sqrt 2))
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(/ (cos th) (sqrt 2))
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
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(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
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(* (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)))))
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(/ (pow a1 2) (sqrt 2))
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(/ (pow a2 2) (sqrt 2))
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(* -1 (pow a1 2))
(- (pow a2 2) (pow a1 2))
(- (pow a2 2) (pow a1 2))
(- (pow a2 2) (pow a1 2))
(pow a2 2)
(* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(pow a2 2)
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(* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(* (pow a2 2) (+ 1 (* -1 (/ (pow a1 2) (pow a2 2)))))
(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) (- (/ (pow a2 2) (pow a1 2)) 1))
(* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))
(* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))
(* -1 (pow a1 2))
(* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))
(* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))
(* (pow a1 2) (- (/ (pow a2 2) (pow a1 2)) 1))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (* (pow a1 2) (- (* -1 (* (pow a1 2) (+ (* -1 (/ (cos th) (* (pow a2 2) (sqrt 2)))) (/ (cos th) (* (pow a2 2) (sqrt 2)))))) (* -1 (/ (cos th) (sqrt 2))))) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* (pow a1 2) (- (/ (cos th) (* (pow a2 4) (sqrt 2))) (+ (* -1 (/ (cos th) (* (pow a2 4) (sqrt 2)))) (* 2 (/ (cos th) (* (pow a2 4) (sqrt 2))))))) (+ (* -1 (/ (cos th) (* (pow a2 2) (sqrt 2)))) (/ (cos th) (* (pow a2 2) (sqrt 2)))))) (* -1 (/ (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)))))
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(* (pow a1 2) (- (+ (* -1 (/ (* (pow a2 2) (+ (* -1 (/ (* (pow a2 4) (cos th)) (sqrt 2))) (/ (* (pow a2 4) (cos th)) (sqrt 2)))) (pow a1 6))) (/ (cos th) (sqrt 2))) (+ (* -1 (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))) (+ (* -1 (/ (* (pow a2 4) (cos th)) (* (pow a1 4) (sqrt 2)))) (/ (* (pow a2 4) (cos th)) (* (pow a1 4) (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)))))
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (* (pow a2 2) (- (* -1 (* (pow a2 2) (+ (* -1 (/ (cos th) (* (pow a1 2) (sqrt 2)))) (/ (cos th) (* (pow a1 2) (sqrt 2)))))) (* -1 (/ (cos th) (sqrt 2))))) (/ (* (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)))))
(* (pow a2 2) (- (+ (* -1 (/ (+ (* -1 (/ (* (pow a1 4) (cos th)) (sqrt 2))) (/ (* (pow a1 4) (cos th)) (sqrt 2))) (pow a2 4))) (/ (cos th) (sqrt 2))) (* -1 (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))))
(* (pow a2 2) (- (+ (* -1 (/ (* (pow a1 2) (+ (* -1 (/ (* (pow a1 4) (cos th)) (sqrt 2))) (/ (* (pow a1 4) (cos th)) (sqrt 2)))) (pow a2 6))) (/ (cos th) (sqrt 2))) (+ (* -1 (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))) (+ (* -1 (/ (* (pow a1 4) (cos th)) (* (pow a2 4) (sqrt 2)))) (/ (* (pow a1 4) (cos th)) (* (pow a2 4) (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)))))
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(/ (+ (pow a1 6) (pow a2 6)) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))) (+ (/ (pow a1 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4)))) (/ (pow a2 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 6) (pow a2 6)) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))) (+ (/ (pow a1 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4)))) (/ (pow a2 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 6) (pow a2 6)) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))) (* 1/24 (/ (+ (pow a1 6) (pow a2 6)) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))))) (+ (/ (pow a1 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4)))) (/ (pow a2 6) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))))
(/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))
(/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))
(/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))
(/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))
(/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))
(/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))
(/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))
(/ (* (cos th) (+ (pow a1 6) (pow a2 6))) (* (sqrt 2) (+ (* (pow a2 2) (- (pow a2 2) (pow a1 2))) (pow a1 4))))
(* (pow a2 6) (cos th))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(* (pow a1 6) (cos th))
(* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))
(* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))
(* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))
(* (pow a1 6) (cos th))
(* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))
(* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))
(* (pow a1 6) (+ (cos th) (/ (* (pow a2 6) (cos th)) (pow a1 6))))
(* (pow a1 6) (cos th))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(+ (* (pow a1 6) (cos th)) (* (pow a2 6) (cos th)))
(* (pow a2 6) (cos th))
(* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))
(* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))
(* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))
(* (pow a2 6) (cos th))
(* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))
(* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))
(* (pow a2 6) (+ (cos th) (/ (* (pow a1 6) (cos th)) (pow a2 6))))
(+ (pow a1 6) (pow a2 6))
(+ (* -1/2 (* (pow th 2) (+ (pow a1 6) (pow a2 6)))) (+ (pow a1 6) (pow a2 6)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 6) (pow a2 6))) (* 1/24 (* (pow th 2) (+ (pow a1 6) (pow a2 6)))))) (+ (pow a1 6) (pow a2 6)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 6) (pow a2 6))) (* (pow th 2) (+ (* -1/720 (* (pow th 2) (+ (pow a1 6) (pow a2 6)))) (* 1/24 (+ (pow a1 6) (pow a2 6))))))) (+ (pow a1 6) (pow a2 6)))
(* (cos th) (+ (pow a1 6) (pow a2 6)))
(* (cos th) (+ (pow a1 6) (pow a2 6)))
(* (cos th) (+ (pow a1 6) (pow a2 6)))
(* (cos th) (+ (pow a1 6) (pow a2 6)))
(* (cos th) (+ (pow a1 6) (pow a2 6)))
(* (cos th) (+ (pow a1 6) (pow a2 6)))
(* (cos th) (+ (pow a1 6) (pow a2 6)))
(* (cos th) (+ (pow a1 6) (pow a2 6)))
(pow a2 6)
(+ (pow a1 6) (pow a2 6))
(+ (pow a1 6) (pow a2 6))
(+ (pow a1 6) (pow a2 6))
(pow a1 6)
(* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))
(* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))
(* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))
(pow a1 6)
(* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))
(* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))
(* (pow a1 6) (+ 1 (/ (pow a2 6) (pow a1 6))))
(pow a1 6)
(+ (pow a1 6) (pow a2 6))
(+ (pow a1 6) (pow a2 6))
(+ (pow a1 6) (pow a2 6))
(pow a2 6)
(* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))
(* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))
(* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))
(pow a2 6)
(* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))
(* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))
(* (pow a2 6) (+ 1 (/ (pow a1 6) (pow a2 6))))
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) (+ 1/2 (* 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))
(* (pow a2 4) (sqrt 2))
(+ (* -1 (* (pow a1 2) (* (pow a2 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))
(+ (* (pow a1 2) (+ (* -1 (* (pow a2 2) (sqrt 2))) (* (pow a1 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))
(+ (* (pow a1 2) (+ (* -1 (* (pow a2 2) (sqrt 2))) (* (pow a1 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))
(* (pow a1 4) (sqrt 2))
(* (pow a1 4) (+ (sqrt 2) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))
(* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))
(* (pow a1 4) (sqrt 2))
(* (pow a1 4) (+ (sqrt 2) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))
(* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))
(* (pow a1 4) (sqrt 2))
(+ (* -1 (* (pow a1 2) (* (pow a2 2) (sqrt 2)))) (* (pow a1 4) (sqrt 2)))
(+ (* (pow a1 4) (sqrt 2)) (* (pow a2 2) (+ (* -1 (* (pow a1 2) (sqrt 2))) (* (pow a2 2) (sqrt 2)))))
(+ (* (pow a1 4) (sqrt 2)) (* (pow a2 2) (+ (* -1 (* (pow a1 2) (sqrt 2))) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 4) (sqrt 2))
(* (pow a2 4) (+ (sqrt 2) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(* (pow a2 4) (sqrt 2))
(* (pow a2 4) (+ (sqrt 2) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(pow a1 3)
(pow a1 3)
(pow a1 3)
(pow a1 3)
(pow a1 3)
(pow a1 3)
(pow a1 3)
(pow a1 3)
(pow a1 3)
(pow a1 3)
(pow a1 3)
(pow a1 3)

Outputs
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 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 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(.f64 (.f64 a1 a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(.f64 (.f64 a1 a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 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 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(.f64 (.f64 a1 a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(.f64 (.f64 a1 a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (.f64 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 a2 a2 (.f64 a1 a1)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (.f64 a2 a2) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (.f64 a2 a2) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (.f64 a2 a2) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (.f64 a2 a2) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (.f64 a2 a2) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (.f64 a2 a2) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 (/.f64 a1 (.f64 a2 a2)) #s(literal 1 binary64))))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 (.f64 th th) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* 1/24 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 (.f64 th th) (.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (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 a2 a2 (.f64 a1 a1))))
(+ (* (pow th 2) (+ (* -1/2 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (* 1/24 (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (*.f64 a1 a1))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.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 a2 a2 (.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 a2 a2 (.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 a2 a2 (.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 a2 a2 (.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 a2 a2 (.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 a2 a2 (.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 a2 a2 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(pow a2 2)
(*.f64 a2 a2)
(+ (pow a1 2) (pow a2 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow a1 2)
(*.f64 a1 a1)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64)))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64)))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(.f64 (.f64 a1 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 (.f64 a1 a1) (fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64)))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 a2 (/.f64 a2 (*.f64 a1 a1)) #s(literal 1 binary64)))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(.f64 (.f64 a1 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 a2 a2 (*.f64 a1 a1))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(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)))
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(fma.f64 (.f64 th th) (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow th 2) (- (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/720 (sqrt 2)) (+ (* 1/48 (sqrt 2)) (* 1/2 (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -61/720 binary64)) (neg.f64 (.f64 th th))) (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/24 binary64) (*.f64 th th) #s(literal -1/2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 a2 (.f64 a1 a1)))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 a2 (fma.f64 a2 (/.f64 (.f64 a1 a1) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 a2 (fma.f64 a2 (/.f64 (.f64 a1 a1) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 a2 (fma.f64 a2 (/.f64 (.f64 a1 a1) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ (pow a2 2) (sqrt 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 a2 (fma.f64 a2 (/.f64 (.f64 a1 a1) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 a2 (fma.f64 a2 (/.f64 (.f64 a1 a1) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(.f64 a2 (fma.f64 a2 (/.f64 (.f64 a1 a1) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
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(/.f64 #s(literal 1 binary64) (cos.f64 th))
(* (pow a2 4) (sqrt 2))
(.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (* -1 (* (pow a1 2) (* (pow a2 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))
(.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (+.f64 a2 a1) (-.f64 a2 a1)))
(+ (* (pow a1 2) (+ (* -1 (* (pow a2 2) (sqrt 2))) (* (pow a1 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 (.f64 a2 (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (.f64 (.f64 a1 a1) (.f64 a1 a1))))
(+ (* (pow a1 2) (+ (* -1 (* (pow a2 2) (sqrt 2))) (* (pow a1 2) (sqrt 2)))) (* (pow a2 4) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 (.f64 a2 (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (.f64 (.f64 a1 a1) (.f64 a1 a1))))
(* (pow a1 4) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a1 a1) (.f64 a1 a1)))
(* (pow a1 4) (+ (sqrt 2) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (neg.f64 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))
(.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 (.f64 (.f64 a2 a2) (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 a1))) (/.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))
(.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 (.f64 (.f64 a2 a2) (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 a1))) (/.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 4) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a1 a1) (.f64 a1 a1)))
(* (pow a1 4) (+ (sqrt 2) (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 a2 a2) (neg.f64 (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))
(.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 (.f64 (.f64 a2 a2) (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 a1))) (/.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (pow a1 2))) (/ (* (pow a2 4) (sqrt 2)) (pow a1 4)))))
(.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 (.f64 (.f64 a2 a2) (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a1 a1))) (/.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 4) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 a1 a1) (.f64 a1 a1)))
(+ (* -1 (* (pow a1 2) (* (pow a2 2) (sqrt 2)))) (* (pow a1 4) (sqrt 2)))
(.f64 (.f64 a1 a1) (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(+ (* (pow a1 4) (sqrt 2)) (* (pow a2 2) (+ (* -1 (* (pow a1 2) (sqrt 2))) (* (pow a2 2) (sqrt 2)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 (.f64 a2 (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (.f64 (.f64 a1 a1) (.f64 a1 a1))))
(+ (* (pow a1 4) (sqrt 2)) (* (pow a2 2) (+ (* -1 (* (pow a1 2) (sqrt 2))) (* (pow a2 2) (sqrt 2)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a2 (.f64 a2 (.f64 (+.f64 a2 a1) (-.f64 a2 a1))) (.f64 (.f64 a1 a1) (.f64 a1 a1))))
(* (pow a2 4) (sqrt 2))
(.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 4) (+ (sqrt 2) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) (.f64 a2 a2)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (*.f64 a2 a2))))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(.f64 (.f64 (.f64 a2 a2) (.f64 a2 a2)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (.f64 a2 a2))) (/.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(.f64 (.f64 (.f64 a2 a2) (.f64 a2 a2)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (.f64 a2 a2))) (/.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 4) (sqrt 2))
(.f64 (.f64 a2 a2) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 4) (+ (sqrt 2) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))
(.f64 (.f64 (.f64 a2 a2) (.f64 a2 a2)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (*.f64 a2 a2))))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(.f64 (.f64 (.f64 a2 a2) (.f64 a2 a2)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (.f64 a2 a2))) (/.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 4) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (pow a1 4) (sqrt 2)) (pow a2 4)))))
(.f64 (.f64 (.f64 a2 a2) (.f64 a2 a2)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (.f64 a2 a2))) (/.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))))
(pow a1 3)
(.f64 a1 (.f64 a1 a1))
(pow a1 3)
(.f64 a1 (.f64 a1 a1))
(pow a1 3)
(.f64 a1 (.f64 a1 a1))
(pow a1 3)
(.f64 a1 (.f64 a1 a1))
(pow a1 3)
(.f64 a1 (.f64 a1 a1))
(pow a1 3)
(.f64 a1 (.f64 a1 a1))
(pow a1 3)
(.f64 a1 (.f64 a1 a1))
(pow a1 3)
(.f64 a1 (.f64 a1 a1))
(pow a1 3)
(.f64 a1 (.f64 a1 a1))
(pow a1 3)
(.f64 a1 (.f64 a1 a1))
(pow a1 3)
(.f64 a1 (.f64 a1 a1))
(pow a1 3)
(.f64 a1 (.f64 a1 a1))

eval285.0ms (2.6%)

Memory: -1.8MiB live, 613.5MiB allocated
Compiler: Compiled 89 525 to 3 166 computations (96.5% saved)

prune342.0ms (3.1%)

Memory

34.3MiB live, 390.4MiB allocated

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	2 333	23	2 356
Fresh	10	3	13
Picked	4	1	5
Done	0	0	0
Total	2 347	27	2 374

Accuracy

100.0%

Counts

2 374 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	68.4%	(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
	68.0%	(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2))))
▶	68.4%	(/.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))
▶	68.3%	(/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 a1 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	68.4%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
	65.4%	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
	60.0%	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	99.6%	(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
	65.4%	(/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
	99.3%	(/.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
	8.8%	(/.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))))) #s(literal 1 binary64)) (.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))))
	21.3%	(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
	99.3%	(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
	99.3%	(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	99.4%	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	68.2%	(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
▶	14.6%	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
	99.2%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
	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))
	65.3%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	99.7%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
▶	99.6%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
	68.4%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
▶	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)))
	99.3%	(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
	52.5%	(.f64 (.f64 a1 a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a2 (/.f64 a2 (.f64 a1 a1)) #s(literal 1 binary64))))
	40.7%	(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 951 to 600 computations (36.9% saved)

simplify197.0ms (1.8%)

Memory

-26.6MiB live, 154.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
✓	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	384	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)))
✓	cost-diff	0	(*.f64 a2 a2)
✓	cost-diff	512	(/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 a1 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	1088	(fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 a1 a1))))
✓	cost-diff	1728	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 a2 a2)
✓	cost-diff	384	(/.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))
✓	cost-diff	960	(fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 a1 a1)
✓	cost-diff	64	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 a2 a2)
✓	cost-diff	0	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	cost-diff	64	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))

Rules

2 250×	`lower-fma.f32`
2 244×	`lower-fma.f64`
2 132×	`lower-*.f32`
2 118×	`lower-*.f64`
1 700×	`times-frac`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	26	211
0	49	204
1	91	182
2	196	180
3	476	180
4	1236	176
5	4369	176
6	6181	176
0	8060	176

Stop Event

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

Calls

Call 1

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

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

localize142.0ms (1.3%)

Memory

-18.2MiB live, 135.8MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	accuracy	99.9%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
✓	accuracy	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)))
✓	accuracy	98.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(neg.f64 (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.7%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 a1 a1)))
✓	accuracy	99.6%	(fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 a1 a1))))
✓	accuracy	98.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(*.f64 a1 a1)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.7%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
✓	accuracy	99.6%	(fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))
✓	accuracy	100.0%	(*.f64 a1 a1)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.7%	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	accuracy	99.7%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
✓	accuracy	99.7%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
✓	accuracy	99.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))

Samples

71.0ms

256×

valid

Compiler

Compiled 222 to 30 computations (86.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 14.0ms (39.5% of total)

ival-div: 9.0ms (25.4% of total)

ival-cos: 6.0ms (16.9% of total)

ival-add: 3.0ms (8.5% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.1%)

Memory

15.8MiB live, 15.8MiB allocated

Counts

19 → 312

Calls

Call 1

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

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

Calls

78 calls:

Time	Variable		Point	Expression
1.0ms	th	@	0	(* (+ (* a1 a1) (* a2 a2)) (cos th))
1.0ms	a2	@	0	(/ (+ (* (* a2 a2) (neg (sqrt 2))) (* (sqrt 2) (neg (* a1 a1)))) (* (sqrt 2) (neg (sqrt 2))))
1.0ms	a1	@	0	(/ (+ (* (* a2 a2) (neg (sqrt 2))) (* (sqrt 2) (neg (* a1 a1)))) (* (sqrt 2) (neg (sqrt 2))))
0.0ms	a1	@	inf	(/ (+ (* (* a2 a2) (neg (sqrt 2))) (* (sqrt 2) (neg (* a1 a1)))) (* (sqrt 2) (neg (sqrt 2))))
0.0ms	a2	@	inf	(/ (+ (* (* a2 a2) (neg (sqrt 2))) (* (sqrt 2) (neg (* a1 a1)))) (* (sqrt 2) (neg (sqrt 2))))

rewrite431.0ms (3.9%)

Memory

16.9MiB live, 329.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 500×	`lower-fma.f32`
5 494×	`lower-fma.f64`
4 512×	`lower-*.f32`
4 498×	`lower-*.f64`
3 062×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	156
0	49	143
1	170	123
2	1152	123
0	8811	123

Stop Event

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

Counts

19 → 1 435

Calls

Call 1

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

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

simplify541.0ms (4.8%)

Memory

-47.2MiB live, 368.8MiB allocated

Algorithm

1×	egg-herbie

Rules

12 124×	`lower-fma.f64`
12 124×	`lower-fma.f32`
5 462×	`lower-*.f64`
5 462×	`lower-*.f32`
3 622×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	155	3568
1	532	3205
2	1958	3119
3	5779	3092
0	8215	2874

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 312

Calls

Call 1

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

Outputs
(/ 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 th th) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 th 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) (fma.f64 (/.f64 (.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 #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)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (cos.f64 th) (/.f64 (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 (cos.f64 th) (/.f64 (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 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (.f64 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 (cos.f64 th) (/.f64 (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)) (* (pow a1 2) (sqrt 2)))))
(.f64 (cos.f64 th) (/.f64 (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)) (* (pow a1 2) (sqrt 2)))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (.f64 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 (cos.f64 th) (/.f64 (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)) (* (pow a1 2) (sqrt 2)))))
(.f64 (cos.f64 th) (/.f64 (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)) (* (pow a1 2) (sqrt 2)))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(.f64 (cos.f64 th) (/.f64 (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 (cos.f64 th) (/.f64 (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 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.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 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.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 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.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 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.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 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (/ (* (pow th 2) (+ (pow a1 2) (pow a2 2))) (sqrt 2))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (.f64 th (.f64 th (.f64 #s(literal -1/2 binary64) (fma.f64 a1 a1 (*.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 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (.f64 th th) (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 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 (.f64 th th) (fma.f64 (.f64 th th) (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(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))))
(fma.f64 a1 a1 (*.f64 a2 a2))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(fma.f64 a1 a1 (*.f64 a2 a2))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(fma.f64 a1 a1 (*.f64 a2 a2))
(pow a1 2)
(*.f64 a1 a1)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(fma.f64 a1 a1 (*.f64 a2 a2))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(fma.f64 a1 a1 (*.f64 a2 a2))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(fma.f64 a1 a1 (*.f64 a2 a2))
(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))))
(fma.f64 a1 a1 (*.f64 a2 a2))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(fma.f64 a1 a1 (*.f64 a2 a2))
(* (pow a2 2) (+ 1 (/ (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))))
(fma.f64 a1 a1 (*.f64 a2 a2))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(fma.f64 a1 a1 (*.f64 a2 a2))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(fma.f64 a1 a1 (*.f64 a2 a2))
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a1 2) (sqrt 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a2 2) (sqrt 2))
(.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a2 2) (sqrt 2))
(.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a2 2) (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a2 2) (sqrt 2))
(.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
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(+ (* (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 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (.f64 th th) (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 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 (.f64 th th) (fma.f64 (.f64 th th) (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (cos th))
(.f64 (.f64 (cos.f64 th) a2) a2)
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a1 2) (cos th))
(.f64 (cos.f64 th) (.f64 a1 a1))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 (cos.f64 th) a2) a2) (.f64 (cos.f64 th) (.f64 a1 a1)))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 (cos.f64 th) a2) a2) (.f64 (cos.f64 th) (.f64 a1 a1)))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 (cos.f64 th) a2) a2) (.f64 (cos.f64 th) (.f64 a1 a1)))
(* (pow a1 2) (cos th))
(.f64 (cos.f64 th) (.f64 a1 a1))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 (cos.f64 th) a2) a2) (.f64 (cos.f64 th) (.f64 a1 a1)))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 (cos.f64 th) a2) a2) (.f64 (cos.f64 th) (.f64 a1 a1)))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 (cos.f64 th) a2) a2) (.f64 (cos.f64 th) (.f64 a1 a1)))
(* (pow a1 2) (cos th))
(.f64 (cos.f64 th) (.f64 a1 a1))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (pow a2 2) (cos th))
(.f64 (.f64 (cos.f64 th) a2) a2)
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(fma.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (.f64 (cos.f64 th) a2) a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(fma.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (.f64 (cos.f64 th) a2) a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(fma.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (.f64 (cos.f64 th) a2) a2))
(* (pow a2 2) (cos th))
(.f64 (.f64 (cos.f64 th) a2) a2)
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(fma.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (.f64 (cos.f64 th) a2) a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(fma.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (.f64 (cos.f64 th) a2) a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(fma.f64 #s(literal 1 binary64) (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (.f64 (cos.f64 th) a2) a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (* -1/2 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (+ (pow a1 2) (pow a2 2)))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (* 1/24 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))))) (+ (pow a1 2) (pow a2 2)))
(fma.f64 th (.f64 th (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (fma.f64 (.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (* (pow th 2) (+ (* -1/2 (+ (pow a1 2) (pow a2 2))) (* (pow th 2) (+ (* -1/720 (* (pow th 2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (+ (pow a1 2) (pow a2 2))))))) (+ (pow a1 2) (pow a2 2)))
(fma.f64 (.f64 th th) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (fma.f64 (.f64 th th) (fma.f64 (.f64 th th) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(* (cos th) (+ (pow a1 2) (pow a2 2)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (* (pow th 2) (sqrt 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(fma.f64 th (.f64 th (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (*.f64 th th) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow th 2) (- (* (pow th 2) (- (* -1 (* (pow th 2) (+ (* -1/720 (sqrt 2)) (+ (* 1/48 (sqrt 2)) (* 1/2 (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2)))))))) (+ (* -1/4 (sqrt 2)) (* 1/24 (sqrt 2))))) (* -1/2 (sqrt 2)))))
(fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (.f64 th (.f64 th (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 61/720 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (*.f64 th th) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(/ (sqrt 2) (cos th))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(* (pow a1 2) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))
(* -1 (* (pow a1 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))
(* -1 (* (pow a1 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))
(* -1 (* (pow a1 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))
(* -1 (* (pow a1 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))
(* -1 (* (pow a1 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))
(* -1 (* (pow a1 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))
(* -1 (* (pow a1 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))
(* -1 (* (pow a1 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))
(* -1 (* (pow a1 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))
(* -1 (* (pow a1 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))
(* -1 (* (pow a1 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))
(* -1 (* (pow a1 2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 (neg.f64 a1)))

eval483.0ms (4.3%)

Memory: 35.5MiB live, 376.0MiB allocated
Compiler: Compiled 56 787 to 3 581 computations (93.7% saved)

prune352.0ms (3.1%)

Memory

-5.2MiB live, 469.0MiB allocated

Pruning

42 alts after pruning (40 fresh and 2 done)

	Pruned	Kept	Total
New	2 193	27	2 220
Fresh	8	13	21
Picked	4	1	5
Done	0	1	1
Total	2 205	42	2 247

Accuracy

100.0%

Counts

2 247 → 42

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.4%	(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
	21.6%	(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (neg.f64 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 a1 a1)))) #s(literal 2 binary64))
	21.6%	(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	68.0%	(/.f64 (fma.f64 (.f64 a2 a2) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 a1 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	68.4%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
	2.3%	(/.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	13.1%	(/.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1)))))
▶	99.6%	(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
	2.3%	(/.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	99.3%	(/.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
	21.6%	(/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a1 a1 (.f64 a2 a2)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	13.0%	(/.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 #s(literal -2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	21.6%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	21.6%	(/.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 a1 a1 (.f64 a2 a2))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	67.8%	(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	2.0%	(/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	12.7%	(/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	99.3%	(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
▶	99.3%	(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	21.6%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	99.4%	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	68.2%	(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
✓	14.6%	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
	68.1%	(/.f64 (neg.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	99.2%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
	21.6%	(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))))
	65.3%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	99.7%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
	99.6%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (cos.f64 th))))))
	68.4%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
	2.0%	(.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))) #s(literal -2 binary64))))
▶	12.8%	(.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))))))
	14.6%	(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)))
	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 (cos.f64 th) a2) a2))
	14.6%	(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) a1) a1)
	68.4%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) #s(literal 1/2 binary64))
	21.6%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) #s(literal -1/2 binary64))
	99.3%	(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
	99.3%	(.f64 (.f64 a2 a2) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))))
	40.7%	(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
▶	68.3%	(.f64 #s(literal 1/2 binary64) (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 1 678 to 1 083 computations (35.5% saved)

simplify283.0ms (2.5%)

Memory

5.0MiB live, 486.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(cos.f64 th)
✓	cost-diff	0	(*.f64 a2 a2)
✓	cost-diff	0	(.f64 (.f64 a2 a2) (cos.f64 th))
✓	cost-diff	0	(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 a2 (.f64 a2 (*.f64 a2 a2)))
✓	cost-diff	0	(fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (*.f64 a1 a1)))))
✓	cost-diff	320	(/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1)))))
✓	cost-diff	832	(.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))))))
✓	cost-diff	0	(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	0	(*.f64 a2 a2)
✓	cost-diff	0	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	cost-diff	0	(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	1088	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th)))

Rules

9 514×	`lower-fma.f32`
9 508×	`lower-fma.f64`
4 356×	`lower-*.f32`
4 324×	`lower-*.f64`
2 494×	`lower-+.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	37	272
0	69	250
1	123	232
2	279	232
3	1007	231
4	4428	228
5	7159	227
0	8176	227

Stop Event

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

Calls

Call 1

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

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

localize124.0ms (1.1%)

Memory

4.8MiB live, 240.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(cos.f64 th)
✓	accuracy	99.9%	(.f64 (.f64 a2 a2) (cos.f64 th))
✓	accuracy	99.7%	(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.6%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1)))
✓	accuracy	98.4%	(/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1)))))
✓	accuracy	86.6%	(fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (*.f64 a1 a1)))))
✓	accuracy	32.9%	(.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))))))
✓	accuracy	99.9%	(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	99.8%	(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.4%	(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.3%	(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.9%	(.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.4%	(*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	accuracy	99.9%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (cos.f64 th))
✓	accuracy	99.7%	(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))

Samples

69.0ms

256×

valid

Compiler

Compiled 280 to 41 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 24.0ms (50.2% of total)

ival-div: 10.0ms (20.9% of total)

ival-cos: 6.0ms (12.5% of total)

ival-add: 4.0ms (8.4% of total)

ival-sqrt: 2.0ms (4.2% of total)

ival-sub: 1.0ms (2.1% of total)

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

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

exact: 0.0ms (0% of total)

series33.0ms (0.3%)

Memory

20.1MiB live, 64.1MiB allocated

Counts

21 → 384

Calls

Call 1

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

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

Calls

96 calls:

Time	Variable		Point	Expression
7.0ms	a1	@	0	(* (+ (* 2 (* a2 (* a2 (* a2 a2)))) (* -2 (* a1 (* a1 (* a1 a1))))) (/ 1 (* 2 (* (sqrt 2) (* (+ a2 a1) (- a2 a1))))))
6.0ms	a2	@	inf	(* 1/2 (* a2 (* a2 (sqrt 2))))
1.0ms	a2	@	0	(* (+ (* 2 (* a2 (* a2 (* a2 a2)))) (* -2 (* a1 (* a1 (* a1 a1))))) (/ 1 (* 2 (* (sqrt 2) (* (+ a2 a1) (- a2 a1))))))
1.0ms	a1	@	inf	(* (+ (* 2 (* a2 (* a2 (* a2 a2)))) (* -2 (* a1 (* a1 (* a1 a1))))) (/ 1 (* 2 (* (sqrt 2) (* (+ a2 a1) (- a2 a1))))))
1.0ms	a2	@	inf	(* (+ (* 2 (* a2 (* a2 (* a2 a2)))) (* -2 (* a1 (* a1 (* a1 a1))))) (/ 1 (* 2 (* (sqrt 2) (* (+ a2 a1) (- a2 a1))))))

rewrite306.0ms (2.7%)

Memory

-8.9MiB live, 638.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 726×	`lower-/.f32`
4 712×	`lower-/.f64`
4 358×	`lower-fma.f32`
4 352×	`lower-fma.f64`
4 134×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	183
0	69	169
1	218	155
2	1472	154
0	8321	154

Stop Event

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

Counts

21 → 811

Calls

Call 1

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

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

simplify328.0ms (2.9%)

Memory

-12.3MiB live, 737.8MiB allocated

Algorithm

1×	egg-herbie

Rules

12 220×	`lower-fma.f64`
12 220×	`lower-fma.f32`
4 672×	`lower-*.f64`
4 672×	`lower-*.f32`
2 356×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	550	5397
1	1882	4390
2	7998	4390
0	8206	4167

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

Calls

Call 1

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

Outputs
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(* (pow a1 2) (cos th))
(.f64 (cos.f64 th) (.f64 a1 a1))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (.f64 a1 a1)) (cos.f64 th)))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (.f64 a1 a1)) (cos.f64 th)))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (.f64 a1 a1)) (cos.f64 th)))
(* (pow a1 2) (cos th))
(.f64 (cos.f64 th) (.f64 a1 a1))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (.f64 a1 a1)) (cos.f64 th)))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (.f64 a1 a1)) (cos.f64 th)))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(.f64 (.f64 a1 a1) (fma.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (.f64 a1 a1)) (cos.f64 th)))
(* (pow a1 2) (cos th))
(.f64 (cos.f64 th) (.f64 a1 a1))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
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(+ (* (pow th 2) (+ (* -1/2 (pow a2 2)) (* 1/24 (* (pow a2 2) (pow th 2))))) (pow a2 2))
(fma.f64 th (.f64 th (fma.f64 th (.f64 th (.f64 (.f64 a2 a2) #s(literal 1/24 binary64))) (.f64 a2 (.f64 a2 #s(literal -1/2 binary64))))) (*.f64 a2 a2))
(+ (* (pow th 2) (+ (* -1/2 (pow a2 2)) (* (pow th 2) (+ (* -1/720 (* (pow a2 2) (pow th 2))) (* 1/24 (pow a2 2)))))) (pow a2 2))
(fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 (.f64 a2 a2) (.f64 (.f64 th th) #s(literal -1/720 binary64)) (.f64 (.f64 a2 a2) #s(literal 1/24 binary64))) (.f64 a2 (.f64 a2 #s(literal -1/2 binary64)))) (.f64 a2 a2))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(* (pow a2 2) (cos th))
(.f64 a2 (.f64 a2 (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 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 (.f64 th 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)
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) (+ 1/2 (* 5/24 (pow th 2)))))
(fma.f64 th (.f64 th (fma.f64 (.f64 th th) #s(literal 5/24 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow th 2) (+ 1/2 (* (pow th 2) (+ 5/24 (* 61/720 (pow th 2)))))))
(fma.f64 (.f64 th th) (fma.f64 (.f64 th th) (fma.f64 (*.f64 th th) #s(literal 61/720 binary64) #s(literal 5/24 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/ 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))
(/ 1 (cos th))
(/.f64 #s(literal 1 binary64) (cos.f64 th))
(/ 1 (cos th))
(/.f64 #s(literal 1 binary64) (cos.f64 th))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow a1 2) (sqrt 2)))
(neg.f64 (.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(+ (* -1 (* (pow a1 2) (sqrt 2))) (* a2 (* (sqrt 2) (+ a1 (* -1 a1)))))
(.f64 a1 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 0 binary64) (neg.f64 a1))))
(+ (* -1 (* (pow a1 2) (sqrt 2))) (* a2 (+ (* a2 (sqrt 2)) (* (sqrt 2) (+ a1 (* -1 a1))))))
(fma.f64 a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a2 #s(literal 0 binary64))) (neg.f64 (.f64 a1 (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(+ (* -1 (* (pow a1 2) (sqrt 2))) (* a2 (+ (* a2 (sqrt 2)) (* (sqrt 2) (+ a1 (* -1 a1))))))
(fma.f64 a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a2 #s(literal 0 binary64))) (neg.f64 (.f64 a1 (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(* (pow a2 2) (sqrt 2))
(.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (sqrt 2) (+ a1 (* -1 a1))) a2)))
(fma.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)) a2))
(* (pow a2 2) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (sqrt 2) (+ a1 (* -1 a1))) a2))))
(.f64 (.f64 a2 a2) (fma.f64 (.f64 (neg.f64 a1) a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (fma.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (sqrt 2) (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))) (/ (* (sqrt 2) (+ a1 (* -1 a1))) a2))))
(.f64 (.f64 a2 a2) (fma.f64 (.f64 (neg.f64 a1) a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a2 a2)) (fma.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (sqrt 2))
(.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (sqrt 2) (/ (* (sqrt 2) (+ a1 (* -1 a1))) a2)))
(fma.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)) a2))
(* (pow a2 2) (+ (sqrt 2) (* -1 (/ (+ (* -1 (* (sqrt 2) (+ a1 (* -1 a1)))) (/ (* (pow a1 2) (sqrt 2)) a2)) a2))))
(.f64 (.f64 a2 a2) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64) (/.f64 (.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) a2)) a2)))
(* (pow a2 2) (+ (sqrt 2) (* -1 (/ (+ (* -1 (* (sqrt 2) (+ a1 (* -1 a1)))) (/ (* (pow a1 2) (sqrt 2)) a2)) a2))))
(.f64 (.f64 a2 a2) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64) (/.f64 (.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))) a2)) a2)))
(* (pow a2 2) (sqrt 2))
(.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(+ (* a1 (* (sqrt 2) (+ a2 (* -1 a2)))) (* (pow a2 2) (sqrt 2)))
(.f64 a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a2 #s(literal 0 binary64))))
(+ (* a1 (+ (* -1 (* a1 (sqrt 2))) (* (sqrt 2) (+ a2 (* -1 a2))))) (* (pow a2 2) (sqrt 2)))
(fma.f64 a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a2 #s(literal 0 binary64))) (neg.f64 (.f64 a1 (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(+ (* a1 (+ (* -1 (* a1 (sqrt 2))) (* (sqrt 2) (+ a2 (* -1 a2))))) (* (pow a2 2) (sqrt 2)))
(fma.f64 a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 a2 #s(literal 0 binary64))) (neg.f64 (.f64 a1 (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow a1 2) (sqrt 2)))
(neg.f64 (.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (* -1 (sqrt 2)) (/ (* (sqrt 2) (+ a2 (* -1 a2))) a1)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 0 binary64) a1))))
(* (pow a1 2) (+ (* -1 (sqrt 2)) (+ (/ (* (sqrt 2) (+ a2 (* -1 a2))) a1) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(.f64 (.f64 a1 a1) (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 0 binary64) a1)))))
(* (pow a1 2) (+ (* -1 (sqrt 2)) (+ (/ (* (sqrt 2) (+ a2 (* -1 a2))) a1) (/ (* (pow a2 2) (sqrt 2)) (pow a1 2)))))
(.f64 (.f64 a1 a1) (fma.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 0 binary64) a1)))))
(* -1 (* (pow a1 2) (sqrt 2)))
(neg.f64 (.f64 a1 (.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (* -1 (sqrt 2)) (* -1 (/ (* (sqrt 2) (+ a2 (* -1 a2))) a1))))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 0 binary64) a1))))
(* (pow a1 2) (+ (* -1 (sqrt 2)) (* -1 (/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) a1)) (* (sqrt 2) (+ a2 (* -1 a2)))) a1))))
(.f64 (.f64 a1 a1) (-.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)) (/.f64 (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) a1)))
(* (pow a1 2) (+ (* -1 (sqrt 2)) (* -1 (/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) a1)) (* (sqrt 2) (+ a2 (* -1 a2)))) a1))))
(.f64 (.f64 a1 a1) (-.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)) (/.f64 (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) a1)) a1)))

eval156.0ms (1.4%)

Memory: 29.1MiB live, 414.4MiB allocated
Compiler: Compiled 39 721 to 2 925 computations (92.6% saved)

prune189.0ms (1.7%)

Memory

-27.2MiB live, 535.1MiB allocated

Pruning

42 alts after pruning (38 fresh and 4 done)

	Pruned	Kept	Total
New	1 321	12	1 333
Fresh	9	26	35
Picked	3	2	5
Done	0	2	2
Total	1 333	42	1 375

Accuracy

100.0%

Counts

1 375 → 42

Alt Table

Click to see full alt table

Status	Accuracy	Program
	68.4%	(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
	68.4%	(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2 (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
	21.6%	(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (neg.f64 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 a1 a1)))) #s(literal 2 binary64))
	21.6%	(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	68.0%	(/.f64 (fma.f64 (.f64 a2 a2) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 a1 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	68.4%	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
	2.3%	(/.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	2.3%	(/.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	99.3%	(/.f64 (/.f64 (*.f64 a2 a2) (/.f64 #s(literal 1 binary64) (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
	99.3%	(/.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 th)))
	21.6%	(/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a1 a1 (.f64 a2 a2)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	13.0%	(/.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 #s(literal -2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	21.6%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	21.6%	(/.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 a1 a1 (.f64 a2 a2))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	67.8%	(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	2.0%	(/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	12.7%	(/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	65.2%	(/.f64 (.f64 (.f64 a2 a2) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓	99.3%	(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
	21.6%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	99.4%	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
	68.2%	(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
✓	14.6%	(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
	68.1%	(/.f64 (neg.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
	21.6%	(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))))
✓	99.7%	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
	2.0%	(.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))) #s(literal -2 binary64))))
	12.6%	(.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1/2 binary64) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
	99.3%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))
	14.6%	(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)))
	14.6%	(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) a1) a1)
	68.2%	(.f64 (.f64 (*.f64 a2 #s(literal 1/2 binary64)) a2) (sqrt.f64 #s(literal 2 binary64)))
	68.4%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) #s(literal 1/2 binary64))
	21.6%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) #s(literal -1/2 binary64))
	34.2%	(.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)))))
	41.1%	(.f64 (.f64 a1 a1) (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal -1 binary64) (fma.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))) a1) #s(literal 0 binary64)) a1)))
	99.3%	(.f64 (cos.f64 th) (.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
	99.3%	(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
	68.2%	(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
	40.7%	(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
✓	68.3%	(.f64 #s(literal 1/2 binary64) (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 2 292 to 779 computations (66% saved)

regimes183.0ms (1.6%)

Memory

15.3MiB live, 456.1MiB allocated

Counts

81 → 1

Calls

Call 1

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

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

Calls

8 calls:

24.0ms	(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
24.0ms	th
24.0ms	a1
23.0ms	a2
22.0ms	(*.f64 a2 a2)

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)

regimes140.0ms (1.3%)

Memory

2.0MiB live, 359.0MiB allocated

Counts

61 → 1

Calls

Call 1

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

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

Calls

8 calls:

19.0ms	th
18.0ms	a2
18.0ms	a1
17.0ms	(cos.f64 th)
17.0ms	(*.f64 a2 a2)

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)

regimes137.0ms (1.2%)

Memory

11.6MiB live, 334.8MiB allocated

Counts

55 → 1

Calls

Call 1

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

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

Calls

8 calls:

25.0ms	(*.f64 a2 a2)
16.0ms	a1
16.0ms	a2
16.0ms	th
16.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Results

Accuracy	Segments	Branch
99.7%	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)

regimes142.0ms (1.3%)

Memory

-17.9MiB live, 381.1MiB allocated

Counts

54 → 1

Calls

Call 1

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

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

Calls

8 calls:

24.0ms	a1
19.0ms	th
17.0ms	a2
17.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
16.0ms	(*.f64 a2 a2)

Results

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

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes133.0ms (1.2%)

Memory

17.2MiB live, 336.7MiB allocated

Counts

52 → 1

Calls

Call 1

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

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

Calls

8 calls:

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

Results

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

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes146.0ms (1.3%)

Memory

6.0MiB live, 289.5MiB allocated

Counts

47 → 2

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (.f64 (*.f64 a2 #s(literal 1/2 binary64)) a2) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) a1) a1)
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
(/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) #s(literal -1/2 binary64))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) #s(literal 1/2 binary64))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 a2 a2) (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2)))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (fma.f64 (*.f64 th th) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 (.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1))) #s(literal 2 binary64))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 a2 a2) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (neg.f64 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 a1 a1)))) #s(literal 2 binary64))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) a2) a2 (.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a2 a2))))
(/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 th th) #s(literal 1 binary64))))
(.f64 a1 (fma.f64 a1 (/.f64 (.f64 a2 a2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(.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)))))
(.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)))))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1/2 binary64) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 a1 a1))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a1 a1 (.f64 a2 a2)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1)))))
(/.f64 (fma.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 a1 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))))))
(.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1))) #s(literal -2 binary64))))
(.f64 (.f64 a1 a1) (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal -1 binary64) (fma.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))) a1) #s(literal 0 binary64)) a1)))
(/.f64 (fma.f64 (.f64 a2 a2) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 a1 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 a1 a1 (.f64 a2 a2))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (+.f64 a2 a1) (-.f64 a2 a1)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))) (.f64 #s(literal -2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (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))))) #s(literal 1 binary64)) (.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 (fma.f64 #s(literal 2 binary64) (.f64 a2 (.f64 a2 (.f64 a2 a2))) (.f64 #s(literal -2 binary64) (.f64 a1 (.f64 a1 (.f64 a1 a1))))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 a2 a1) (-.f64 a2 a1)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))

Outputs

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

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

Calls

8 calls:

40.0ms	a1
15.0ms	th
15.0ms	(*.f64 a2 a2)
15.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
15.0ms	(cos.f64 th)

Results

Accuracy	Segments	Branch
68.4%	1	`a1`
72.7%	2	`a2`
70.4%	2	`th`
82.6%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
82.6%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
82.6%	2	`(cos.f64 th)`
68.4%	1	`(*.f64 a1 a1)`
68.4%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

regimes22.0ms (0.2%)

Memory

-25.2MiB live, 53.7MiB allocated

Counts

22 → 2

Calls

Call 1

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

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

Calls

3 calls:

7.0ms

(cos.f64 th)

7.0ms

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

6.0ms

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

Results

Accuracy	Segments	Branch
82.6%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`
82.6%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
82.6%	2	`(cos.f64 th)`

Compiler

Compiled 35 to 23 computations (34.3% saved)

regimes11.0ms (0.1%)

Memory

-4.4MiB live, 35.1MiB allocated

Counts

9 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

4.0ms

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

3.0ms

(cos.f64 th)

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
82.6%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
82.6%	2	`(cos.f64 th)`
82.6%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 35 to 23 computations (34.3% saved)

regimes10.0ms (0.1%)

Memory

32.6MiB live, 32.6MiB allocated

Counts

8 → 2

Calls

Call 1

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

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

Calls

3 calls:

3.0ms

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

3.0ms

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

3.0ms

(cos.f64 th)

Results

Accuracy	Segments	Branch
82.4%	2	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
82.4%	2	`(cos.f64 th)`
82.4%	2	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))`

Compiler

Compiled 35 to 23 computations (34.3% saved)

regimes25.0ms (0.2%)

Memory

-15.2MiB live, 65.7MiB allocated

Accuracy

Total -34.5b remaining (-169.7%)

Threshold costs -34.5b (-169.7%)

Counts

7 → 1

Calls

Call 1

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

Outputs
(.f64 #s(literal 1/2 binary64) (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))

Calls

8 calls:

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

Results

Accuracy	Segments	Branch
68.3%	1	`a1`
68.3%	1	`(*.f64 a1 a1)`
68.3%	1	`(*.f64 a2 a2)`
68.3%	1	`th`
68.3%	1	`a2`
68.3%	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)))`
68.3%	1	`(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))`
68.3%	1	`(cos.f64 th)`

Compiler

Compiled 59 to 40 computations (32.2% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.004363032378182339	0.01448713975535538

Compiler

Compiled 24 to 18 computations (25% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-8.075251813908024e-298	0.0

Compiler

Compiled 25 to 18 computations (28% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-8.075251813908024e-298	0.0

Compiler

Compiled 25 to 18 computations (28% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-8.075251813908024e-298	0.0

Compiler

Compiled 25 to 18 computations (28% saved)

simplify13.0ms (0.1%)

Memory

-19.0MiB live, 19.4MiB allocated

Algorithm

1×	egg-herbie

Rules

38×	`*-commutative_binary64`
12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	219
1	66	219
2	72	219
3	79	219
4	89	219
5	94	219
6	97	219
7	98	219

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (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 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 (cos.f64 th) #s(literal -1152921504606847/288230376151711744 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (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 -5890680864316837/11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056587776 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) #s(literal -1/2 binary64)) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (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 -5890680864316837/11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056587776 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) #s(literal -1/2 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) #s(literal 1/2 binary64)))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) #s(literal -5890680864316837/11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056587776 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 #s(literal 1/2 binary64) (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))

Outputs
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (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 (/.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))))
(/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 (cos.f64 th) #s(literal -1152921504606847/288230376151711744 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 (cos.f64 th) #s(literal -1152921504606847/288230376151711744 binary64)) (neg.f64 (/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(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 -5890680864316837/11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056587776 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) #s(literal -1/2 binary64)) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (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 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) #s(literal -5890680864316837/11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056587776 binary64)) (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (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 -5890680864316837/11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056587776 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) #s(literal -1/2 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) #s(literal 1/2 binary64)))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) #s(literal -5890680864316837/11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056587776 binary64)) (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))) #s(literal -5890680864316837/11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056587776 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (.f64 a2 a2))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(if (<=.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) #s(literal -5890680864316837/11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056587776 binary64)) (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 a2 (.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 #s(literal 1/2 binary64) (.f64 a2 (*.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))

soundness1.5s (13.3%)

Memory

33.6MiB live, 1 110.7MiB allocated

Rules

34 694×	`lower-fma.f64`
34 694×	`lower-fma.f32`
16 070×	`lower-fma.f64`
16 070×	`lower-fma.f32`
12 124×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	315	5987
1	1062	5586
2	4014	5381
0	8415	5106
0	12	44
0	20	38
1	58	38
2	411	38
3	7331	38
0	8434	37
0	155	3568
1	532	3205
2	1958	3119
3	5779	3092
0	8215	2874
0	26	156
0	49	143
1	170	123
2	1152	123
0	8811	123
0	37	183
0	69	169
1	218	155
2	1472	154
0	8321	154
0	111	1498
1	343	1366
2	1205	1262
3	3898	1233
0	8422	1172
0	32	223
0	61	168
1	227	149
2	1672	149
0	8273	149

Stop Event

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

Compiler

Compiled 592 to 284 computations (52% saved)

preprocess84.0ms (0.7%)

Memory

-0.3MiB live, 154.2MiB allocated

Remove

(abs a2)

(abs th)

Compiler

Compiled 1 028 to 472 computations (54.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample1.6s (14.2%)

preprocess136.0ms (1.2%)

explain216.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.1%)

localize45.0ms (0.4%)

series14.0ms (0.1%)

rewrite341.0ms (3.1%)

simplify688.0ms (6.2%)

eval55.0ms (0.5%)

prune75.0ms (0.7%)

simplify289.0ms (2.6%)

localize127.0ms (1.1%)

series41.0ms (0.4%)

rewrite384.0ms (3.4%)

simplify413.0ms (3.7%)

eval285.0ms (2.6%)

prune342.0ms (3.1%)

simplify197.0ms (1.8%)

localize142.0ms (1.3%)

series13.0ms (0.1%)

rewrite431.0ms (3.9%)

simplify541.0ms (4.8%)

eval483.0ms (4.3%)

prune352.0ms (3.1%)

simplify283.0ms (2.5%)

localize124.0ms (1.1%)

series33.0ms (0.3%)

rewrite306.0ms (2.7%)

simplify328.0ms (2.9%)

eval156.0ms (1.4%)

prune189.0ms (1.7%)

regimes183.0ms (1.6%)

regimes140.0ms (1.3%)

regimes137.0ms (1.2%)

regimes142.0ms (1.3%)

regimes133.0ms (1.2%)

regimes146.0ms (1.3%)

regimes22.0ms (0.2%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

regimes25.0ms (0.2%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify13.0ms (0.1%)

soundness1.5s (13.3%)

preprocess84.0ms (0.7%)

end0.0ms (0%)

Profiling